Essays and Reviews

ON THE PHYLLOTAXIS. [From Astronomical Journal 5.99 (December 1856): 22-24.] ¹

By Chauncey Wright,
ASSISTANT IN THE OFFICE OF THE AMERICAN EPIIHMERIS AND NAUTICAL ALMANAC.

§ 1. General Properties of the Phyllotactic Surds.

The fractions 1/2, 1/3, 2/5, 3/5, &c., each of which has a numerator equal to the sum of the two preceding numerators, and a denominator equal to the sum of the two preceding denominators, have been shown to be the successive approximations of the continued fraction

The value of this fraction is obtained from the expression

The sum of these two surds is unity, and the latter is equal to the square of the former; hence they divide unity in extreme and mean ratio.

The equation

x2 x = 1

becomes by transposition

x2 = 1 - x

which, in the form of a proportion, is

1 : x = x : 1- x

that is, x and 1 - x divide unity in extreme and mean ratio.

Again, by geometry, if the base of a right-angled triangle = 1, and its altitude = 1/2, the hypothenuse is 1/2 √5. Subtracting the altitude from the hypothenuse, we have remaining 1/2 (√5 - 1), and this subtracted from the base leaves 1/2 (3 - √5 ).

This process is the method in geometry of dividing a line in extreme and mean ratio.

If two quantities are in extreme and mean ratio, their sum is to the greater as the greater is to the smaller, or as the smaller is to their difference; hence the surds

each equal to the difference of the two preceding, are in geometrical progression with the ratio of the extreme and mean proportion. The first term 1/2 (√5 - 1) is equal to the common ratio, which we will indicate by k; hence these surds are the successive powers of the first; that is

The reciprocal of each of these surds is obtained by changing the sign - to +, since the difference of the squares of the two terms within the parenthesis of each surd is equal to 4; moreover each surd may be represented by a continued fraction of the form

in which a is the rational term of the surd, and the signs are + for the odd surds, and - for the even surds; thus,

The odd surds 1°, 3°, 5°, &c., may also be expressed by continued fractions of the form

And the even surds 2°, 4°, 6°, &c., by continued fractions of the form

§2. Geometrical Properties of the Phyllotactic Surds.

1. If leaves be supposed to follow each other in succession around their axis, with the constant interval k between them, we have the typical arrangement from which other arrangements may be produced by variations following a very simple law. Let the radii of the following figures represent the directions of the leaves in their typical arrangement. The numbers at the ends of the radii indicate the order of the leaves.

The leaves 1 and 2 of Fig. 1 divide the circumference into the spaces 1° and 2°, or into the fractions k and k2, and therefore in extreme and mean ratio. The leaf 3 of Fig. 2 divides the space 1° into the spaces 2° and 3°; the leaves 4 and 5 of Fig. 3 divide each of the spaces 2° into the spaces 3° and 4°; the leaves 6, 7, and 8, of Fig. 4, divide each of the spaces 3° into the spaces 4° and 5°; and the leaves 9, 10, 11, 12, and 13, of Fig. 5, divide each of the spaces 4° into the spaces 5° and 6°; — all in the same ratio, namely, that expressed by k. In general any leaf whatever, falling between two older leaves, divides the included space in extreme and mean ratio. This arrangement effects the most rapid and thorough distribution of the leaves around their axis.

If we consider each leaf as produced by that older leaf which stands nearest to it, we find that 1 produces 2, then 3, and then 4, while 2 produces 5; then 1 produces 6, 2 7, 3 8; then 1 9, 2 10, 3 11, 4 12, 5 13; then 1 14, 2 15, &c. Leaf 1 in producing 2, 3, 4, 6, 9, 14, &c., introduces successively, and alternately on its left and right, the intervals 1°, 2°, 3°, 4°, 5°, 6°, &c., which are the successive powers k, k2, k3, k4, k5, k6, &c. of the first and largest interval.

The suppression of any interval kn brings the leaf which introduces this interval over leaf 1, and produces one of the systems of arrangement expressed by the fractions

1/2, 1/3, 2/5, &c.

The interval 3° of Fig. 2 may be suppressed by moving back 2 one half, and 3 two halves of the interval 3°. This will give the alternate system expressed by the fraction

The suppression of interval 4° by moving forward the leaves 2, 3, and 4 respectively 1/3, 2/3, and 3/3 of the interval 4°, gives the system expressed by the fraction

In the same manner, the suppression of the intervals 5°, 6°, &c. gives the systems

If we subtract each member of these equations from unity, we obtain the following:

Certain anomalous forms of arrangement occur in nature, which cannot be expressed by any of the approximations of k. It has been shown, however, that all forms may be expressed by approximations of the fraction

in which m is an integer.

The distribution produced by this more general typical arrangement is, in effect, the same as that which we have

discussed; that is, the intervals 1°, 2°, 3°, &c. of this arrangement are in geometrical progression with the ratio of the extreme and mean proportion for

2. If the ratio of the mean motions of two planets be indicated by r, and if x represent the fraction of the circumference between two successive heliocentric conjunctions, then


and if r be any one of the approximations of k2, 1/2, 1/3, 2/5, &c., then x is equal to the corresponding approximation of k; 1, 1/2, 2/5, &c.- Thus, if r = 2/5, x = 2/5 ÷ 3/5 = 2/3.

Since, as Professor Peirce has shown, the mean motions of the planets form a progression in which the ratios are nearly expressed by a series of phyllotactic fractions, it follows that the intervals between the successive conjunctions of neighboring planets are also expressed by these fractions, and that their points of conjunction are thus distributed around the sun as leaves are around their axes, in the several systems. If the ratio of the mean motions of two planets were exactly k\ their points of conjunction would be distributed in the most rapid and thorough manner.

The idea of thorough distribution (in the leaves of plants with reference to the formation of wood, and in the conjunctions of planets with reference to their mutual perturbations) seems to be a central thought or typical principle of these natural arrangements. Variations from the typical arrangement produce in plants specific forms of symmetry, while in the planets they fulfil conditions as yet imperfectly understood.

The progression of the mean motions ought not to be geometrical, lest through the common ratio there occur constant repetitions of the same configurations in the whole system of planets, which would cause their action through one another to be always of the same character.

The ratios of this progression, therefore, while each approaches the typical ratio k2, ought to differ as much as possible among themselves, and most for the larger planets; as in fact they do.

§3. The Phyllotactic Function.

Required the form of the function which by the substitution for the variable of the common series of numbers

1, 2, 3, 4, 5, 6, &c.

gives the phyllotactic series of numbers

1, 1, 2, 3, 5, 8, &c.

Each of the phyllotactic numbers is equal to the sum of the two preceding; hence the required function is subject to the condition

Autobiographical Entry in Harvard Classbook of 1852. [From Harvard College Classbook of 1852, pp. 530-533. Harvard University Archives, HUD 252.714.] ²

Wright
Proprietor of Jack Knife
Nautical Almanac office Cambridge.

I was born in Northampton Mass. on the 20th day of September A.D. 1830; near the autumnal equinox; just as the Sun was about to enter the Balance. To this circumstance and to my equable temperament I ascribe the subsequent monotony of my life. My father Ansel Wright is descended without interruption from one of the first settlers of the town of N. who came to this place from the colony of Massachusetts Bay; doubtless himself descended from a series of English Wrights, who in their day and generation were well known to their friends.

My mother Elisabeth Bullen was born in the state of Connecticut. I am the third of nine children seven brothers and two sisters of who three brothers only beside myself, are now living.

My memory of the earliest events of my life is nearly uniform but as years advanced a few salient events stand as landmarks, with no particular propriety that I can discover, except perhaps the fact that they happened at moments in my life when I was unusually conscious, and serve to indicate this state of mind. The baby on which I was founded, was, I suppose, like other babies, except in respect to its destiny of which however its friends knew nothing at that time. At an early period in its life its grandmother discovered on its head, which was born with hair, a light down from which she predicted the present color of my hair.

This child though unusually sober and good natured, was in no way remarkable, except at the time, as being the baby; but this I have observed is ever a source of wonder. I bear at the present moment upon my forehead the mark of a wound which this child received in its first attempt at walking, and by which among other features I was afterwards distinguished.

My father was a democrat and an ardent supporter of Andrew Jackson, then president, and I escaped only by the skin of my teeth, (not then grown,) from receiving the name of this statesman. Fortunately the Fates and my Mother interfered and gave to this infant the name I now bear.

The first day at the infant school I distinctly remember as one of the saddest in my early life, a day of grief inconsolable. My teacher, or the lady who, I suppose, afterwards became my teacher endeavored to comfort me by offering me something to drink, — what I do not distinctly remember. It may have been milk or some sweet

beverage. My fainting spirit with all its tender outlets, rudely torn from home, could find no sustenance in earthly fluids; and so I came to my letters in tears.

From the earliest period of my conscious life, I have shrunk from everything of a startling or dramatic character. I was indisposed to active exercise; to any kind of excitement or change. I was never remarkable at any kind of sport; never could see the value or significance of any kind of formality. In illustration of this I remember a circumstance in my earliest school-days. The schoolmistress wished to introduce the custom of kneeling at morning prayer. This I obstinately refused to do, or at least obstinately did not do. The penalty for my disobedience was to kneel by the teacher's side; a position of dramatic interest by which my spirit was broken.

I was in general a very tractable boy and never was flogged at school, though I remember some slight corrections. I had some little ambitions, such as all boys have, but they were for the most part of a solitary nature. I never aspired to be a leader among boys, and never cared for their quarrels and parties. If I aspired to a place, it was to a solitary place and a peculiar one, not within the general aim of the boys. At one time however my ambition took a social turn.

While I was still in the district school I conceived an ardent attachment for one of the school-girls, which I have never mentioned before this writing to any living soul. I did not even intimate it to the young lady herself, but rather built small castles, or very diminutive houses in the air, wherein I dwelt in fancy with her I fancied,— I will not say adored. Such was the character of all the attachments or fancies I have subsequently had.

Another social turn of my ambition was at the high-school, where I studied hard for one of a series of prizes. I obtained one, not the first of the series, but the first and last in my past life. I carried to this school and retained the character of good-boy. I was never flogged, and on the occasion of receiving the prize I have mentioned, I was publicly praised as the only boy who had received, in that term of school, no marks for tardiness or bad behavior. This virtue of punctuality I have since lost in college, principally in the senior year, in which I received two private admonitions for cutting prayers. In this respect, then the boy was not father to the man; though I think, this can be explained, when we consider that I was not tempted like other boys by their sports, and that I was carefully trained to punctuality at home. Tardiness is the natural result of an indolent disposition, and this I have always had.

I had in my boyhood a violent temper, but I was not quarrelsome,

nor did I ever cultivate pugnacious qualities. My indolence has since completely mastered my temper.

At the age of ten I formed a liking for the study of astronomy, and my zeal in this easily overcame all the fondness for those surprises which had previously constituted the great attraction of New-years gifts. So I asked my father for that puerile book, Burrits Geography and Atlas of the heavens; but I afterwards lost my interest in this study.

In the higher English and Classical branches of the Northampton High-School, I came under the care of a most kind and zealous teacher, Mr. David S. Sheldon, now a Professor in Iowa College. I was inspired by him with a zeal for natural-history, which I have also since lost. I tramped in his company and under his guidance through most of the wilds of N. collecting, preparing and naming specimens of plants, bugs, birds, and reptiles. We drew into our pursuits nearly the whole school, and founded a museum of natural-history, which, I think, is still in existence. My private collection of plants was partly destroyed by fire a few years before I went to college, but not till my whole interest in them had perished, never to rise from its ashes.

The comet of 1843 roused my sleeping interest in astronomy but this soon disappeared again with the comet. At the age of fifteen and a half I left school without any definite interests ambitions or prospects. Through the influence of my friend, schoolmate and classmate James B. Thayer and of his brother William S. I was induced to apply to my father to send me to college. This he most willing consented to do. So after nearly two years of an uncertain, aimless, though not useless life, I went to school in East-Hampton to brush up my faded knowledge. In one term of this school I so far succeeded that with the aid of good-fortune and under the Balance I entered Harvard College, though with several conditions. With the unequalled Class of '52 I followed my destiny through the four years of college, never so much disturbing the Balance as to remember much about my college life, more than these incidents of general interest which are known to us all, among which may be mentioned the armorial honor I won of becoming the possessor of the prepossessing Jack-Knife. At the close of our course the world was deprived of the results of my learning, as embodied in my commencement part, by an accident, which for a time disabled me as to my power of walking. When I recovered I limped from Holworthy to the Nautical Office and I have remained in its employments to the present time.

July 24th 1858

1858 - About Thanksgiving time. Began to teach Nat. Phil in Agassiz's school. Thayer says Jan 25/60

1859. Elected a member of the American Academy of Arts and Sciences

1863 May 26. Recdg.-Secy. Am. Acad. till May 24/70

1864. July 1 - Chosen member of The Examiner Club.

1867 Recdig secy Am Acay. Of A. &S.

1870 Still living at Cambridge. Left Nautical Alm. Office. University Lecturer (H. C.)

1871

1872 “ “ “

1873

1874-5 Instructor in Physics (H.C.)

1875

1875 Sep. 12. Died suddenly of congestion of the brain.

1877 J. P. Thayer published letters of C. W. with some acct of his life.

The Winds and the Weather [From Atlantic Monthly 1.3 (January 1858): 272-279.] ³

By CHAUNCEY WRIGHT

The Physical Geography of the Sea. By M.F. MAURY. New York: Harper &Brothers. 1857.

Climatology of the United States and of the Temperate Latitudes of the North American Continent. By LORIN BLODGET. Philadelphia: J.B. Lippincott &Co. 1857.

Proceedings of the British Association for the Advancement of Science. 1857.

An eloquent philosopher, depicting the deplorable results that would follow, if some future materialist were "to succeed in displaying to us a mechanical system of the human mind, as comprehensive, intelligible, and satisfactory as the Newtonian mechanism of the heavens," exclaims, "Fallen from their elevation, Art and Science and Virtue would no longer be to man the objects of a genuine and reflective adoration." We are led, in reflecting upon the far more probable success of the meteorologist, to similar forebodings upon the dulness and sameness to which social intercourse will be reduced when the weather philosophers shall succeed in subjecting the changes of the atmosphere to rules and predictions, when the rain shall fall where it is expected, the wind blow no longer "where it listeth," and wayward man no longer find his counterpart in nature. But we console ourselves by contemplating the difficulties of the problem, and the improbability, that, in our generation at least, we shall be deprived of these subjects of general news and universal interest.

During the last half-century, the progress of experimental philosophy in the direction of the weather, though its results are for the most part of a negative character, has yet been sufficient to excite the apprehensions of the philanthropist. We have unlearned many fables and false theories, and have made great advancement in that knowledge of our ignorance, which is the only true foundation of positive science.

The moon has been deposed from the executive chair, though she still has her supporters and advocates; and an

innumerable host of minor causes are found to constitute, upon strictly republican principles, the ruling power of the winds and the rain. That regularity, however complicated, which reason still demands, and expects even from the weather, is not found to be so simple as our rules and signs of the weather indicate; for the operation of these innumerable causes is so complicated, that the repetition of similar phenomena or similar combinations of causes, to any great extent, is the most improbable of events. Perhaps the meteorologist will ultimately find that Nature has succeeded, in what seems, indeed, to be her aim, in completely retracing her steps, and reducing the operation of that simple and regular system of causes, which she brought out of chaos, back to a confusion of detail, from which all law and regularity are obliterated.

Meteorological observations have, however, determined many regular and constant causes and a few regular phenomena. The method pursued in these investigations is, for the most part, the elimination, by general averages, of limited and temporary changes in the elements of the weather, and the determination of those changes which depend upon the constant influences of locality, of season, and of constant or slowly varying causes. These constant influences constitute the climate; and the study of climates is thus the first step towards the solution of the problem of the weather. Climates, in their changes and distribution, are very important elements in the determination of the movements of the weather, and are to the meteorologist what the elements of the planetary orbits are to the astronomer; but, unlike planetary perturbations, the weather makes the most reckless excursions from its averages, and obscures them by inconsequent and incalculable fickleness.

Whether mechanical science will hereafter succeed in calculating these perturbations of climate, as we may style the weather, or will find the problem beyond its capacity, it will yet, doubtless, account for much that is now obscure, as observation brings the facts more distinctly to view. We propose to give a brief general survey of the mechanics of the atmosphere in its present state, and to indicate the nature and limits of our knowledge on this subject

Among the first noticed and most remarkable features of regularity in atmospheric changes are constant, periodic, and prevailing winds. The most remarkable instances of these are the trade-winds of the torrid zone, the monsoons of the Indian Ocean, and the prevailing southwest wind of our northern temperate latitudes. Of these, the trade-winds are the most important to science, as furnishing the key to that general explanation of the winds which was first advanced by the distinguished Halley.

In Bailey's celebrated theory, the trade-winds are explained as the effects of the unequal distribution of the sun's heat in different latitudes. The air of the equator, heated more than the northern or southern air, expands more, and overflows, moving in the upper regions of the atmosphere toward the poles; while the lower, colder air on both sides moves toward the equator to preserve equilibrium. Thus an extensive circulation is carried on. The air that moves from the equator in the upper atmosphere, gradually sinking to the surface of the earth, finally ceases to move toward the poles, and returns as an undercurrent to the equator, where it again rises and moves toward the poles.

Now the air of the equator, moving with the earth's rotary motion, has a greater velocity than the earth itself at high northern or southern latitudes, and consequently appears to gain an eastward motion in its progress toward the poles. Without friction, this relative eastward motion would increase as the air moves toward the poles, and diminish at the same rate as the air returns, till at the equator the velocity of the earth and of the air would again be equal; but friction reduces the motion of the returning air

to that of the earth, at or near the calms of the tropics; so that the air, passing the tropics, gains a relative westward motion in its further progress through the torrid zone. The southwestward motion thus produced between the tropic of Cancer and the equator is the well-known trade-wind.

Now, according to this theory, the prevailing winds of our temperate latitudes ought to have a southeastward motion as far as the calms of Cancer or "the horse latitudes." Moreover, instead of these calms, there should still be a southward motion. But observation has shown, that though the prevailing lower winds of our latitude move eastward, still their motion is toward the north rather than the south; so that they appear to contradict the theory by which the trade-winds are explained.

To account for these anomalies, Lieut. Maury has invented a very ingenious hypothesis, which is published in his "Physical Geography of the Sea." He supposes that the air, which passes from the equator toward the poles in the upper regions of the atmosphere, is brought down to the surface of the earth beyond the calms of the tropics, and that it thence proceeds with an increasing eastward motion, appearing in our northern hemisphere as the prevailing northeastward winds. Approaching the poles with a spiral motion, the air there rises, according to this hypothesis, in a vortex, and returns toward the equator in the upper atmosphere, gradually acquiring a westward motion; till, returning to the tropics, it is again brought down to the earth, and thence proceeds, with a still increasing westward motion, as the trade-winds. At the equator the air rises again, and, according to Lieut. Maury, crosses to the other side, and proceeds through a similar course in the other hemisphere.

The rising of the air at the equator is supposed to cause the equatorial rains; and the drought of the tropics is also explained by that descent of the air, in these latitudes, which this hypothesis supposes.

Now although this hypothesis explains the phenomena, it has still met with great opposition. The motions which Lieut. Maury supposes can hardly be accounted for without resorting, as is usual in such cases, to electricity or magnetism, - to some occult cause, or some occult operation of a known cause. Moreover, it has been difficult for the mechanical philosopher to understand how the winds manage to cross each other, as Lieut. Maury supposes them to do, at the equator and the tropics, without getting into "entangling alliances." If this hypothesis were advanced, not as a physical explanation of the phenomena, but, like the epicycles and eccentrics of Ptolemy, "to save the appearances," its ingenuity would be greatly to its author's credit; but, like the epicycles and eccentrics, though it represents the phenomena well enough, it contradicts laws of motion, now well known, which ought to be familiar to every physical philosopher. But these speculations of Lieut. Maury will now be superseded by a new theory of atmospheric movements, an account of which was presented by its author, Mr. J. Thompson, at the recent meeting of the British Association for the Advancement of Science. A fuller discussion of this theory the author reserved for the Royal Society. The London Athenaeum gives a brief abstract of his paper, in its report of the proceedings of the Association. ⁴

Mr. Thompson's theory takes account of forces, hitherto unnoticed, which are generated by the eastward circulation of the atmosphere in high latitudes. He shows that these forces cause the prevailing northeastward under-current of our latitudes, while above this, yet below the highest northeastward current, the air ought still to move southward according to Halley's theory.

This under-current is not the immediate effect of differences of temperature, but a secondary effect induced by the friction of the earth's surface and the continual deflection of the air's eastward motion from a great circle, (in which the

air tends to move,) into the small circle of the latitude, in which the air actually does move. The force of this deflection, measured by the centrifugal force of the air as it circulates around the pole, retards the movement from the equator, and finally wholly suspends it; so that the upper air circulates around in the higher latitudes as water may be made to circulate in a pail; and the air is drawn away from the polar regions as this circulatory motion is communicated to it, and tends to accumulate in the middle latitudes, as the circulating water is heaped up around the sides of the pail. Hence, in the middle latitudes there is a greater weight of air than at the poles, and this tends to press the lower air to higher latitudes. Centrifugal force, however, balances this pressure, so long as the lower air moves with the velocity of the upper strata; but as the friction of the earth retards its motion and diminishes its centrifugal force, it gradually yields to the pressure of the air above it, and moves toward the poles. Near the polar circles it is again retarded by its increasing centrifugal force, and it returns through the middle regions of the atmosphere.

Thus there are two systems of atmospheric circulation in each hemisphere. The principal one extends from the equator to high middle latitudes and partly overlies the other, which extends from the tropical calms to the polar circles. These two circulations move in opposite directions; like two wheels, when one communicates its motion to the other by the contact of their circumferences.

In the middle latitudes the lower current of the principal circulation lies upon the upper current of the secondary circulation, and both move together toward the equator. This principal lower current first touches the earth's surface beyond the tropical calms, and having lost its relative eastward motion and now tending westward, it appears as the trade-wind, regular and constant; while the upper secondary current returns without reaching the tropics, as an under-current, and in our latitude appears as the prevailing northeastward wind, - a very feeble motion, usually lost in the weather winds and other disturbances, and only appearing distinctly in the general average.

Mr. Thompson illustrates the effect of the friction of the earth's surface on the eastward circulation of the air by a very simple experiment with a pail of water. If we put into the pail grains of any material a little heavier than water, and then give the water a rotatory motion by stirring it, the grains ought, by the centrifugal force imparted to them, to collect around the sides of the pail; but, sinking to the bottom, they do in fact tend to collect at the centre, earned inward by those currents which the friction of the sides and bottom indirectly produces.

Thus Mr. Thompson's beautiful and philosophical theory completes that of Halley, and explains all those apparent anomalies which have hitherto seemed irreconcilable with the only rational account of the trade-winds. The rainless calms of the tropics are explained by this theory without that crossing and interference of winds which Lieut. Maury supposes; for the secondary circulation returns as an under-current toward the poles without reaching the tropics, and the dry lower current of the principal circulation passes over the tropical latitudes, in its gradual descent, before it reaches the earth as the trade-winds.

These trade-winds, absorbing moisture from the sea, precipitate it as they rise again, and produce the constant equatorial rains; and these rains, doubtless, tend much more powerfully than the mere unequal distribution of heat to direct the wind toward the equator; for the fall of rain rapidly diminishes the pressure of the air and disturbs its equilibrium, so that violent winds are frequently observed to blow toward rainy districts. Thus, primarily, the unequal distribution of heat, and, more immediately, the equatorial rains cause the principal circulation of our atmosphere; and this indirectly produces the secondary

circulation of Mr. Thompson's theory. Both these regular movements are, however, greatly disturbed, and especially the latter, by winds which are occasioned by local and irregular rains.

In these movements and their causes we have the general outline of our subject, within which we must now sketch the weather. The causes of atmospheric movement, which we have thus far considered, are the unequal distribution of the sun's heat, the absorption and precipitation of moisture, the direct and the inductive action of the earth's rotation and friction. If to these we should add the tidal action of the sun's and moon's attractions, we should perhaps complete the list of veræ causæ which are certainly known to exert a more or less general influence upon the atmosphere. But this short list is long enough, as we shall soon see.

If the earth were wholly covered with water of a uniform depth, its climates would be distributed with greater regularity, and the perturbations of climate would be comparatively small and regular; though even under such circumstances there would still exist a tendency to discontinuity and complexity of movements from that influence of rain, the peculiar character of which we shall soon consider.

The irregular distribution of land and water, and the peculiar action of each in imparting the heat of the sun to the incumbent air, - the irregular distribution of plains and mountains, and their various effects in different positions and at different altitudes, - the distribution of heat effected by ocean currents, - all these tend to produce permanent derangements of climate and great irregularities in the weather. To these we must add what the astronomer calls disturbing actions of the second order, - effects of the disturbances themselves upon the action of the disturbing agencies, - effects of the irregular winds upon the distribution of heat and rain, and upon the action of lands and seas, mountains and plains. Though such disturbances are comparatively insignificant in the motions of the planets, yet in the weather they are often more important than the primary causes.

The aggregate and permanent effect of all these disturbing causes, primary and secondary, is seen in that irregular distribution of climates, which the tortuous isothermal lines and the mottled rain-charts illustrate. The isothermal lines may be regarded as the topographical delineations of that bed of temperatures down which the upper atmosphere flows from the equator toward the poles, till its downward tendency is balanced by the centrifugal force of its eastward motion. This irregular bed shifts from month to month, from day to day, and even from hour to hour; and the lines that are drawn on the maps are only averages for the year or the season.

In the midst of these irregular, but continuous agencies, the rain introduces a peculiar discontinuity, and turns irregularity into discord. We have shown that the rain is an immediate cause of wind; but how is the rain itself produced? For so marked an effect we naturally seek a special cause; but no adequate single cause has ever been discovered. The combination of many conditions, probably, is necessary, - such as a peculiar distribution of heat and moisture and atmospheric movements; though the immediate cause of the fall of rain is doubtless the rising, and consequent expansion and cooling, of the saturated air.

The winds that blow hither and thither, vainly striving to restore equilibrium to the atmosphere, burden themselves with the moisture they absorb from the seas; and this moisture absorbs their heat, retards their motion, and slowly modifies the forces which impel them. Now when the saturated air, extending far above the surface of the earth, and carried in its movements still higher, is relieved of an incumbent weight of air, it becomes rarefied, and its temperature and capacity for moisture are simultaneously diminished; its moisture, suddenly

precipitated, appears as a cloud, the particles of which collect into rain-drops and fall to the earth. Thus the air suddenly loses much of its weight, and instead of restoring equilibrium to the troubled atmosphere, it introduces a new source of disturbance. Though the weight of the air is diminished by the fall of rain, yet the bulk is increased by the expansive force of the latent heat which the condensed vapors sot free. Thus the rainy air expands upwards and flows outwards, and no longer able to balance the pressure of the surrounding air, it is earned still higher by inblowing winds, which rise in turn and continue the process, often extending the storm over vast areas. The force of these movements is measured partly by the force of latent heat set free, and partly by the mechanical power of the rain-fall, a very small fraction of which constitutes the water-power of all our rivers. Such a fruitful source of disturbance, generated by so slight an accident as the upward movement of the saturated air, expanded by its own agency to so great an extent, so sudden and discontinuous in its action, so obscure in its origin, and so distinct in its effects, - such a phenomenon defies the powers of mathematical prediction, and rouses all the winds to sedition.

A storm not only disturbs the lower winds, but its influences reach even to the upper movements. The sudden expansion and rising of the rainy air delay these movements, which afterwards react as violent winds.

The forces stored away by the gradual rise of vapor and its absorption of heat, and then suddenly exhibited in a mechanical form by the effects of rain, afford an illustration of that principle of conservation and economy of power, of which there are so many examples in modern science. No power is ever destroyed. Whether exhibited as heat or mechanical for products and forces of chemical or of vital action, in movement or in altered conditions of motion, - whether charged by the growth of plants into fuel or into food, and converted again to heat by combustion or by vital processes, and brought out a mechanical power in the steam-engine or in the horse, - it is still the same power, and is measured in each of its forms by an invariable standard. It first appears as the heat of the sun, and a portion escapes at once back into space, while the rest passes first through a series of transformations. A part is changed into moving winds or into suspended vapor, and a part into fuel or food. From conditions of motion it is changed into motion; from motion it is changed by friction or resistance into heat, electric force, molecular vibrations, or into new conditions of motion, and passing through its course of changes, it remains embodied in its permanent effects or escapes into space as heat.

Though mechanical science will probably never be able to predict the beginning or duration of storms, it will yet, doubtless, be able to account for all their general features, and for such distinct local peculiarities as observation may determine. Great advancement has already been made in the determination of prevailing winds and in the study of storms. Two theories have been brought forward upon the general movements of storms; both have been proved, to the entire satisfaction of their advocates, by the storms themselves; and probably both are, with some limitations, true. The first of these theories we have already described. According to it, the winds move inward toward the centre of the storm; according to the other theory, they blow in a circumference around the centre.

Observations upon storms of small extent, such as thunder-storms or tornadoes, show very clearly that the winds blow toward the stormy district. But when observations are made upon the winds within the district of such extensive storms as sometimes visit the United States, the directions of the wind are found to be so various, that the advocates of either theory, making due allowance for local disturbances, can triumphantly refute their adversaries, in such storms

there are doubtless many centres or maxima of rain, and whether the wind move around or toward these centres, it would inevitably get confused.

The opinion, that the winds move around the central point or line of the storm, was strenuously maintained by the late Mr. Redfield, whose activity in his favorite pursuit has connected his name inseparably with meteorology. Others have maintained the same opinion, and the rotatory motion of the tropical hurricanes is offered as a principal proof. It is obvious from the causes of motion already considered, that, if the air is carried far, by its tendency toward a rainy district, it will acquire a secondary relative motion from its change of latitude; and this, in our hemisphere, if the air move toward the south, will be westward, - if toward the north, eastward. Hence the motion of the air from both directions toward a stormy district is deflected to the right side of the storm; and this gives rise to that motion from right to left which is observed in the hurricanes of the northern hemisphere.

To suppose, as many do, that regular winds, arising from constant and extensive causes, can come into bodily conflict and preserve their identity and original impetus for days, without immediate and strongly impelling forces to sustain their motion, implies a profound ignorance of mechanical science, and is little better than those ancient superstitions which gave a personal identity to the winds. The momentum of ordinary winds is a feeble force in comparison with those forces of pressure and friction which continually modify it. Hence sudden changes in the direction and intensity of winds must primarily arise from similar changes in these forces. But there are no known forces which change so suddenly, except the pressure and latent heat of suspended vapor; and therefore the fall of rain is the only adequate known cause of those storm-winds which, interpolated among the gentler winds, keep the atmosphere in perpetual commotion.

Storms have, however, certain habits and peculiarities, more or less regular and distinct, which depend upon locality and season. And this is what ought to be expected; for, though the storms themselves are essentially anomalous, yet many of the causes which cooperate to induce them are constant or periodic, while others are subject to but slight perturbations. It is obvious that no more moisture can be precipitated than has been evaporated, and that the winds only gain suddenly by the fall of rain the forces which they have lost at their leisure in the absorption of moisture. Thus the rage of the storm is kept within bounds, and though the exact period at which the winds are set free cannot be determined, yet their force and frequency must be subject to certain limitations. The study of the habits and peculiarities of storms is of the greatest importance to navigation and agriculture, and these arts have already been benefited by the labors of the meteorologist.

The lawlessness of the weather, within certain limitations, though discouraging to the physical philosopher, has yet its bright side for the student of final causes. The uses of the weather and its adaptation to Organic life are subjects of untiring interest. The progression of the seasons, varied by differences of latitude, is also diversified and adapted to a fuller development of organic variety by irregularities of climate.

The regular alternations of day and night, summer and winter, dry seasons and wet, are adapted to those alternations of organic functions which belong to the economy of life. The vital forces of plants and of the lower orders of animals have not that self-determining capacity of change which is necessary to the complete development of life; but they persist in their present mode of action, and, when they are not modified by outward changes, reduce life to its simplest phases. Changes of growth are effected by those apparent hardships to which life is subject; and progression in new directions is effected by

retrogression in previous modes of growth. The old leaves and branches must fall, the wood must be frost-bitten or dried, the substance of seeds must wither and then decay, the action of leaves must every night be reversed, vines and branches must be shaken by the winds, that the energies and the materials of new forms of life may be rendered active and available.

Some of the outward changes of nature are regular and periodic, while others, without law or method, are apparently adapted by their diversity to draw out the unlimited capacities and varieties of life; so that as inorganic nature approaches a regulated confusion, the more it tends to bring forth that perfect order, of which fragments appear in the incomplete system of actual organic life.

The classification of organic forms presents to the naturalist, not the structure of a regular though incomplete development, but the broken and fragmentary form of a ruin. We may suppose, then, with a recent physiological writer, that the creation of those organic forms which constitute this fragmentary system was effected in the midst of an elemental storm, a regulated confusion, uniting all the external conditions which the highest capacities and the greatest varieties of organized life require for their fullest development; and that as the storm subsided into a simpler, but less genial diversity, - into the weather, - whole orders and genera and species sank with it from the ranks of possible organic forms. The weather, fallen from its high estate, no longer able to develope, much less to create new forms, can only sustain those that are left to its care.

Man finds himself everywhere mirrored in nature. Wayward, inconstant, always seeking rest, always impelled by new evils, the greatest of which he himself creates, - protecting and cherishing or blighting and destroying the fragmentary life of a fallen nature, incapable himself of creating new capacities, but nourishing in prosperity and quickening in adversity those that are left, - he sees the workings of his own life in the strife of the elements. His powers and activities are related to his spiritual capacities, as inorganic movements are related to an organizing life. The resurrection of his higher nature is like a new creation, secret, sudden, inconsequent. "The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth; so is every one that is born of the Spirit."

The Prismoidal Formula. [From Runkle's Mathematical Monthly 1.1 (October 1858): 21-24.] ⁵

BY CHAUNCEY WRIGHT.

The formula (B + 4 B' + B″) l/6, in which B, B', B″ are three equidistant parallel surfaces, sections of a solid, and l the distance between B and B″, is the expression for the solid contents between

B and B″, not only for the prismoid from which it was first derived, but also for several solids of revolution, as the sphere, ellipsoid, &c. What is the extent of its application?

Let X be the axis perpendicular to which the sections are made, and f(x) the area of the section at the distance x from the origin. The problem then is, What function f will fulfil the conditions of the formula?

Let three sections be made through any solid at the distances (x - h), x, (x + h) from the origin. Then h = l/2 and f(x - h), f (x),f (x - h) will be the areas of the sections, and if the formula apply the solid contents between f (x - h) and f (x+ h) will be [f (x - h) + 4 f (x) + f (x + h)]h/3. But the solid contents is also equal to the integral of the differential solid f(x)dx between the limits x - h and x+h.

Equating these two expressions for the solid contents, we have, if the function f fulfils the conditions of the formula,

To find what form of f will satisfy this equation, develop both its members by Taylor’s theorem. The first member becomes,

The second member becomes

Comparing the last members of (A) and (B) we find the equation

which is satisfied only when the terms beyond the second disappear; that is, by functions which have no fourth and higher derivatives. Hence f(x) must be an algebraic expression of positive integral powers not exceeding the third degree.

In general
f(x) = ax3 + bx2 + cx + e = area of section.

The error in applying this formula, when f(x) is of the fourth or fifth degree is

If h is taken so small, that terms containing its fifth power may be neglected, the prismoidal formula may be applied to any solid. Simpson’s rule, which includes a series of prismoidal formulas, is sufficiently accurate when n is so large that (l/n)5 may be neglected.

The prismoid comes within the limits of this formula. For, being a solid bounded by planes, and the sections perpendicular to its sides being dissimilar polygons, but with the same number of sides, it may be decomposed into prismoids with triangular sections. These prismoids are bounded by one plane and two warped surfaces; the plane

surface being one of the surfaces of the original prismoid; the other two being generated by the varying sides of the triangular section. Since these triangles are not similar, their sides must change at dissimilar rates in passing along the axis, or their base and altitude will not change proportionally.

Let b be the base and a the altitude of any triangle at the origin of x; let α and β be their respective rates of change, in passing along x. Then b + βx and a + αx will be the base and altitude at any distance x from the origin, and its area will be 1/2(a + αx)(b+ βx). Hence the area of the whole polygonal section is f(x) = 1/2 Σ [a + αx)(b+ βx) = 1/2 Σ [ab + (aβ + ba)x + α β x2] which is an expression of the second degree, and is therefore one to which the formula applies.

The formula also applies to the solids generated by the revolution of the conic sections about their axes of symmetry, the general equation of these sections being y2 = mx + nx2. The sections of these solids taken perpendicularly to the axis of x are circles, having y for a radius, and πmx + πnx2 = πy2 = f(x) = area, to which also the formula applies.

But if the conic section be revolved about any axis for which the general equation does not hold, then the prismoidal formula does not apply, because the expression for the area of the section f(x) will involve radicals which have fourth and all higher derivatives. The formula applies in like manner to the solid of revolution of the semicubic parabola, of which the equation is y2 = mx3.

The principles involved in this discussion of the prismoidal formula, may be applied to finding a formula, for solid contents, which shall hold good for bodies, of which the sections are expressed in terms of higher degrees than the third; and also for cases in which the sections are taken at unequal intervals.

This discussion is reserved for the next number of the Monthly.

Extension of the Prismoidal Formula. [From Runkle's Mathematical Monthly 1.2 (November 1858): 53-57.] ⁶

BY CHAUNCEY WRIGHT

We have shown that the Prismoidal Formula is an exact definite integral for algebraic expressions of positive integer powers not exceeding the third degree, and that it is sufficiently accurate in all cases where the fourth order of differences may be neglected. We propose now to determine similar formulas, which shall include higher orders of differences.

If we represent by

a series of sections made perpendicular to the axis of X, through a solid or plane figure, and at the distances x, x + h1, x - h1, &c. from the origin of x, then the expression


which contains 2 n + 1 terms, n + 1 coefficients a, a1, a2, &c., and n values h1, h2, &c., may be made to represent the contents of any portion of the solid or plane figure for which f(x) is an algebraic expression of positive integer powers not exceeding the (4 n — l)th degree.

Formula (A) may be written thus: —

and developed by Taylor’s Theorem, it becomes

Now, the definite integral

becomes, when developed,

and, if we make the corresponding terms of (B) and (C) equal, we have the following equations

and so on, in which a, a1, a2, &c., are the coefficients of the sections, and r1, r2, &c., the ratios of their distances from the middle section to the distance A, of the extreme sections from the middle.

If by l we denote the whole distance between the extreme sections, then hn = l/2.

The number of the equations (D) which can be satisfied is equal to the number of undetermined quantities a, a1, a2, ...an; r1, r2, ... rn-1, that is, to (n + 1) + (n - 1) = 2 n. But the (2 n + 1)th

terms of the expressions (B) and (C) contain the coefficients of the 4nth derivative of f(x), which are therefore the first not included in the equations (D); hence (-4) may be made accurate for (4 n — 1) derivatives of f(x). When the sections are made at equal intervals, the distances h1, h2, &c., and the ratios r1, r2, &c., are determined by their number, and (A) can be made accurate only for as many derivatives of f(x) as there are sections, that is, for 2 n + 1. Since there are 2 n equations (D) the last will be of the form

and the error of (A) for functions of two higher orders of derivatives, that is for functions which have 4 n, or 4 n + 1 derivatives, is

EXAMPLES.

1. When there are only three sections, n = 1, and the equations (D) become 1 = 1/2 a + a1 and 1/3 = a1, hence a = 4/3 and (A)

which is the common prismoidal formula.

2. When n = 2, there are five sections, and the equations (D) become

If these sections are made at equal intervals, then r1 is determined, and only three of these equations can be satisfied; that is, only five orders of derivatives can be included by them. As the second and fourth sections will in this case bisect the intervals between the middle and the extreme sections, r1 = 1/2 and the equations

so that the formula (A) becomes

and its error for functions of six or seven derivatives is

If r1 be taken so that the coefficient a of the middle section shall disappear, then

and we obtain a formula of four sections,

This formula is accurate for five derivatives, and its error for functions of six or seven derivatives is

If r1 is left indeterminate, then the solution of the four equations above will give

and we obtain the formula of five sections

This error and those of formulas (1) and (2) may be estimated in terms of the finite differences of f(x) by the following transformations. If the length l be divided by sections into so many parts m that the corresponding differences of f(x) of a higher order than the ith, may be neglected, then

Hence, if the number of parts m into which l is divided be about the eighth root of 237081600, or about 11, and if the corresponding value of Δ8f(x) be inappreciable, then formula (3) is sufficiently accurate. In the same way the accuracy of formulas (1) and (2) may be estimated in practice.

In the application of formulas (1), (2), and (3) to symmetrical figures, as for instance for determining the contents of casks, since the sections at equal distances from the middle section are equal, these formulas may be written thus: —

Cases in practice might arise in which sections at equal intervals could not be obtained. For such cases special formulas might be easily obtained from the equations (D).

In some future number of this journal we shall apply the formulas of the preceding discussion to a variety of problems in Engineering, Tonnage of Vessels, Cask Gauging, &c.

The most thorough Uniform Distribution of Points about an Axis. [From Runkle's Mathematical Monthly 1.7 (April 1859): 244-248.] ⁷

ByChauncey Wright, Nautical Almanac Office, Cambridge, Mass.

Let it be required to place at equal successive intervals round and round upon the circumference of a circle, an indefinite number of points, so that the circumference shall at any time be divided by them into the smallest parts; that is, so that the circumference shall be most thoroughly divided at every step of the distribution.

If we were not limited to equal intervals between the successive points, the distribution might be very simply effected either by continually bisecting or trisecting the parts of the circumference. Thus two points placed oppositely would divide the circumference into two equal parts, and with two other points these semi-circumferences might be bisected, according to the arrangement of cruciform flowers

and whorls; and further, four more points might bisect the quadrants, and so on. Or, again, the circumference might at first be divided by three points into three equal parts, and these might be bisected or trisected by the three or six following points, and so on.

To divide the parts of the circumference into smaller fractions than thirds would be to neglect the distribution at first, though the ultimate division of the circumference would be quite as perfect But if now we seek a uniform and symmetrical distribution as well as a thorough one, the interval between the successive points must be constant, and if the circumference is to be indefinitely subdivided, this interval is of course incommensurate.

Let x denote the ratio of this interval to the whole circumference; then 1/x is the number of times the interval is contained in the whole circumference. Let q denote the integer part of 1/x and r' the remainder after subtracting q x from the whole circumference.

In the second revolution around the circumference each of the parts x is divided into the parts r' and x - r' . In the third revolution each of the parts x - r' into the parts r' and x - 2 r' , and so on as many times as r is contained in x. Let this number be q', and let the remainder, x - q' r' , be denoted by r''.

By further revolutions each of the intervals r' is subdivided into q″ parts r'' with a third remainder r'''; and so on. The numbers and spaces q, q', q'', &c., r', r'', r''' &c., are such as are obtained by the method for finding the greatest common divisor or for forming a continued fraction, and since

Now in order that the circumference may be at every step most thoroughly divided, the magnitudes of the parts into which it is divided should be as nearly equal as possible; that is, the smaller should be contained in the larger the least number of times; hence, in general, the numbers q[n], which express the ratios of successive sub-intervals, should be unity. It may not be necessary that the distribution should begin till after the first revolution. In this case the first quotient q may be any number, but all the other quotients, q', q'', q''', &c., must be unity, hence

This ratio k and the continued fraction, which expresses it, have hitherto been obtained by mathematical induction from the fractions of the Phyllotaxis. On the other hand we shall be able by further deductions, still subject to the conditions of our problem, to obtain these fractions as special solutions. For, in cases where the circumference is to be divided into a limited number of parts, the interval

x becomes commensurate, and the last remainder or space of the foregoing analysis is contained exactly twice in the last but one; that is, the last step of the distribution consists in bisecting the previous parts of the circumference. ' Or, what comes to the same, the last remainder but one is contained in the preceding remainder once, with a remainder equal to itself, so that the last two remainders are equal. Hence, for a distributive commensurate interval, all the values q[n] are unity, but are limited in number; and the interval is therefore one of the approximations of the continued fraction (1).

When q = 1 these approximations are 1, 1/2, 2/3, 3/5, 5/8, &c. When q = 2 they are 1/2, 1/3, 2/5, 3/8, &c., the arithmetical complements of the former, and they therefore express the same arrangements, but in an opposite direction around the circumference. When q = 3 we obtain 1/3, 1/4, 3/7, &c.

In general the third approximation

or two divided by any odd number, expresses the intervals which, in the second revolution, are bisected. The fractions 2/3, 2/5, and 2/7 are the only ones of this simplest form of distribution which are found in the arrangements of leaves around their stems. In all the arrangements of the Phyllotaxis every point after the first revolution is so placed with reference to the two points, between which it falls, that its distance from the middle is never more than one sixth of the whole interval between the two points. The distributive property of these fractions clearly explains their office in nature.

Many other fractions are apparently as well adapted to the symmetry of vegetable forms, and the limitation of natural arrangements to the Phyllotactic system seems, therefore, at first sight, unaccountable. Two hypotheses have been advanced to explain this limitation; the one attempting to deduce these arrangements mechanically from a hypothetical law of formation; and the other

regarding them as typical forms or models which nature has chosen to follow by an arbitrary limitation of her means. The latter hypothesis certainly agrees best with the principles of animal and vegetable Morphology, according to which organized forms are not determined simply by their functions, but are rather certain typical structures or models, modified and metamorphosed by their functions.

There are three ways in which we may seek to account for natural forms and phenomena. First, by deducing them from the law. of their development, as in the mechanical sciences; or, secondly, we may account for them by the discovery of their functions or offices as in Physiology; or, thirdly, by referring them to fundamental types or natural methods, as in the Morphology of organized forms. To the latter class of explanations belongs the most generally received account of the Phyllotaxis; that is, the arrangements of this system are regarded as the models by which nature works, and not as the result of any discoverable law of formation, nor as performing any special function in the vegetable economy. But we have shown that there is a purpose which these arrangements fulfil, and that no other arrangements are adapted to the same office. This office in plants is to effect the most thorough distribution of leaves and petals around their axes; to expose them most effectively to the influences of light and air, and to distribute their fibres most thoroughly in the stem. Thus the functions of leaves and petals determine not only their general forms, but also in general their relative positions. Expansion and exposure are the conditions required by the functions, and the Phyllotaxis is only a simple mathematical deduction from these conditions.

Properties of Curvature in the Ellipse and Hyperbola. [From Runkle's Mathematical Monthly 2.6 (March 1860): 198-204.] ⁸

By Chauncey Wright, Nautical Almanac Office, Cambridge, Moss.

The equation of curvature, (which, as furnishing a direct and simple means of constructing points m the evolute of the ellipse or hyperbola by the method of the fourth proportional, was published in No. X. Vol. I. of this Journal, among the Prize Problems,) can itself be easily deduced from a simple geometrical construction.

1. In this equation r and r' denote the radii vectores from the foci to any point of the curve; p denotes the perpendicular line from the centre to the tangent of this point, and g the radius of curvature.

Further, let p1 and p2 denote the perpendicular lines from the foci to the tangent, and let ε denote the angle formed by both the radii with the tangent; A and B the semi-axes of the curve, and φ the angle formed by the radius r with the axis A.

If to two points, M and N, of an ellipse or an hyperbola, distant from each other by the element of arc d s, radii be drawn from both foci, and if the angle included by the radii from the first focus F be

denoted by d φ, and if a tangent be drawn through one of these points M, and the radius from the first focus F to the other point N be extended to this tangent (an infinitesimal distance of the second order), and from the point of intersection the line N L be drawn, forming the same angle with the tangent as the intersecting radius; then the angle included between this line N L and the radius r' from the second focus F' to the first point M, will be d φ, and the distance apart of these two lines at the second focus F' will be in the ellipse, (r + r' d φ, and in the hyperbola (r' - r) d φ, or in both 2 A d φ.

The angle which the line NL forms with the other radius N F' from the second focus is obviously equal to twice the angle which the tangents of the two points M and N form with each other, and we may express it by 2 d τ. The distance apart of these lines at the second focus is therefore 2r' d τ; hence the distances 2Adφ and 2 r' d τ are equal or

The construction of the centre of curvature O is given in the figures.

which is easily proved as follows.

The angle included by the radii vectores to any point is in the ellipse the supplement of 2 ε and in the hyperbola it is equal to 2 ε. If now the distance between the foci be denoted by 2 C we have by trigonometry

3. The mechanical properties of the ellipse and hyperbola may be easily deduced from the equations

in the two cases of central forces for which these curves are the paths described.

First, if the centre of attraction or repulsion be the centre of the ellipse or hyperbola, and if v denote the velocity with which the material point is at any time, t, moving, and re the radius vector of this point from the centre, εe, the angle which it forms with the tangent

and φe the angle which it forms with the axis A; the principle of equal areas may be expressed by the equation,

p v = a = a constant,

If the area and time be reckoned from the same origin, and if T denote the time of one complete revolution, a is equal to twice the


or the force is proportional to the distance from the centre.

hence the time of revolution is independent of the magnitude or form of the ellipse. The small oscillations of a free pendulum are therefore isochronous. .

Secondly, when one of the foci F of the ellipse or hyperbola is the centre of force, we have the mechanical equations

and the equations of curvature

The time of revolution is therefore independent of the minor axis B, and its square is proportional to the third power of the major axis, according to Kepler’s third law.

The general equation

includes the two cases above, and all cases in which rx and px are the radius and perpendicular to the tangent from any centre of force whatever.

If we substitute in it the radius and perpendicular from the centre, re, and p = A sin ε, or the radius and perpendicular from the

focus, r and p1 = r sin ε, the force R becomes independent of direction, and is a function of the radius only.

If we resume the mechanical equations

and the equation of curvature

we have in general

hence

The square of the velocity is therefore proportional in the first case to the product of the radii from the foci; and in the second case to their ratio. Moreover, it is obvious that in the second case the product of any two velocities in two positions at equal and opposite distances from the minor axis is the constant m/A; that is,

These values of v2 may also be deduced, though not so readily, by integration, and the determination of constants from the fundamental equation d(v2) = 2 R d rx.

Remarks on Bees. [From Proceedings of the American Academy of Arts and Sciences 4 (8 May 1860): 432-433.] ⁹

Mr. C. Wright made some remarks on the architecture of bees, in reference to previous discussions upon the instinct of the honey-bee.

Mathematicians have regarded the economical characteristics of the honey-cell too exclusively, to the neglect of those symmetries which Maraldi pointed out.

The more prominent of these symmetries are the regularity of all the solid angles of the cell, and the consequent equality of all the angles made by the sides and rhombs with each other to 120°, or to 4/3 of a right angle. Another important symmetry which follows from these is seen in the position of that point in the axis of the cell which is directly over the middle points of the rhombs; for this point is at the same distance from all the nine planes of the cell, and just opposite similar points in the nine contiguous cells; so that little spheres which would just fit the honey-cells would, if pressed to the bases of the cells on both sides of the comb, touch the rhombs in their middle points, and the sides in their middle lines, by points in the spheres themselves, at which they would touch each other but for the thickness of the intervening walls.

While the common mode of considering the form of the honey-cell regards it as the effect of rational economy, these symmetries show how the cell might be the natural result of simple or sensible economy, as applied to the building of simple nests, the common type of which is a cylindrical cavity with a hemispherical base. The construction of a series of such nests side by side, and with the bases of two opposite series in closest contact, would, by the simple removal of the interstitial material, result in two series of cells like the normal ones of the honeycomb, both in the forms and the arrangement of the sides and bases. Hence, as the bee builds the two series of cells from their common bases, making the incipient depressions on one side form the interstitial elevations

around the cavities of the other side, and as it builds by continual trimming and saving, we may infer that the form of the honey-cell does not require, in the bee’s instinct, any reference to supersensible properties of form, but only a reference to sensible economy and facility of construction; especially as no one would contend that the utility, to innumerable nest-building animals, of spherical and cylindrical surfaces, depends upon their economy (which is still greater than that of the honey-cell), rather than upon their far more obvious symmetries and facilities for construction. It appears, therefore, that the instinct of the bee does not differ in kind from instincts in general.

The Economy and Symmetry of the Honey-Bees' Cells. [From Runkle's Mathematical Monthly 2.9 (June 1860): 304-319.] ¹⁰

By Chauncey Wright, Nautical Almanac Office, Cambridge, Mass.

The economical characteristics of the honey-cell have claimed so great attention from mathematicians, that other and even more prominent properties of its structure, though not unnoticed, have received too little attention. Psychologists, accordingly, following the testimony of mathematicians, have treated of the instinct of bees as if economy were not simply the most important, but even the only useful and noticeable feature of the bees’ architecture. In reconsidering therefore the geometrical properties of the hive-cell we have chiefly in view the inferences which may be drawn from them in regard to the nature and powers of the bee’s instinct.

In this review we shall first recount the reasoning a priori by which the structure of the hive-cell is deduced from considerations of rational economy, and then, in the second place, deduce the same results from considerations of symmetry applied to those modifications of the simple nest which are required by simple economy.

It is necessary here to premise a division of economy into two species, which we may denominate rational and sensible, or the

economy of forethought and simple economy; that which forestalls waste, and that which remedies waste or simply saves. The importance of this distinction will be apparent when, in the third place, we consider the two previous lines of argument in their relation to the faculties of instinct.

1. It is a proposition of elementary geometry that of all polygons or rectilinear plane figures with a given number of sides and a given perimeter, that figure contains the greatest area which is regular, or both equilateral and equiangular; and hence, that regular prisms have the greatest solid contents for a given convex surface. Again it is proved that a given perimeter encloses the greatest area in that regular polygon which has the greatest number of sides, so that among plane figures the circle has the greatest area for a given perimeter; and hence, also, the cylinder has the greatest solid contents among prismatic bodies for a given convex surface.

If now we seek among all regular polygons, or prisms, for those which are capable of dividing space into equal and similar parts without interstices!, we readily perceive that the angles of such a figure must be aliquot parts of the circle or of four right angles. All the angles of any such figure are equal to twice as many right angles as the figure has sides minus four right angles, or if a be the number of sides, the sum of all the angles is (2 n - 4) right angles; hence each angle of a regular figure must bear the ratio 2n -4/n to a right angle, and as 4 right angles must be divisible by each of these angles, we have 4n/2n-4, or 2n/n-2 = integer. But this number is equal to 2 + 4/n-2; hence (n - 2) must be a divisor of 4, that is, either 1, 2, or 4, and n must therefore be either 3, 4, or 6; so that triangular, quadrilateral, and hexagonal regular polygons and prisms are the only ones which can collectively fill space without interstices. Now of these the one which has the greatest

number of sides is the most economical. Hence the partition into regular hexagonal prisms is the most economical division of space in respect to two dimensions; but the third dimension is left undetermined.

If we suppose a hollow space, bounded by the surface of a regular hexagonal prism, to be open at one end, but closed at the other, so as to form a cell, it is clear that the base of this cell is most economized, if, like the sides, it be made also a boundary to another cell, or partially to several other cells. Hence, if two series of hexagonal cells, opening in opposite directions, have common bases, they present another feature of economy which is also exhibited in the form of the honeycomb. To this extent the bees’ economy was known to the ancients.

There are two forms in which the bases of the cells might be fashioned so as to fit them as bases also of the opposite cells in the comb. They might be either plane hexagons perpendicular to the sides of the cells, or be composed of three rhombs inclined to the sides of the cells, and forming a solid angle in the central line or axis of the cell. If in the first form all the bases be in the same plane the relative positions of cells on opposite sides of the comb are immaterial to economy. But as each angle of the regular hexagonal prism is 4/3 of a right angle, or 1/3 of the circle, three regular hexagonal prisms have one common comer or line of contact, and this common comer must, in the second form of the bases, be in the same line with the axis of an opposite cell, the base of which is therefore composed of three thirds of the three contiguous bases.

The dimensions of these rhombic segments of the bases vary with their inclinations to the sides and axes of the cells. One diagonal however is the same in position and length for all inclinations of the rhombs, while the other diagonal will vary with its inclination to the axis of the cell from the length of the shorter diagonal in the rhombs of a plane hexagonal base to any length whatever. This increase in the length of the variable diagonal increases the area of the rhombs, while the sides of the cells are more and more cut off and their area diminished as the rhombs become larger and more obliquely inclined.

In passing from the form of the plane hexagonal base, the sides at first diminish more rapidly than the rhombs increase, while the solid contents of the cell is the same for all the inclinations and corresponding forms of the rhombic segments of its base. It becomes a problem, therefore, of economy to determine that inclination and form of the rhombs which will give the least value to the sum of the areas in the sides and bases, or to the whole surface of the cell.

Instead of giving here the ordinary algebraic solution of this problem, which gives the same form to the rhombs as that determined by Maraldi's measurements of the honey-cell, we shall proceed . upon the second line of argument to deduce the same form from considerations of symmetry, and we will then prove by geometrical reasoning that this form is a minimum. We may remark here, however, that Maraldi determined by measurement, not merely the angles of the rhombs, but also a symmetry in the structure, which, as some geometricians have supposed, might have enabled him by calculation to give these angles, 109° 28' and 70° 32', with so great precision. The symmetry which Maraldi observed was the equality of the angles that the planes of the rhombs make with each other to the angle 120° which the sides of the cell make with each other, and also with the rhombs. This symmetry depends

directly on the regularity of all the solid angles in the cell, which Maraldi also pointed out. Indeed, if we regard only the angles which the planes make with each other, there is but one angle, 120°, in the whole structure. This one symmetry affords a perfect rule to the insect architect.

If we wish further to determine the angles which the lines make with each other, it is not necessary to make any direct measurements, but only to calculate the angles at the vertex of a triangular pyramid of which the sides make with each other the angle 120°. These angles are incommensurate in the circle, but in the triangle they are as simple as the angles 120° and 60°; for while the cosines of the latter are ± 1/2 the former angles and their supplements (approximately 109° and 71°) have cosines exactly ± 1/3; and as the trigonometrical measurement of angles is the most easy and natural, these angles are as easily constructed as the others.

2. But why, it may be asked, should the bees’ instinct prefer a structure, in which all the angles of the planes are 120°, to any other, unless this structure be also the most economical? That it is the most symmetrical structure of cells that can be imagined will be granted, in spite of its seeming complexity; but of what advantage is elegant symmetry to the bee, unless it also economizes labor and material? And what therefore could have fashioned the instinct of the bee except a supersensible principle of rational foresight, superior to mere sensible perception? In considering these questions let us look at the hive-cell from another point of view. Having built it up a priori from general principles, let us see in what relations it stands a posteriori to other cells.

We learn from naturalists that the cell is a species of nest or open cocoon, and that cocoons and nests are of two kinds, excavations and structures; but both kinds have these general characteristics of form. If closed, they are either spheres or cylindrical

figures with, hemispherical ends; and if open, they are either hemispheres or cylindrical figures open at one end and terminated at the other by hemispheres. The latter form of cocoon, nest, or cell is then the natural type of the honey-cell. When finished the cells resemble a series of excavations in wax, though in fact they are structures. That a single excavation in sand or wood—a cylindrical pit terminated spherically—has even less surface for the same contents than the honey-cell, has never excited remark on account perhaps of other and more obvious utilities in such a simple symmetrical form.

If a series of such excavations be made as closely together as possible, there would result an arrangement like that of a pile of equal cylinders, each pit surrounded by six other pits, and though the surface of each cell would be enlarged in a greater proportion than the enclosed space by changing the figures of the excavations, still space would be gained, and, in case of a structure, material would be saved, by converting the cylindrical cells into regular hexagonal prisms, (as may be seen in Fig. 2); and this too by simple saving, or by the economy of afterthought. Again, if equal spherical excavations be made as closely together as possible there would result an arrangement like that of a pile of equal spheres (Fig. 2), each cavity surrounded by six others in the same layer, and by three others in each of the contiguous layers,—in all, by twelve spherical cavities. The walls that would be left by removing

the superfluous material of the interspaces or comers would bound regular hexagonal prisms, terminated at both ends by pyramidal bases (Figs. 4,5), each of which would be composed of three rhombs of the same form as the rhombs of the honey-cell. If, therefore, we were to put into the cells of the honey-comb little spheres which would just fit them, and should press them to the bottoms of the cells on both sides of the comb, the spheres would touch the middle points of the rhombs and the middle lines of the sides, so that the sides and bases of the cells would be tangent planes to those points at which the spheres would touch each other but for the thickness of the intervening walls.

To prove this, let us consider two spheres in contact in two contiguous layers of a pile. It will be seen from Fig. 2 that the projections of the centres of two such spheres upon the ground plane are distant from each other by the length of a side of the circumscribed hexagon. If, therefore, in Fig. 3 we draw two vertical parallel lines, at the distance O M apart, equal to the side of the hexagon circumscribed around the circle O, then O and O′ upon these two lines, at a distance apart of twice the radius of the circle, will represent the positions of the centres of the two spheres in contiguous layers. A, bisecting O O′, is the point of contact of the two spheres, and B C, perpendicular to O O′, is tangent to the two spheres, and is the shorter axis of the tangent rhomb. But O O′, equal to P R or to twice the radius of the spheres,

is equal to the longer axis of the rhomb. Hence by drawing C O′ and B O we have a figure, G O B O′, of the same form as the tangent rhomb. If this figure were tinned around its shorter axis, B C, to a position perpendicular to the plane of the diagram, it would coincide with the tangent rhomb. Its dimensions can be readily computed.

If r denote the radius of the spheres or circles, then the side of the circumscribed hexagon is obviously r √4/3, and as O O′ = 2r we find O′ M =r √4/3. As the ratio of the axes of the rhomb is equal to the ratio of O′ M to O M or to √8/3 ÷ √4/2 = √2, we find B C = 2r/√2 = r √2. Hence the sides of the rhomb are equal to r √3/2. B M is therefore equal to r(√8/3- √3/2) = r √1/6 and the ratio of B M to B O is √1/6 ÷ √3/2 = 1/3, which is therefore the cosine of the angles of the rhomb. Hence these angles are the same as the angles in the rhombs of the honey-celL This may be shown still simpler, without computation, by observing after Maraldi, that the solid angles of the honey-cell are all regular, that is, composed of equal plane angles. The triangular ones, which are formed by the intersections of the three rhombs and by the intersection of each rhomb with two sides of the cell, have the common plane angle 109° 28′ nearly, while the quadrilateral solid angles formed by the intersection of two rhombs and two sides have the common plane angle 70° 32′ nearly (see Figs. 4, 5). Now as all the spheres which can be drawn tangent to all the sides of a regular solid angle must touch them in lines that bisect them, it follows that a sphere touching all the sides and rhombs of the honey-cell must touch the rhombs in the intersections of these bisecting lines or in their middle points, and the sides in their middle lines. In fine, the form of the honey-cell is that which would be obtained by placing equal spheres in two layers, as in Fig. 2, and drawing tangent planes through their points of contact, and terminating these planes in

their mutual intersections. These planes may be regarded, without reference to the contact of spheres, as planes midway between equidistant points in two parallel series. They would therefore pass through the intersections of such equal spheres as have radii greater than half the distance between their centres. Fig. 3 also represents portions of two sides of the cell turned up into the plane of the rhomb around the comers O B and O′ B. It also shows that the angle made by the plane of the rhomb, or by its shorter axis with the axis of the cell, is half the larger angle of the rhomb.

We have thus determined the form of the honey-cell from principles of symmetry alone. That this form is the most economical is easily shown by supposing it to vary, and by determining the changes of area in the sides and bases.

Let us suppose, as before, the rhomb C O B O' to be turned upon the axis B C by a right angle, so that the corners O and O' may fall in direction upon A, and let the sides that are attached be turned downward into their positions as vertical planes tangent to the sphere around O. In turning the rhomb now around its longer axis, the comers C and B must remain in the vertical lines C O and B O', so that the shorter axis is diminished if B is raised, and increased if B is depressed. Let i be the amount by which B is raised or depressed; then the projection of i upon the shorter axis B C of the rhomb is half of the amount by which this axis is made shorter or longer. The projection of i upon B C reduces it in the proportion of the semi-minor axis to the side of the rhomb or by the ratio r √½ ÷ r √3/2 hence the projection is i × √⅓. Half of this multiplied by the semi-major axis r is the change of area on each edge of the rhomb; hence the whole rhomb is decreased or increased by 2 r . i . √⅓. But ½ i multiplied by the breadth of the side of the cell is the corresponding change in each of the sides attached to the rhomb, and hence both sides together are increased or decreased by

i · r √4/3 = 2 r.i.√1/3. The sides gain as much therefore as the rhombs lose, or lose as much as the rhombs gain, by an infinitesimal change in their positions, and form; and the whole surface is therefore either a maximum or a minimum, while the contents of the cell is. unchanged by such a change of form.

Again, the infinitesimal triangles on either side of the line B C, resting on the bases i, are the amounts which the sides of the cell are made to gain or lose, while the smaller infinitesimal triangles on either side of B C, and resting on the projections of i, are the amounts which the edges of the rhombs lose or gain. These smaller triangles are in vanishing equal to half the larger ones, since the infinitely smaller right triangles resting upon i are similar to O' A B, the hypothenuse of which, O' B, homologous to i, is bisected by the line D E, and to this line the sides of the smaller infinitesimal triangles become parallel. If i be finite, the decrease of the minor axis of the rhomb will be less than twice the projection of i upon B C, and its increase will be more than twice this quantity; hence the rhomb will lose less than the sides gain, or gain more than the sides lose, by a finite change in the positions and form of the rhombs. The whole surface is therefore a minimum. Thus the symmetrical form of the honey-cell is seen to be also a minimum form.

This economy however has no reference to the depth of the cell, so that geometricians have conceived of a further limitation of the cell’s form, which is not observed by the bee. Having determined the most economical arrangement of the sides and bases, we may further limit the length and breadth of the sides to that ratio, which gives what has been called and determined as the minimum minimorum form of the cell. If A denote the whole area of the cell’s surface, C the whole solid contents, and l the length of the longer edges of the cell, or of those which terminate in the longer axes of the rhombs, (Figs. 4, 5,) and if, as before, we denote by r the radius of

the inscribed sphere or cylinder, then from the dimensions already computed we find
A = 2 r2 √2 + 4 lr √3, C = 2 r2 l√3.

If one of these be supposed constant and the other a minimum, their derivatives must both be equal to zero. Hence by differentiation and reduction we have the equations
r√2 + r Dr l√3 = 0, 2l + r Dr l =0,

from which, eliminating Dr l, we obtain l r√2/3. Hence, l in the minimum minimorum cell is half the distance O′ M between the two planes on which the centres of the contiguous inscribed spheres are arranged. This form of the honey-cell is therefore what the bee would fashion if, instead of its deep nests, it should construct hemispherical nests like the bird, and then convert them into polyhedral figures with sides tangent to the contiguous hemispheres on both sides of the comb. Two such cells would exactly enclose a sphere with tangent planes, as in Figs. 4, 5. Of all figures, therefore, which can divide space into equal and similar parts, without interstices, the polyhedrons of Figs. 4, 5 have the least surface for a given contents.

These figures are such as would be formed by drawing tangent planes through the twelve points of contact on a sphere surrounded by twelve equal spheres. The two forms arise from the two ways in which the three spheres, in each of the outside layers, may be arranged. It may be seen in Fig. 2 that the three superposed spheres occupy alternate interstices; so that there are two ways in which they may be placed in contact with the central one. If the three spheres, which are in contact with the central one from below, be opposite

the three superposed ones, we have the polyhedron of Fig. 5; if alternately disposed, we have that of Fig. 4, the sides of which are all equal and similar rhombs, like the rhombs of the honey-cell. Fig. 5 may be produced by turning the lower half of Fig. 4 one sixth of its circumference around its vertical axis.

Geometricians have also criticised the economy of the bee by computing the difference between the surface of cells with plane bases and the surface of honey-cells having the same contents; and by showing that this difference is only about 1/50 part of the whole surface of a completed cell; so that the bee is enabled by the pyramidal form of the base to make 51 completed cells, instead of 50, out of the same material,—a gain hardly worth so great precision in construction.

3. But this criticism would be just only on the suppositions, 1st, that a plane base could be more readily made than a pyramidal one, and 2dly, that the instinct of the bee is determined to a structure the most economical a priori and on the whole. These suppositions are not however necessary, nor are they supported by facts.

It is true, indeed, as we have seen, that tire form of the honey-cell requires less material than any similar one for the construction of a double series of cells like the honeycomb. But we have also seen that simple nests are bounded by still less surface than the honey-cell, in proportion to their contents, and that the deviation of the single honey-cell from the cylindrical nest with a hemispherical base does in fact increase the surface in a greater proportion than it increases the Enclosed space,—with a gain however of material when the cells are contiguous. As their bases are boundaries between

between cells on opposite sides of the comb, the pyramidal form would be possible as a modification of the hemisphere only in case of a close symmetrical arrangement of the opposite cells. But for such an arrangement,—of two series of spherical bases in closest contact, — a modification to the pyramidal form of the honey-cell is not merely the most economical, but also the simplest, and one perfectly analogous to the hexagonal modification of the sides.

That the cell ought to be regarded as such a modification of the simple nest by ample economy will be evident when we consider the mode of its construction. If the cells were excavated nests made in a costly material, they would by the closest arrangement and the removal of the interstitial material, receive through the agency of simple economy the hexagonal form of the honey-cell; but the bases of opposite cells could only by accident meet as they do in the honeycomb, and hence they would either retain, without reference to each, other, the hemispherical form, or be flattened to plane hexagonal bases. But the hive-bee does in fact build up its nests from their bases which are rudely fashioned at first on the edges of the comb in the form of little cavities at equal distances. On one side of the comb these cavities form by their depressions the interstitial elevations between the cavities of the other side; and hence the symmetrical arrangement of the two series of cells, and hence also the pyramidal form of the bases and their economy.

It has been observed that mechanical pressure alone is capable of changing the elongated cells of cellular tissues—as in the fruits and piths of some plants—into the polyhedral form of the honey-cell. This however is not the way in which the honey-cell is formed, for the bees fashion the corners of their cells as they build, by continual trimming and saving.

Again, the bee builds with great precision; indeed, the exactness of the structure is more surprising than its economy. But precision

is not required by economy at those limits of form which determine maxima and minima values; for these values are determined by the condition that they shall vary least by slight changes in the forms on which they depend. Symmetry, on the contrary, requires absolute precision and affords the means of effecting it. Thus, when the bee’s point of view is just over each one of the middle points of the rhombs it ought to be at the same distance, from all the nine places of the cell, and just opposite similar points of view in the nine contiguous cells. This symmetry affords a working guide to the bee as perfect as the regularity of the solid angles or the equality of all the angles made by the planes with each other.

It is true that these symmetries also determine the economy by which the honey-cell is characterized; so also does the still simpler symmetry of the cylindrical and hemispherical nest determine a still greater economy of work and surface in the architecture of innumerable other nest-building animals. But have psychologists, therefore, thought it necessary to regard the instincts of these animals as determined by supersensible properties of form, instead of that facility of construction and simple saving which are apparent to the senses?

Many deviations not only from the strictest economy, but also from symmetry, are observed in the honeycomb, and are required by the various sizes and uses of the cells.

In the normal form of the comb the triangular comers are formed by the meeting of four cells or by the intersection of six planes, three belonging to the bases and three to the sides; while the quadrilateral comers are formed by the meeting of six cells, or the intersection of twelve planes, six belonging to the bases and six to the sides. Now the bees very frequently in finishing their cells do not make these twelve planes meet in a common point, but connect them by a thirteenth very small plane, forming a tenth partition or

a fourth basal segment to two such cells on opposite sides of the comb as would otherwise only touch each other by a common comer. This supplementary basal segment is however perpendicular to the line which joins the symmetrical centres of the two cells, and is therefore easily included in the symmetries of the cell by the following considerations.

We have seen that if the lines joining equidistant points in two parallel planes be bisected by planes perpendicular to them, these planes terminating in their mutual intersections will form the corners of the honey-comb. Such lines of juncture form the edges of the regular tetrahedrons and octohedrons into which the space between the two planes may be divided; each tetrahedron surrounded by three octohedrons, and each octohedron by six tetrahedrons. The six planes that bisect the six edges of each tetrahedron meet in the centre of the figure and form four contiguous triangular comers. The twelve planes that bisect the twelve edges of each octohedron form in the centre of the figure six contiguous quadrilateral comers; and if in addition to these planes three be drawn midway between each pair of diagonal comers in the octohedron, they will also pass through the centre of the figure, but would be of no service as partition walls between these comers in a perfectly regular figure. If, however, the points in the parallel planes be not exactly equidistant, and the included figure vary from a regular octohedron, the twelve planes cannot at the same time bisect the edges of the figure and meet in the centre; and the bee accordingly, forced by this necessity, instead of making these planes meet in a common point, chooses to join them by another small one midway between two diagonal comers of the figure. Thus the bees separate the central points of their nests by planes midway between the centres of contiguous nests on the same side and on opposite sides of the comb, and also in irregular structures, by smaller planes

between the centres of such nests on opposite sides of the comb, as would otherwise only touch each other in a common quadrilateral comer. This way of remedying irregularities of structure shows conclusively that the bee’s instinct is chiefly governed by symmetries of partition instead of those that belong to any particular figure.

Though it is to be presumed from what we have seen, that special facilities and economies of labor and material govern all abnormal forms, yet habit, undoubtedly, must greatly modify them from special adaptations to general conformities of structure.

The symmetries which we have studied are obviously not the same to the bee and to the geometrician, for what the latter comprehends abstractly as symmetry of form, is only perceptible to the former concretely, as facility of construction. Like the two kinds of .economy, the one is rational, the other sensible.

An unreflective and unforeseeing economy, which, without reference to an end, simply saves, through sensuous preference, what the conditions of life render useful and costly to the race, characterizes the whole animal kingdom. For even those animals which do not store food or build structures for themselves or their offspring, still select through sensuous preference the food that is nutritious and appropriate to them, without foreseeing its use. An application of such a simple saving to the typical structure of the nest results in the honey-cell. The bee’s instinct ought not therefore to be regarded as an exception to animal instincts in general; much less ought animal instincts in general to be so interpreted as to include a misconception of the bee’s instinct.

A natural choice from simple feelings and from heritable sensuous associations — empirical in form, whatever their origin—is all that is required to account for the most perfect work of instinct.

A Manual of Spherical and Practical Astronomy. [Review of William Chavaunet, A Manual of Spherical and Practical Astronomy. North American Review 98.2 (April 1864): 611-612.] ¹¹

By William Chauvenet, LL. D., Chancellor of Washington University, St. Louis, Mo. Philadelphia: J. B. Lippincott &Co.

This work of Professor Chauvenet will hold a high place among the works of American astronomers. Admirably adapted to the wants of American students, whose access to astronomical libraries and to memoirs in foreign languages is necessarily very limited, this work contains a fuller discussion of a greater number of problems in the sciences of astronomical observation and calculation, than have ever before been presented in a connected form in any language; and it cannot fail to be of the greatest service in stimulating to increased activity the astronomical talent of this country.

In all the mechanical appliances of astronomy we have availed ourselves of the best work of the age, and in the invention of instruments and methods of observation have even won applause from European astronomers; while in that skill of workmanship which is competent to the construction of the finest instruments, our countrymen have latterly begun to rival European artists. During the last thirty years, more than twenty observatories — several of the first class — have been erected and equipped in this country, and many valuable astronomical publications, in annals, memoirs, and journals, prove the industry of our scholars. The patronage of Congress, in establishing the National Observatory, in perfecting our admirably conducted Coast Survey, and in the publication of the American Ephemeris and Nautical Almanac, attests the interest of our people in this — we might almost say — our favorite national science.

Scholarship in this science has not, however, been so successfully cultivated among us as the inferior kinds of skill, and few of our countrymen have been able to make available to our students the best thoughts —the labors of genius —in the higher branches of the science. We ought, therefore, to welcome such services as Professor Chauvenet has performed for us with the greater satisfaction.

In the work upon Plane and Spherical Trigonometry, by Professor Chauvenet, published in 1850, embracing the latest improvements and most elegant theorems of that branch of mathematics, we had an assurance of the ability which the present work demanded, and of that fidelity which has in the present work given us, in a most luminous and accessible form, the improvements in the trigonometrical methods of astronomy which we owe to the great German astronomers of the present century.

But besides the scholarly labor of compiling this material, Professor Chauvenet has given us in his first volume evidence of no ordinary originality, in several new methods of treating problems in Spherical Astronomy. This is shown in his treatment of the problems of Eclipses and Occultations, and in several problems relating to Navigation.

An Appendix to the second volume contains an exposition of the Method of Least Squares, — that numerical method of dealing with the values of observed quantities, by which, in modern physical inquiries, the accidental errors of many observations are made to cancel each other in the final results. This method is here for the first time presented to American students with full and clear explanations, and with such exemplifications as make evident the value of this important instrument of physical research.

Review of Correlation and Conservation of Forces [From North American Review 100.2 (April 1865): 619-622.] ¹²

The Correlation and Conservation of Forces: a Series of Expositions, by Prof. Grove, Prof. Helmholtz, Dr. Mayer, Dr. Faraday, Prof. Liebig, and Dr. Carpenter; with an Introduction and brief Biographical Notices of the chief Promoters of the New Views. By Edward L. Youmans, M. D. New York: D. Appleton &Co. 1865. 12mo. pp. xlii., 438.

The essays collected in this volume have already an established reputation as summary expositions of the most interesting and instructive results of modern physical researches; and Dr. Youmans has done a great service to the American public, in presenting it with selections so well chosen and in such compact and readable shape.

That Dr. Youmans has great skill in book-making appears both in the present volume and in his recently published class-book of Chemistry. In the latter he has incorporated modern ideas of physical science with an apparently distinct apprehension of their true range and value. But this is strangely at variance with the vague talk with which he introduces these essays. It is unfortunate that the impression this Introduction is calculated to make about the scope and character of the essays should be allowed to prepossess the mind of the reader.

Dr. Youmans speaks of the general subject of these essays as “a new philosophy” and as “the new doctrine of force.” But the emphatic part of the general doctrine is not about the nature of force

as an entity or a causal agency, but about the quantitative elements and relations in those general orders of succession in physical phenomena which are manifested in motions. The word “force” is used only for a convenience, and by most of the writers with the same careful limitation and separation from any substantive signification as in mathematical mechanics. Dr. Mayer says: —

“The exact sciences are concerned with phenomena and measurable quantities. The first cause of things is Deity, — a being ever inscrutable by the intellect of man; while ‘higher causes,’ ‘supersensuous forces,’ and the rest, with all their consequences, belong to the delusive middle region of naturalistic philosophy and mysticism.”

The other essayists hold similar views, and disconnect the objects of scientific inquiry from those of religious thought and feeling. But their editor, occupying that “delusive middle region of naturalistic philosophy” which Dr. Mayer describes, and without heeding his warning, speaks of the progress which these essays are designed to illustrate, as showing a tendency “ever from the material toward the abstract, the ideal, the spiritual.” He confounds the scientific distinction between concrete material objects and abstract formal relations, with the philosophical distinction between the material and the spiritual, and illustrates what he understands by materialism, by instancing the crude devices of ancient astronomy.

“At length,” he says, “the labors of astronomers, terminating with Newton, struck away these crude devices, and substituted the action of a universal immaterial force. The course of astronomic science has thus been on a large scale to withdraw attention from the material and sensible, and to fix it upon the invisible and supersensuous. It has shown that a pure principle forms the immaterial foundation of the universe. From the baldest materiality we rise at last to a truth of the spiritual world, of so exalted an order that it has been said ‘to connect the mind of man with the Spirit of God.’

“The tendency thus illustrated by astronomy is characteristic in a marked degree of all modern science. Scientific inquiries are becoming less and less questions of matter, and more and more questions of force; material ideas are giving place to dynamical ideas.”

The editor speaks throughout this essay as if he were publishing a new Gospel of Force, according to Grove, Helmholtz, Mayer, Faraday, and others, — a design which no one would more earnestly reprobate than these distinguished physicists. Nothing can be conceived more erroneous than presenting these remarkable essays as illustrations and proofs of Mr. Herbert Spencer’s dynamism. The editor may honestly admire Mr. Spencer’s vagaries, but it is difficult to conceive how any

one with the scientific attainments which Dr. Youmans’s books exhibit, can have undesignedly so misrepresented the character of the writings he has here collected.

Modern science uses the words “force” and “cause” always under protest, and not to express any substantive object of scientific research. The are used to avoid paraphrase, and to express in each particular case that part of a series of related phenomena which, for some scientific reason, is to be separately considered; and they generally comprise those antecedent conditions of any phenomenon which bring it into the most extensive rational connection with other and more general phenomena. Professor Grove says of causes: —

“The common error, if I am right in supposing it to be such, consists in the abstraction of cause, and in supposing in each case a general secondary cause, — a something which is not the first cause, but which, if we examine it carefully, must have all the attributes of a first cause, and an existence independent of and dominant over matter.”

Of forces he says: —

“Do we know more of the phenomenon, viewed without reference to other phenomena, by saying it is produced by force? Certainly not. All we know or see is the effect; we do not see force, — we see motion or moving matter.”

Scientific ideas of cause and force are the same as those of the Positive Philosophy, though they are not derived from this source; the Positive Philosophy being itself derived from a one-sided attention to the ideas of modern science.

Dr. Mayer uses “force” and “phenomenon,” not as antithetical, but as species and genus. He divides phenomena into two species, “forces” and “properties.” Properties are unchangeable phenomena; forces are convertible phenomena, but convertible according to unchangeable laws, through balanced and correlated processes. The “indestructibility of matter” and “the conservation of force” mean in science only that certain measurable properties of matter persist unchanged throughout all natural changes, and that forces or convertible phenomena are so related that no changes can affect the measures according to which these forces are mutually convertible. Both these doctrines are concerned with measurable phenomena, and have nothing to do with the vague “matter” and “force” of naturalistic philosophy. There is nothing of an a priori or philosophic character about them.

If there be anything which should be credited exclusively to empirical science it is the establishment of these doctrines, which have only a superficial resemblance to anything which speculative philosophy has ever excogitated. Nevertheless Dr. Youmans, who ought to have known better, claims for Mr. Herbert Spencer

“the honor of crowning this sublime inquiry by showing that the law of the conservation, or as he prefers to term it ‘the Persistence of Force,’ as it is the underlying principle of all being, is also the fundamental truth of all philosophy. With masterly analytic skill he has shown that this principle, of which the human mind has just become fully conscious, is itself the profoundest law of the human mind, the deepest foundation of consciousness. He has demonstrated that the law of the Persistence of Force, of which the most piercing intellects of past times had but partial and unsatisfying glimpses, and which the latest scientific research has disclosed as a great principle of nature, has a yet more transcendent character; is, in fact, an a priori truth of the highest order, — a truth which is necessarily involved in our mental organization, which is broader than any possible induction, and of higher validity than any other truth whatever.”

The extravagant absurdity of this claim is only surpassed by that of Mr. Spencer’s pretensions, who is quoted as follows: —

“We might, indeed, be certain, even in the absence of any such analysis as the foregoing, that there must exist some principle which, as being the basis of science, cannot be established by science. All reasoned out conclusions whatever must rest on some postulate. As before shown, we cannot go on, merging derivative truths in these wider and wider truths from which they are derived, without reaching at last a widest truth, which can be merged in no other or derived from no other. And whoever contemplates the relation in which it stands to the truths of science in general will see that this truth, transcending demonstration, is the Persistence of Force. . . . . Such, then, is the foundation of any possible system of positive knowledge. Deeper than demonstration, deeper even than definite cognition, deep as the very nature of mind, is the postulate at which we have arrived.”

Mr. Spencer’s “Persistence of Force” may be deeper than definite cognition, — indeed, we have found it so; but the law of the conservation of force is essentially comprehensible and definite. It is exclusively concerned with the phenomenal and the measurable; and though it has not yet been demonstrated with mathematical certainty as a universal law of nature, yet experiment has rendered its universality so probable that no reasonable doubt of it remains in the minds of physicists.

The introductory remarks of Professor Grove’s essay on “the Correlation of Physical Forces,” contain an excellent discussion of the scientific use of the words “cause” and “force,” and may serve to correct the false impressions which the reader will get from the editor’s Introduction.

Review of Bowen’s Logic. [From North American Review 99.2 (October 1865): 592-605.] ¹³
4. — A Treatise on Logic, or the Laws of Pure Thought; comprising both the Aristotelic and Hamiltonian Analyses of Logical Forms, and some Chapters of Applied Logic. By Francis Bowen, Alford Professor of Moral Philosophy in Harvard College. Cambridge: Sever and Francis. 1864. pp. xv., 450.

The publication, a few years ago, of Hamilton’s Lectures on Logic, with an Appendix containing various papers, in which his new views

on logical forms were developed, placed before the students of this science the best materials, new and old, which the genius and scholarship of the author had collected during twenty years of study and reflection, and as the fruits of a discussion which has associated his name as closely with the science of Logic as that of its great founder, Aristotle. Though we had already a foretaste of these novelties of the science in Mr. Baynes’s New Analytic of Logical Forms, and in Dr. Thomson’s excellent little treatise on the Laws of Thought, yet the great superiority of these Lectures over any work on pure Logic which had appeared in the English language gave them at once a prominent place among books of instruction, in spite of the great defects incident to a posthumous publication of writings not intended for such use, nor especially adapted to the purposes of a text-book in the instruction of classes.

To secure the excellences of these Lectures, as well as of other modern treatises, and at the same time to present their materials in a more systematic form, and within a compass convenient for a textbook, appears to have been the aim of Professor Bowen in the preparation of his treatise. In performing this important service to the study of Logic, Professor Bowen has gone over the ground of the science as it now exists in the best modern treatises. In what is by far the most important and original feature of his book, the parallel presentations of the old and new analyses of the logical elements and forms, under each of the several divisions of the subject, our author exhibits the fruits of a diligent and careful study, and we owe him much for the lucid expositions he has given of this part of the science. That skill in clear and forcible exposition which his previous writings evince is in this book turned to the best account, on subjects in which it is especially serviceable.

When we consider the unsettled state in which modern discussions of the principles and forms of Logic have left the science, and the interest which has thus been created in controverted points, at the expense of the integrity of the science, we cannot too much admire the judiciousness of the plan the author has pursued, by which he has been enabled, to include so many interesting topics under a regular and systematic development of the subject. He has, of course, assumed the position of a liberal conservatism, assenting to what the friends of the scholastic system still agree upon, and presenting in a fair and impartial manner their different views, but dissenting from views which are hostile to the science in its essential features.

The introduction of cognate terms front different authors is happily done in several instances; thus, in the use of the terms “connote” and

“denote,” which Mr. Mill revived from the usages of the schoolmen to designate the two functions of names, and in the use of the derivative terms “connotation” and “denotation” as synonymes of the “intension” or “comprehension” and the “extension” of concepts, — terms in more general use, — he has added clearness by regarding the same distinction under slightly different points of view. His treatment of the important distinction of the two quantities of concepts is, in all its applications, especially happy.

As an illustration of the unsettled state in which the science of Logic remains, we will instance the great diversity of opinion which still obtains among writers on Logic in regard to so fundamental a matter as the proper meaning of the word “inference.” While such writers as Mr. Mill would include in the meaning of the word “inference” the real force of an argument, or that which really determines belief in its conclusion, writers who follow more closely the scholastic system of Logic would confine this meaning to what they term the formal validity of an argument, or that which constitutes a truly logical procedure. But on this point there is still a want of harmony, for the advocates of the scholastic system do not agree among themselves as to what constitutes the proper distinction between a logical and a grammatical transformation of a proposition, or as to what kinds of verbal changes in a proposition should be regarded as changing its logical import or meaning. This dissension exists in respect to those inferences which are called “immediate,” in which a single proposition is supposed to be the proof of another with a different formal or logical import. The various kinds of immediate inference are all rejected by the modern or inductive school of Logic, on the ground that what, even in thought, can really determine belief in the derived proposition must be identical with what can render the original proposition credible, so that the two propositions should be regarded as identical in relation to proof. But such inferences, or some of them, are still regarded by the school logicians as having some logical value. They all agree that an interchange of subject and predicate, or a conversion, and a change of “quantity” in the terms of a proposition, are changes of meaning sufficiently important to be regarded as logical transformations, while some are disposed to regard a change of “quality” in a proposition effected by infinitating its terms, or by the double negative, as only a verbal or grammatical change. The latter appears to be the opinion of Hamilton, though not of our author. A form of immediate inference, called inference by æquipollence or infinitation, which, according to Hamilton, is of mere grammatical relevancy, is introduced with a development due to Mr. De Morgan. We cannot but regard one phase of this development

as at least a redundancy in the enumeration of simple forms of inference; tor whatever may be thought of the logical value of the double negative, a union of it with inference by simple conversion ought not to be regarded as a simple inference, even supposing it to be more than a mixture of a logical with a grammatical transformation of a proposition. Thus, to infer from “All metals are fusible,” that “All infusible substances are unmetallic,” is equivalent to “No metals are infusible” by the double negative, and hence, by simple conversion, “No infusible substances are metallic,” and lastly, by the double negative again, “All infusible substances are unmetallic.” This process may be summed up, it is true, in a single rule, which may be derived directly from logical axioms; but since it is resolvable into elementary steps, which are also given, it should not be regarded as an elementary form of inference. And we may repeat, that it should not be regarded as a proper form of inference at all, if we define logical inference, according to the inductive school, to be a relation between real grounds of belief and the proposition to be proved, formally exhibited or explicated in a reasoning. According to this definition, a reasoning indicates, but does not contain, proof, —just as a name, or its mental counterpart, a concept, indicates, but does not contain, the evidence of the coexistence of the attributes connoted by it, or of the resemblance of the things which it denotes; and just as a proposition indicates, but does not contain, the ampliative experience by which significance is added to what is already collected in the mind through the instrumentality of language.

This leads us at once to the consideration of the criticism on the mediate or syllogistic inference of the logic-books, by which modern writers have brought in question the very foundations of the science,— namely, the criticism that all syllogisms involve a petitio principii, since the truth of the premises presupposes the truth of the conclusion, and that nothing can be proved by referring a case to a rule (as is done in the syllogism), since the rule is not true unless what is supposed to follow from it is also true. Our author follows Sir William Hamilton in thinking that the analytic arrangement of the syllogism, in which, instead of the premises followed by the conclusion, the more natural order is observed, — the quæsitum or proposition in question being propounded, and the reasons made to follow, — “effectually relieves the syllogism of the imputation which has been thrown upon it for more than three centuries of being founded upon a mere petitio principii, or a begging of the question”; and this, forsooth, because “we appeal to the admitted universal truth only after we have established, what is the main point of the argument, the applicability of the truth” to the case in question. As, for example, when we argue, “Socrates is mortal, because

he is a man, and all men are mortal.” But we conceive that the more natural order of the syllogism is relieved of this imputation only in so far as it exhibits better than the synthetic order the true function of formal inference, — namely, its indication of the ground of real inference. It amounts to the same whether we virtually assume in a premise, or virtually reaffirm in a reason, the proposition we wish to prove. If the illative value of the syllogism resides in itself, then truth is nothing but verbal consistency, whatever be the order of the consistent parts. Nor does the relative importance of the premises or reasons in an argument affect this point. It is doubtless true that in most arguments the minor premise, by which a question is referred to a rule, is the one requiring emphasis, and, indeed, is the only one for which, in general, there is any need of explicit statement; nevertheless, its true function is to indicate the existence of a general rule, and, through this general rule, to indicate the existence of cases parallel to the case in question, — cases from which the rule may be justly inferred, along with the case in question. And this is the whole argument in a syllogism. It is not merely an explication of propositions, but is much more nearly what Mr. Mill describes as an interpretation of a rule to meet a case in question, though we think this description to be defective on several accounts. In the first place, it gives too great prominence, in the formal process, to the major premise, which, as our author justly thinks, is not the most emphatic part of the syllogism. In the second place, the inquiry, or the search, which leads to the discovery of an argument in answer to the question, “Why or for what reason is a given proposition true?” refers as much to the discovery of a rule through which it may be verified as to the interpretation of the rule when found, so that an argument answers, — to use Mr. Mill’s illustration, — not simply how the short-hand record of experience, the general rule, applies to the case in question, but what particular record is applicable to the case. In other words, the formal process conducts us at the same time to the discovery and the interpretation of the major premise through the minor. But the gist of the objection to the syllogism, which Mr. Mill has discussed with the greatest fairness, is, that what is expressed in the syllogism is not the whole of the process of real inference; what justifies the rule or major premise being an integrant part of the whole inference, and, indeed, the most essential part. So far from having “laboriously attempted to restrict the range, and depreciate the utility, of the syllogistic process,” as our author accuses Mr. Mill, among others, with having done, he has done much, we think, to determine its true range, and to appreciate its real utility.

It is obvious, from what has been said, that the two propositions of a so-called immediate inference should not be regarded as constituting an argument or proof proper, since neither serves to indicate more distinctly than the other the real ground on which both must be received or rejected together. It may be questioned, however, whether there are not some cases where an immediate inference will have a real validity; as when in inferring a particular proposition from a universal one in the same terms, we argue, “This cloud is composed of vapor, because all clouds are composed of vapor.” For we exclude the possible supposition that some clouds are composed of smoke or some other substance, and base the particular proposition on evidence which might not be essential to it. There is an apparent inference sometimes in these transformations, since the simpler grammatical structure indicates more clearly than the more complex one the real meaning of both, and through this the real grounds of both, so far as the meaning of a proposition can reveal the grounds of its truth or falsity. But in all true arguments a case is brought under a rule, and through the rule is brought under the evidence or authority which the rule represents; and this is oftenest effected without an explicit announcement, or even an explicit thought of the rule itself.

What words are to our first apprehensions of things, such are general propositions to that ampliative experience by which our knowledge of things is perfected, and as a word is assumed to stand equally for everything denoted by it, so a general proposition, framed of words, is assumed to hold equally for every case included under its signification, whether in actual or in possible experience. These assumptions give to words and propositions their formal value. The appeal that is made through them is not to the sum of actual experiences merely, but to the assumed universal validity of these experiences. Independently of these assumptions the knowledge we embody in language is ideal only, and truth is only consistency in thought and language. And this leads us to the consideration of the much-mooted questions, the grounds of induction and analogy and the origin of necessary truths. These questions are regarded by the followers of scholastic logic as extra-logical, and are treated in a supplement to the formal science under what is improperly called Applied Logic. As affecting real inference, they are properly regarded by the modern inductive school of logic as integrant parts of the science itself. “Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition?” asks Mr. Mill; and he adds, that “Whoever can answer this question

knows more of the philosophy of logic than the wisest of the ancients, and has solved the great problem of induction.” Overlooking this important question, or rather answering it after the manner of metaphysicians, by stating the facts to be explained in language which implies that they are ultimate and inexplicable, the school logicians, and among them our author, content themselves with dividing all universal propositions into two classes, — the so-called necessary truths, and the contingent or empirical truths. The former are those which require but one observation for their induction, and no experience at all, according to these writers, for their verification. With the latter or contingent truths logic proper, they say, is not concerned. These belong to the matter, and not to the form of thought; and this is also true, they admit, of the greater number of necessary truths; yet, as these are referred, not to vulgar experience, but to a special power of the mind, assumed for the purpose,—namely, the reason, nous, or locus principiorum,—they are of sufficient dignity to claim attention from philosophers. Such philosophers lump together all the degrees of certainty in experimental science, and patronizingly lend an a priori principle to eke out any deficiency in that demonstrative certainty on which they take their stand. To the vulgar empiricist there is no greater certainty than what the sum total of experience, inductive and ratiocinative, can afford; but as there are some truths in science so elementary and so incessantly presented that their contradictories cannot be represented in imagination or conceived in the understanding as possibly true, the empiricist is constrained to rise occasionally to the heights of certainty, whence, according to the logicians, all truth is derived.

Instead of dividing universal truths into the two great classes we have mentioned, a more fundamental analysis would, we conceive, establish many grades of certainty, according to the character of the evidence and the range of our experience. The determination of what we may call the inductive weights of experiments and observations — to borrow a technical term from the mathematical theory of probabilities — depends on a preliminary induction which in fact has already been performed, perhaps involuntarily and unconsciously, by every experienced mind. These inductive weights have in common the one universal presumption, that the course of nature is uniform, which is more formally explicated in what we may call, by way of distinction, the phenomenal Law of Causation, in order to discriminate it from the ontological Principle of Causality, which is quite a different matter. The presumption expressed in the Law of Causation, that all precisely similar antecedents must be followed by precisely similar consequents, should not be confounded with the Principle that nothing can be conceived

to begin to exist, or as having a really new and independent existence. The Principle of Causality is probably nothing else than a succinct but indirect statement of the history and character of all knowledge, or of the fact that everything is known along with, or as proceeding out of, something else, which in a vague and general sense is called its cause; so that we have no experience of, and no ground for representing, anything without a cause. But the character of this cause need not necessarily be that defined in the Law of Causation. And indeed this law does not possess the universal credibility or the character of necessity in thought, which belongs to the Principle of Causality. Whatever certainty the law does possess is regarded by our author as derived from this principle. The law doubtless implies the principle, but its characteristic significance, the uniformity of nature and experience, can hardly be regarded as certified by a necessary principle, unless we are prepared to admit that the law itself is also a necessary truth. The author says, “It is only necessary to show that the Law [Principle] of Causality is readily and naturally explicated into the maxim that nature’s course is uniform, so that the absolute and imperative conviction which belongs to the former as an a priori cognition of the human mind is transferred, by an easy association of ideas, to the latter, though not logically belonging to it.” The author is here obviously steering between Scylla and Charybdis. In shunning empiricism he fears to fall into fatalism. It is a new logic to us, which can explicate a maxim out of a necessary principle to which it does not logically belong; or can retain an imperative conviction in the reason and withhold it from the consequent, or transfer it only “by an easy association of ideas.” If the author is attempting to explain rather than justify the belief in the uniformity of nature, we have no grave objections, except to the phraseology of his argument, though we see no necessity for appealing to an a priori principle to account for belief in an empirical fact. Either the Principle of Causality does, or does not, prove the Law of Causation. If it does, our author is swallowed up in the yawning gulf of fatalism, and he has proved the “astounding theory,” which he quotes, in his chapter of Fallacies, from Mr. Mill, the confutation of which, he says, “is the business of the metaphysician or the theologian.” The following is the conclusion of the obnoxious passage from Mill: “The state of the whole universe at any instant we believe to be the consequent of its state at the previous instant; insomuch, that one who knew all the agents which exist at the present moment, their collocation in space, and their properties, —in other words, the laws of their agency, — could predict the whole subsequent history of the universe, at least unless some new volition of a power capable of controlling the universe should supervene.” ¹⁴ But if the Principle of Causality does not prove the Law of Causation, then the uniformity of nature must be regarded as a generalization from experience, and our author is lost in the equally obnoxious doctrine of empiricism. Independently of inductive evidence, however, this law has a formal or regulative value like that of words and general propositions. If not a universal fact, it is at least true of all we can properly learn about facts. All else is chaos. It is true as far as we know. All the evidence is for it, and of the evidence against it we are ignorant. The empiricist acknowledges his helplessness against arbitrary doubt, except in those inveterate cases where habit or primitive association in ideas is too strong to allow it. In these cases he is as resolute as the dogmatist, but his strength is the force of inertia.

Too little regard is paid, in treating of Induction and Analogy in logic-books, to what we have denominated the inductive weight of an experiment or observation. This constitutes a limitation to the general presumption of uniformity in Nature, and is of an a priori character relatively to the particular matter under investigation, but is derivable by induction and ratiocination from our experience of our liabilities to error in the given kind of matter. A single determination of the sum of two numbers by counting them together, will be regarded by any person experienced in numbers as a sufficient induction of the universality of the fact which such an experiment discloses; especially if the result be verified by any one of the many deductive processes by which the same result might be inferred. Such is the inductive weight of experiments in numbers. A physical or chemical experiment, performed with the precautions which experience has discovered, has nearly as great an inductive weight. The inductive weight in other branches of science, and in common observation, is rarely defined or definable, except in a rough way; but it is estimated and applied by all experienced observers with the same kind of subtle, unconscious sagacity which determines the bestowal of names in the formation of language.

One turns naturally to the chapter on Fallacies in the logic-books for the raciest portions of their rational festivities. Here the author descends from the lofty pure forms of thought and the contemplation of second intentions, to deal with embodied materialized forms of thought, the time-honored tricks of the dialectic art, or with the novelties of recent heresies. What the opinions of the Calvinist ministers were to the Port-Royalist logicians, such appear to be the heresies of modern theories of Natural History to our author, who essays to entrap his antagonists within the lines of pure thought, and in the very citadel of demonstration. He has managed somehow (we do not clearly understand how) to bring Mr. Darwin’s theory of “The Origin of

Species by Natural Selection” under “the Fallacy of the Composite and Divisive Sense,” but in the process a singular definition occurs: “We are often misled by the use of the word tendency. We rightly say that a given result tends to happen only when there is more than an even chance of its occurrence; if there is less than an even chance, it tends not to happen.” The application of this definition to the doctrine of the derivationists, that there is a tendency to variation in the specific characters of organic races, is obvious and fatal, because the cases of variation are greatly in the minority. But the destructive power of the definition does not stop here. The conviction we have entertained from our youth, that stones tend to roll down hill, and that the loose materials of the earth’s surface tend by every practicable route to approach nearer to the centre of the earth, must be materially modified if the definition we have quoted always holds. For the occasions of stones rolling down hill, or the occurrence of land-slides, are rather infrequent and exceptional phenomena, and cannot, therefore, according to our author, tend to happen. The existence of permanent conditions, which, if not contravened by other causes, will be constantly followed by a given result, constitutes what, in accordance with scientific usage, we should denominate a tendency, Archbishop Whately says, in treating of Ambiguous Terms, “By a tendency towards a certain result is sometimes meant, the existence of a cause which, if operating unimpeded, would produce that result.” The tendency, for example, of individual characters in animals and plants to become specific characters by inheritance. “But sometimes, again, a tendency towards a certain result is understood to mean, the existence of such a state of things that the result may be expected to take place.” The tendency, for example, in the opponents of the theory of derivation to misunderstand it. ¹⁵ and as the causes which may hinder a tendency from showing itself except in rare and occasional instances do not thereby destroy the tendency, so, on the other hand, the hypothesis of a tendency from the occasional occurrence of a phenomenon is not invalidated by the mere infrequency of the phenomenon. The real ground of induction in such cases is too subtle to be discussed under the coarse criteria of scholastic logic. And this is also true of another doctrine in natural science, which our author also burdens with a fallacy; namely, the fallacy of ignoratio elenchi, or “answering to the wrong point.” The uniformitarian school of geologists are guilty of this fallacy, the author thinks, when “they argue that the geological phenomena now visible, many of which are of stupendous magnitude, can be accounted for by the ordinary working of physical causes now in operation, if we only assign a sufficient lapse of time for the cumulation of their results,” etc. “Their ignoratio elenchi consists,” he adds, “in multiplying proofs that slow-working causes might have effected all these stupendous results, and then jumping at the conclusion that these causes did so produce them. They propound this dilemma: Accept this solution of the problem or propose a better one. We may logically decline to do either.” “An Elenchus” the author defines as “a syllogism which will confute the argument of your opponent, and ignoratio elenchi is ignorance of what will confute him, — ignorance of the fact that your conclusion, even if it were established, would not contradict his conclusion,” — and if the uniformitarians were really bent on confuting our author’s assumed logical indifference to geological theories, they might be found guilty of the fallacy. But in this the author himself ignores the point in question. The uniformitarians really adduce their arguments in confutation of the counter-arguments of those who believe that geological phenomena might have been produced by the purely hypothetical causes called Cataclysms, and then jump at the conclusion that such causes did produce them. Accept the cataclysm or propose a better solution, say the orthodox geologists, and the uniformitarians, instead of declining to do either, propose an hypothesis which more nearly accords with all that is really known of natural forces, but which demands an immense quantity of that very abundant element, Time, and as Red-Jacket said of those who complain that they haven’t time enough, “they have all there is.”

Mathematicians will be somewhat surprised to learn from the author’s chapter on the sources of evidence, etc., that “what is called ‘the Method of Least Squares ’ has been adopted as a mode of finding the most probable result, since it was ascertained that the arithmetical mean is not the best mean of a number of observed quantities [!]. This Method proceeds upon the assumption that all errors are not equally probable, but that small errors are more probable than large ones.” Now in all the treatises on this Method, it is shown to involve the principle of the rule of the arithmetical mean. Indeed, this Method is only an analytical device for computing the most probable values of such unknown quantities as are indirectly determined through the observation of other quantities on which they depend, and the most probable values in such cases — as in the cases to which the rule of the arithmetical mean is more directly applicable — are those which render the sum of the estimated errors of the observed quantities (the algebraic sum, of course) equal to zero. Or, what comes to the same, the sum of the squares of the estimated errors is required to be a minimum. This Method also gives certain conventional rules for estimating the degrees of probable accuracy in results so obtained. Our author has doubtless confounded the rule of the arithmetical mean with the method of the least absolute sum of the errors, which was used by Laplace,

and which the Method of Least Squares has superseded, with the greatest advantage to Practical Astronomy and Geodesy. But it is not easy to see why Applied Logic should take more notice of Least Squares than of the Logarithm or the Arabic system of numerals. We may add, that the rule of the arithmetical mean does not presuppose that the errors in observed quantities are all equally probable, but that any two of these quantities, considered by themselves, have an equal a priori probability of error. Considered in conjunction with the others, this probability is modified, and those observed quantities which differ least from the arithmetical mean of the whole set are regarded as the most correct, or as having probably the least error.

Among the many matters of thought through which our author has added an individual interest to his work is a doctrine almost exclusively his own, and already promulgated in his previously published writings, — namely, his doctrine of the mental constitution of the higher brute animals. Its logical interest is brought out in the Psychological Introduction of this work to illustrate the fundamental characteristics of Thought proper, the elementary operations of the Understanding, and the value of Language to that kind of knowledge it enables men to attain through its instrumentality. And the illustration is very clear and apt, provided the doctrine be admitted. Brutes not only have nothing equivalent to language proper, but they do not, according to our author, have even the elements of understanding; not a ray of true intelligence visits their darkened minds, — if mind that be which can perceive without abstracting, know without comparing, and effect what is tantamount to inference without generalizing. This theory, admitting many of the effects of abstract knowledge, denies all their known causes, and does so, we suppose, on the ground that brutes have a very imperfect comprehension of signs as such, and no proper command of them at all, and perhaps, also, because it is commendable to establish as broad a line of demarcation as possible between our intelligence and theirs. On the little logical capacity of these poor creatures our author says: “As they have only Intuitions, the only names which they can apply or understand are Proper Names, — the appellations of this or that particular, thing. These they can understand. A dog can easily be taught to know the name of his master, even when pronounced by another person. They can even be taught to know the names of particular places and buildings, so that they can understand and obey when they are told to go to the barn, the river, or the house. But it is always the particular barn, or other object, with which they have been taught to associate this sound or significant gesture as its proper name.” It would be interesting to inquire, in this connection, what happens when

one says “rat” to a terrier, or addresses the various words of command, “out,” “down,” “whoa,” and the like, to dogs and horses. Does the terrier think of the last particular victim of his sport, or the horse of his last particular act of stopping? And if so, why is the dog’s fancy apparently so filled with visions of the chase, and why does the horse stop again? That words and other signs have a generic power in all intelligences, though not always, in strict propriety, a generic significance, is a conclusion, we think, warranted by all the facts and analogies which bear upon the question. Significance is the proper attribute only of a sign cognized as such, or brought prominently under attention in its capacity as a sign, and not merely acting to direct the attention to what it suggests or reveals. The cognition of a sign, as such, involves a reversal of the natural order of association in mental acts. In our intuitions of sense, the sensations and impressions, which are the real signs of what they suggest, or direct the attention upon, are not cognized in themselves, — are not consciously cognized at all, in so far as they are significant, — but are as it were lost in the brighter light of that which they imply or reveal. The mind is unconscious of light while occupied with vision. To reverse this primitive order, to bring into equal or greater prominence in the attention that which directs attention to an object of thought, is to cognize a sign as such. But in this there is nothing added to the primitive powers of the understanding; there is rather an addition to the power of the attention. Comparison, abstraction, generalization, and even inference, depend on those fundamental laws of association common to all intelligences, through which resemblances and differences are cognized. Such acts must be relatively very imperfect when not “fixed and ratified by signs”; still the powers of understanding do not depend on language itself, but on the laws of mental association. Language is an efficient instrument of these powers, and that faculty of attention which renders it an available instrument is probably characteristic of the human mind, at least in the degree and perfection of its development.

To allow, then, that brutes can apply or understand proper names, while all cognizance of the generic power of names is denied them, is hardly a logical procedure; for Denomination is more essentially an act of clear and definite thought than Abstraction. The definition which Sir William Hamilton gives of the primum cognitum seems to us an apt description of the probable application of names in the brute intelligence. Such applications are probably “neither precisely general nor determinately individual, but vague and obscure.” A name may be applicable to all resembling objects, but will be applied on every occasion to some particular one, and may never rise to that indifferent

application to each and every one of the resembling objects which would constitute it the name of a class. For this reason it can hardly be regarded as a true name at all, even though it be applicable, like a proper name, to only one object; for in this case the sound of the word is associated with the single object in no other way than that which determines all other mental associations. But the same laws which would determine such an association would also associate the representations of resembling objects, and would direct the attention more or less definitely to their points of resemblance, and thus store the memory with generalized pictures of experience, from which would spontaneously flow such simple inferences as the actions of the higher brute animals seem, at least, to imply. And all this could take place without the instrumentality of language, or any distinct consciousness of signs, or of their significance as such.

Review of The American Ephermeris and Nautical Almanac for the Year 1867. [From North American Review 101.2 (July 1865): 134-146.] ¹⁶

Art. V. — The American Ephemeris and Nautical Almanac for the Year 1867. Published by Authority of the Secretary of the Navy. Bureau of Navigation, Washington. 1865.

This volume is the thirteenth of the series which was begun in 1852 by the publication of the Ephemeris for 1855. These publications were authorized by act of Congress in 1849, and the work was placed in charge of Admiral (then Lieutenant) C. H. Davis. With that zeal in the cause of science for which many officers of the United States Navy have been distinguished, Admiral Davis undertook the difficult task of giving the materials and form of this work such a value as should not only adapt it to the needs of the Navy, hitherto dependent on a foreign country for so important a part of its equipment, but should adapt the work also to the scientific wants of the country, and make it worthy to take the place of the British Nautical Almanac in our geographical surveys and in the numerous observatories which have been established in this country. By the aid of our most skilful astronomers, and especially through the co-operation of Professor Peirce and Mr. Sears C. Walker, the more serious difficulties were surmounted; fundamental tables were prepared from the best determined astronomical data, and a corps of computers was trained for the work.

To appreciate adequately the value of this important enterprise some account of the history and use of such publications will be of service.

The principal nations of Europe have for two centuries given public support to the cultivation of the science of astronomy, as well as of the art of navigation; and this support was the more earnestly and generously given, when it became evident, near the close of the seventeenth century, that the most refined and complete results of astronomical research could be made directly and in the highest degree serviceable to the needs of the navigator. The celebrated problem of finding the longitude at sea by astronomical means, arose from the insufficiency of the magnet for guiding the navigator with the requisite degree of certainty on the pathless sea. By astronomical determinations of latitude, and a careful observation of the course of the ship

by means of the magnet, and the rate of the ship’s sailing by means of the log, navigators had been able to estimate rudely their positions on the sea, and the relative positions of distant ports, headlands, and islands. But the insufficiency of these means, when the “dead-reckoning” was interrupted by storms or disturbed by sea-currents, was at all times aggravated by the uncertainty of the magnet itself, which points rarely to the exact north, and deviates in different parts of the earth’s surface by different amounts from the north, and varies in direction from time to time in the same locality. The laws of these variations have been carefully studied, yet at the present day less is known about the complex phenomena of magnetic variation than was then known (two centuries ago) about the complexities in those movements of the heavenly bodies which astronomers have since completely unravelled and reduced to calculation.

While astronomical observations afforded direct and simple means of determining the latitude of any place, and the distance in a north or south direction from one place to another on the earth’s surface, means were still wanting for independent determinations of longitude, and the distance from one place to another in an east or west direction. As the tables afforded means for determining the latitude and local time of any place by observations of the sun, it was seen that, if this local time could be compared with that of any fixed place of reference, the port of departure for example, then the problem of longitude would be solved. For this purpose sea-clocks, or chronometers, were invented, to be carried in the ship, and regulated to keep the time of the port of departure, or some standard meridian of longitude. But as these clocks could not be secured from the accidents and variations to which long voyages exposed them, their indications could hardly be trusted more than the use of the magnet in “dead-reckoning,” unless some means could be devised for testing and correcting them from time to time. To accomplish this end—to determine by astronomical means alone, at any time, and at any place on the earth’s surface, the local time of the standard meridian of longitude — has been the aim steadily pursued by practical astronomy down to the present time.

For this purpose the famous Royal Observatory was established

at Greenwich, and those illustrious observers, the Astronomers Royal, were in succession severally commissioned and expressly commanded each “to apply himself with the utmost care and diligence to the rectifying the tables of the motions of the heavens, and places of the fixed stars, in order to find out the so much desired longitude at sea, for the perfecting the art of navigation.”

The labors of the earlier Astronomers Royal, extending through nearly a century, were finally crowned with a partial success, and the celebrated Dr. Maskelyne devoted his genius and energy to making this success practically available to the art of navigation; and his efforts resulted in the establishment of the English Nautical Almanac, the first volume of which was published in 1766 for the following year.

The long-continued series of accurate observations and measurements made at the Greenwich Observatory have become so famous for their value to theoretical astronomy, have led to so many brilliant discoveries, and have been so long regarded as the common property of the scientific world, that the purpose for which this Observatory was primarily established by the eminently practical English nation — the perfecting the art of navigation — is almost lost sight of. This purpose was partially accomplished in the establishment of the English Nautical Almanac.

The tables which the Greenwich observations were designed to perfect were derived from those mathematical theories of the movements of the heavenly bodies which astronomers had elaborated from the whole course of observations from the earliest to the latest records, and had finally greatly improved and enlarged by the mathematical development of the Newtonian theory of gravitation. To adapt these theories to an accurate representation of the positions of the heavenly bodies observed from time to time, to embody them in tables for facilitating computation, and finally to predict from them future positions with sufficient accuracy for nautical purposes, were the problems of nautical astronomy.

From such predicted positions, made for equal intervals of time, and arranged in tables called ephemerides, all other astronomical predictions are derived; such as eclipses of the sun

and moon, the occultations of the stars by the moon, the passages of any heavenly body over the meridian of any place, the apparent distances of the moon from other luminaries, and many other phenomena useful to the navigator, the surveyor, and the astronomer.

Such ephemerides, or tables of position, predicted several years in advance for the sun, the moon, the planets, and the principal fixed stars, together with the “lunar distances,” and such special phenomena as are of chief use or interest, form the principal contents of a nautical almanac, and their value to the navigator or astronomer depends entirely on the accuracy of the tables from which they are derived.

As the moon moves with a comparatively great rapidity among the stars, its constantly varying relative positions are used as time-signals, predicted beforehand and observed by the navigator or astronomer in the various forms of lunar distances, occultations, eclipses, and meridian transits or culminations. Accurate tables of the moon are thus of primary importance in the construction of a nautical almanac for the solution of the problem of longitude, and nearly a century elapsed from the first proposal of the problem before lunar tables of sufficient accuracy were produced.

Such, however, has been the subsequent progress of astronomy, that the lunar tables now used in the construction of the American Ephemeris, as well as those now employed in Europe, have more than twenty times the accuracy attained in those which were first used for the British Almanac. At first, the navigator was fortunate if he determined his position at sea within one degree of longitude, or sixty nautical miles. With his present facilities, he can fail to determine his position within three miles only by the imperfection of his instruments, or by errors in their use.

This surprising progress in astronomy, for which the present century is especially distinguished, is in great measure due to the continuous publication of the British Nautical Almanac, and of similar works on the continent of Europe. For, important as the Almanac was to the navigator, and indispensable as it soon became, it was quite as useful to the astronomer. Not only was the observer saved much labor and watching by the

predictions in the pages of the Almanac of the phenomena to be observed, but sources of error, both in theory and in observation, were easily detected, and improvements in astronomical tables greatly facilitated. It was by comparing the. observed places of the planet Uranus with its predicted places in the Almanac, that those discrepancies were noticed which guided astronomers to the discovery of the new planet Neptune on the confines of the solar system, whose influence on the motions of the planet Uranus betrayed its existence, and led to its discovery. In this, and in many other ways, the Nautical Almanac repaid the debt it owed the astronomer, and received again new and improved means of usefulness; thus serving at once the noblest of the sciences and the most useful of the arts. No ship at sea and no astronomical observatory can dispense with the Nautical Almanac. The numberless minor observatories in Europe and America complete their equipment with it, and become serviceable to the progress of astronomy, with its aid. All geographical and nautical surveys require its use, and depend for their value on its accuracy.

A few years before the establishment of the Observatory at Greenwich, the French government founded the Royal Observatory at Paris, and a few years later, 1679, the publication of the French Almanac, the Connaissance des Temps, was begun, at first, under the direction of the French Academy of Sciences, but afterwards, when its utility to navigation became a prominent object, it was placed under the direction of the Bureau des Longitudes. Several other European states have, from time to time, established and continue the publication of almanacs and ephemerides, both in connection with public observatories and for use at sea, — namely, Prussia, Sardinia, the Roman States, Spain, and Portugal.

The accumulation of astronomical knowledge during the past century has been so rapid, and improvements in the arts of observation and computation have been so great, that frequent improvements in the tables used for the preparation of Almanacs have been demanded, both for the needs of practical astronomy and to render the increased knowledge available for nautical purposes; and these improvements have in some cases been so long delayed as to render the Almanac almost useless

to the astronomer, and only a miserable necessity to the navigator.

The Connaissance des Temps, for instance, was greatly improved under the superintendence of the astronomer Lalande in the last century; but from that time the work had remained substantially as he left it, even down to our own times, when, in the volume for 1862, the long needed improvements in the lunar ephemeris were introduced. In other respects, however, the work still remains as deficient as when, in 1856, Le Terrier announced in the French Academy that it had been for a long time of no scientific value. This charge against the Connaissance des Temps was repeated so late as 1860, when Le Terrier again called the attention of the Academy to its insufficiency and want of accuracy, remarking that “The Connaissance des Temps is no longer of use to astronomers. A fundamental reform is urgent, which shall raise it from its inferiority as compared with foreign Ephemerides.” (Comptes Rendus, No. 6, 1860.) To these charges the only response which could be made in behalf of the Bureau des Longitudes was the insufficiency of the pecuniary means which the French government had appropriated for its support.

During the lifetime of Dr. Maskelyne, numerous changes were made in the tables used in the preparation of the English Nautical Almanac; but from the time of his death, 1811, till very recently, only two important changes in astronomical tables had been made, — the introduction of the French tables of the moon (Burckhardt’s) in 1821, and of the Italian tables of the sun (Carlini’s) in 1834.

In the year 1830, the construction of the Almanac was found to be so defective, that the subject was referred by the Commissioners of the British Admiralty to the Astronomical Society, requesting that body to consider what improvements could be made. The council of the society presented their report upon the subject the same year. This was immediately approved by the Admiralty, and the proposed changes in the form of the Almanac were carried into effect in 1834. From that date till very recently no material changes were made.

In the important matter of lunar tables no change was made in 1834, although the researches of geometers had already

brought the lunar theory to a much greater degree of perfection than belonged to the tables then in use; and the French, German, and English Almanacs continued to use the obsolete tables of Burckhardt long after the advance in practical astronomy and the requirements of nautical astronomy had rendered their further employment inexcusable.

Accurate determinations of longitude depended at that time chiefly on the perfection of the lunar tables, yet the tables in use were serviceable only for the approximate determinations of the positions of ships at sea. The importance of greater accuracy cannot be better expressed than in the words of the committee of the very council that proposed the changes just referred to.

In their report this distinguished committee expressed “their decided opinion, that it is not by the mere helps with which the seaman is furnished for the purpose of determining the position of his vessel at sea, that the full intent and purpose of what is usually called nautical astronomy are answered, since this object is a part only of that comprehensive and important subject. An equally important and more difficult portion of it consists in the exact determination of the position of various interesting points on the surface of the earth (equally essential and almost solely applied to the purpose of navigation),— such as remarkable headlands, ports, and islands, together with the general trending of the sea-coast between well-known harbors, — and which may properly be designated by the name of nautical geography; this can only be effectually and properly executed by methods not available on board a ship, and by delicate instruments placed firmly on solid ground. And the observer in such cases requires all the astronomical aid which can be afforded him from the best tables, arranged in the most convenient form for immediate use. This was evidently Dr. Maskelyne’s view of the subject, when he first proposed the formation of the Nautical Almanac, as appears from his ‘Explanation and Use of the Articles’ annexed to that work; and the propriety and accuracy of his opinion have been confirmed by the repeated wants and demands of those distinguished navigators who have been employed in several recent scientific expeditions. There are, moreover, many individuals in various parts of the world attached to the science of astronomy, who, by the encouragement and facilities thus given, render considerable assistance to the improvement of astronomy and geography by their exertions; and neither private nor national observatories, on which many thousands are annually expended, can proceed with activity or good effect, unless some aid of this kind is afforded them.”

The United States Coast Survey is an example of the scientific department in nautical astronomy referred to in the above extract. This Survey labored under great disadvantages, on account of the imperfections of the British Almanac during the long time it was obliged to depend on a foreign Ephemeris. Many observations of “moon culminations” made on the Pacific coast for determinations of longitude were laid aside “for want of moon’s places more reliable than the British Almanac can give us.” (Letter of A. D. Bache, Superintendent of the United States Coast Survey, to the Superintendent of the Nautical Almanac, 1851.) Expensive chronometric expeditions were undertaken for the same reason, to determine by chronometers alone, and without the aid of lunar observations, the difference of longitude between our eastern coast and the western coast of Europe.

In this condition of national dependence on an inferior foreign Ephemeris, the design of establishing an American Ephemeris was favorably entertained by Congress. In other departments of astronomy, America had already achieved great distinction. The establishment of the National Observatory and of the Coast Survey; the achievements of many private observatories, and those improvements in means of observing, which have been adopted in foreign observatories under the name of the “American Method”; the success of American mathematicians in the most recondite researches, by which America has shared with Europe the glory of the most famous discoveries in the present century, — such examples of the independent cultivation of astronomy in America rendered our dependence on a foreign Ephemeris an anomaly and a disgrace. When, moreover, we consider the chief and indispensable uses of the Nautical Almanac, and that independence of foreign nations in all practical matters which every American has at heart, it is strange that our navy and merchant marine should have been left so long dependent on their rivals for the means of navigating the seas on which they aspire to pre-eminence. It was as if our navy had been armed with foreign ordnance, and our merchant-ships equipped in foreign dockyards. In our present relations to foreign nations these considerations are of special significance.

In the preliminary preparations for publishing the American Ephemeris care was taken to improve upon the form and construction of foreign almanacs, as well as upon the tables and other data. For a clear statement and unprejudiced estimate of these improvements, we will quote the words of the Rev. Robert Main, late President of the English Royal Astronomical Society. Writing for the Encyclopædia Britannica soon after the publication of the American Ephemeris was begun, this distinguished astronomer says (Vol. III., Art. Astronomy): —

“Very recently an American Ephemeris and Nautical Almanac has appeared, which promises to be of great service. It is printed in a large octavo, and is published under the authority of the Secretary of the Navy. It is at present under the superintendence of Lieutenant C. H. Davis, U. S. N., the theoretical part being placed under the special direction of Professor Peirce of Harvard College, Cambridge.

“This work does not copy implicitly any existing Nautical Almanac, but, retaining what is best in our own and others, modifies the arrangement in a way which promises to be more generally convenient. One great peculiarity in this work is the separation between the part designed exclusively for the purpose of navigation, and that which is generally useful for the theoretical or practical astronomer.

“In the second part the places of the fixed stars and the planets are referred to the meridian of Washington, and in the computations the best elements at present known are scrupulously employed. Thus, for the star corrections, Peters’s constants of precession, nutation, &c. have been adapted to Bessel’s formulae; and with regard to the lunar computations, the elements are based on Plana’s theory, but include Hansen’s inequalities and secular changes of the mean motion and perigee, and Airy’s corrections of the elements derived from the reduction of the Greenwich observations. For the planetary computations, the latest corrections of the elements of each planet have been employed. For Mercury, Leverrier’s theory has been used (Conn. des Temps for 1848); for Venus and Mars, Mr. H. Breen’s corrections have been applied to Lindenau’s elements (Memoirs of Royal Astronomical Society, Vols. XVIII. and XX.); for Jupiter and Saturn, Bouvard’s tables have been used, with some changes, and Bessel’s value of the mass of Jupiter is employed; for Uranus the elliptic elements of Bouvard are used as the basis, with Leverrier’s corrections and perturbations caused by Jupiter and Saturn (Conn. des Temps for 1849), and with Peirce’s corrections and perturbations arising from the action of Neptune; finally, for Neptune, Peirce’s theory and Walker’s orbit have been used in the construction of the Ephemeris.”

Such are the many and important improvements introduced in the American Ephemeris. Of the esteem in which this enterprise was held by the English astronomers, very gratifying proofs were received by the Hon. J. P. Kennedy, late Secretary of the Navy, under whose authority the publication of the American Ephemeris was conducted. While in London, in 1857, this distinguished gentleman was invited to attend the annual visitation of the Greenwich Observatory by the Astronomical Society, where, among many commendations of the organization and efficiency of the scientific departments of our Navy from members of the Society, he had the gratification to receive from the Astronomer Royal “generous and earnest praise of the great merit of our Almanac,” of which he said, u It is very admirable, and does great credit to the science of your Navy.”

The superiority of the lunar tables prepared under the direction of Professor Peirce for the use of this Almanac rendered its practical value more prominent even than its general scientific merit. Numerous tests of their accuracy have been made, with the most gratifying results. While these tables were in the course of preparation, the Superintendent of the Nautical Almanac was authorized to publish his predictions and elements of the total eclipse of July 28, 1851, for the express purpose of testing the accuracy of the new tables. From observations of this eclipse, made at Cambridge, the British Almanac was found in error eighty-five seconds, and the American Almanac only twenty seconds. From Washington observations, the British Almanac was found in error for the beginning of the eclipse seventy-eight seconds, and for the end sixty-two seconds. The American Almanac was in error for the beginning only thirteen seconds, and for the end only one second and a half. Where the eclipse was total, and where, for this and other reasons, the test was more rigid and conclusive, the result was still more gratifying and decisive as to the superiority of our own lunar tables. The same tables were used in the French and Prussian Almanacs as in the British, and the errors were, therefore, the same. The errors of the old tables exposed in this eclipse may give rise to an error of from fifteen to twenty miles in the determination of the longitude at sea by

means of lunar distances, and to an uncertainty of twice that amount. The possibility of so great an error arising from this source was removed in the American Ephemeris. Before the new tables were completed, important corrections were introduced, which rendered them still more exact, and from tests by meridian observations, made several years later, these tables were found to be sufficiently accurate for the most refined determinations of nautical astronomy. These later tests were made in the office of the Nautical Almanac by Professor Newcomb, by comparing the American Lunar Ephemeris for the years 1856, 1857, 1858, with Greenwich observations. These comparisons were communicated by the Superintendent of the Almanac to the Astronomical Journal, and were published in Nos. 129 and 142. They show that the mean error of the tables is quite within the limits of errors of observation, and less than one fourth the error of the tables then used by other almanacs. Concerning these observations Sir J. W. Lubbock says (Memoirs of the Royal Astr. Soc., Vol. XXX.): “The errors of the observations of the moon at Greenwich vary up to ± 6″, and the small differences which exist between the place given by the American tables and the observations at Greenwich are due as well to the errors of the observations as to the errors of the tabular places. This is confirmed by the extreme irregularity of the differences. And it should be remarked, that the large differences which occasionally occurred before have been entirely got rid of by the American tables.” And again he says: “As it appeared to me that astronomers would view with greater confidence a comparison of places given by the American tables, made by persons who could have no interest in enhancing their value, I made application to Mr. Hind, the Superintendent of the [English] Nautical Almanac; and, in consequence, he directed Mr. Parley to procure places of the moon from the American Almanac, and compare them with the observations made at Greenwich for the years 1856, 1857, and 1858; and as Mr. Hind has kindly allowed me to publish them with this paper, any one can see at once how extremely accurate the places given by these tables are, and how much more so than places given by Burckhardt’s tables.”

In consequence of this great inferiority in the tables of Burckhardt,

which had been used for more than forty years by the British and other European Almanacs, they were at last, very recently, discarded, and the new tables of Professor Hansen, published by the Board of Admiralty, were introduced. Ephemerides prepared from these tables first appeared in the British and French Almanacs for 1862. From such tests as have been applied to them in the National Observatory and in the office of the Nautical Almanac they show but slight improvement upon the American tables; the apparent “probable errors” of the two Ephemerides, as tested by observations made at Washington in 1862, being in the ratio of eight to nine. In both comparisons, however, the magnitudes of the apparent errors bear such relations to their relative frequency as to indicate that they are chiefly composed of errors of observation. In the Ephemerides of later years there is an increase in the magnitudes of the greatest discrepancies; and though the test of observation has not yet shown any decisive or important inferiority in the American tables, yet the more elaborate and more recent investigations embodied in Professor Hansen’s tables make it probable that at some future day the former will be superseded either by the latter, or by new tables which shall incorporate still better astronomical determinations. At present, both Ephemerides are as perfect as nautical uses require, and are vastly superior to the tables they have superseded.

Modern observations have shown that material corrections are required in the tables of most of the planets, and a systematic revision of the elements and theories of the four outer planets, Jupiter, Saturn, Uranus, and Neptune, was accordingly undertaken several years ago by the Nautical Almanac, under the direction of Professor Peirce; and considerable progress in this work has already been made.

The present Superintendent, Professor Winlock, has added much to the astronomical value of the Almanac, by increasing the number of the ephemerides of the fixed stars, in the volume for 1865; and in the volume for 1867, a list of occultation phenomena is given for the year 1866, to facilitate the geographical exploration of California and the adjacent territory.

The Almanacs of all maritime nations are designed to contain

all that can be of importance to nautical astronomy, but in other respects they have each an individual character, and are devoted to such special service to astronomy as each can best render. Thus the Connaissance des Temps has always been the vehicle for the publication of some of the most valuable papers of the French astronomers. One of the objects of the Prussian Almanac, the Berlin Jahrbuch, was “to obtain a repertory for all observations, information, remarks, and treatises connected with astronomical science.” The Milan Ephemeris contains many valuable observations and papers of the Italian astronomers. The American Ephemeris has already published valuable papers, — two of great practical importance in navigation, and another of great use to astronomers in facilitating the computation of planetary perturbations. Even the nautical part of the Almanac requires, in one respect, different tables for different nations. For although the subject of the tides is an astronomical problem, yet geographical data are necessary to render accurate predictions possible. From the times of the occurrence of high tides, as given in the British Almanac for British ports, only approximate predictions can be made for the American Atlantic coast, while the tides on the Pacific coast are quite distinct and peculiar. Tide-tables have accordingly been prepared, for the use of navigators, from the Coast Survey observations, by Professor A. D. Bache, the Superintendent. These are prepared for the principal ports on our Atlantic and Pacific seaboards, and published with directions for their use in the nautical part of the Almanac.

To support the publication of works like these, which are not only of great scientific value, but of material importance to the useful arts and industries, ought to be regarded not merely as creditable to the government, but as a peculiarly incumbent duty; since a public patronage is especially demanded for the furtherance of such enterprises as cannot command the resources of individuals by the inducements of profit or honor, but which are none the less important to the uses of life and the advancement of civilization. And in the performance of this duty the government ought to consider, beside the immediate wants of the public service, those ultimate utilities of science to the welfare of mankind, of which the history of Astronomy affords so signal an example.

Chapin on Gravitation and Heat. [From North American Review 101.2 (July 1865): 330-331.] ¹⁷

The Correlation and Conservation of Gravitation and Heat, and some of the Effects of these Forces on the Solar System. By Ethan S. Chapin. Springfield, Mass.: Lewis J. Powers and Brother. 1867. 12mo. pp. 120.

If we were to compare Mr. Chapin’s powers of mathematical and speculative insight with those of eminent modern physicists, it would be greatly to his disparagement. We think, nevertheless, that he reasons on physics much better than Aristotle, and has much clearer ideas on many scientific subjects. But if Aristotle had had the advantages, in early life, of a training in the maturest results of modern science, prior to the development in his own mind of speculative opinions grounded on his own unaided observations and reflections, — if, in other words, he had had a truly educational discipline in science, — he would doubtless have excelled our author. How it would have been had he acquired a knowledge of modern science later in life, and after his opinions were in great measure formed, it would be more difficult to decide. How far later instruction can supply the deficiencies of early education is indicated, however, in certain historical examples, to which our author refers in his Preface. Newton, at the time of his death, “had not above twenty followers out of England”; and Kepler said of his immortal work, “It may well wait a century for a reader, as God has waited six thousand years for an interpreter of his works.’’ The author adds, “Therefore, when I not only introduce new theories, but combat the errors of accepted ones, I may expect to wait long for an impartial reader.” It will be seen that our author here compares himself to these eminent philosophers. But to our mind he much more nearly resembles the majority of their contemporaries. The self-made

made man of our day is, with reference to the more abstruse matters of science, in the position of the instructed man of former times, whose maturity was contemporary with great discoveries in science, and with whom later instruction could not efface the prepossessions of an earlier education. To set out in the study of nature with the guidance of the results already reached has the supreme advantage of avoiding that greatest obstacle in the path of learning, the necessity of retracing our steps, and remodelling our fundamental ideas. If our author had had this advantage, we are sure, from the original mental power which his book discloses, that the book would not have been written, or else would have been made much more worthy of attention from students in science.

Mill on Hamilton [From The Nation 1.9 (31 August 1865): pp. 278-281.] ¹⁸, “An Examination of Sir William Hamilton’s Philosophy, and of the principal Philosophical Questions discussed in his writings. By John Stuart Mill.” Boston: William V. Spencer. 1865. 2 vols., pp. 330 and 354. ¹⁹.
4. — A Treatise on Logic, or the Laws of Pure Thought; comprising both the Aristotelic and Hamiltonian Analyses of Logical Forms, and some Chapters of Applied Logic. By Francis Bowen, Alford Professor of Moral Philosophy in Harvard College. Cambridge: Sever and Francis. 1864. pp. xv., 450.

The subject of this work “is not Sir William Hamilton, but the questions which Sir William Hamilton discussed.” Many of these, though originating in the school of philosophy of which Sir William Hamilton is the most eminent representative of the present generation, and though often ignored under the general designation of metaphysics by the school to which Mr. Mill belongs, are questions which he regards as important enough to justify his elaborate work. “A true psychology,” he says, “is the indispensable scientific basis of morals, of politics, of the science and art of education, and “the difficulties of metaphysics lie at the root of all science.” In his work on logic, and in many of his shorter essays, there is manifested the same appreciation of metaphysical studies, with which, however, he always deals warily, and he has reserved as the work of his maturest powers the complete definition and defence of his metaphysical opinions. Questions which often engage the attention and tempt the powers of immature thought Mr. Mill has reserved for his latest work, and he has thereby contributed to philosophy most important additions.

Much more space is given, it is true, to dissecting and estimating Sir William Hamilton’s special opinions and characteristics than the proposed design of the work seems to warrant, but this does not diminish in the least its interest, nor in fact its positive value as an exposition of the opinions it. advocates. A master in the tactics of philosophical polemics, Mr. Mill

strikes very effective blows for his own opinions, and builds on the ruin he makes of the best accredited rival philosophy. Disciples of this philosophy may justly object, however, that the opinions they hold are not responsible for the defects of a teacher, even of so unquestionable a master as Sir William Hamilton; and his very excellences seem to us to furnish the vantage ground from which his critic makes so effective an assault on the opinions of his school. Few writers of this school present so clearly and distinctly the fundamental questions of metaphysics as Hamilton. His statements have such precision and scientific distinctness that his critic is able to exhibit even in his own words the contradictions and inconsistencies which abound in his writings.

Many of these, however, are, we think, apparent rather than real, and are explicable from the metaphysician’s point of view, which Mr. Mill does not appear to us to have clearly comprehended. We willingly concede that so far as perfect candor, most patient study, and an earnest desire to ascertain Sir William Hamilton’s opinions could avail, Mr. Mill’s examination is all that could be desired. But something more than justice is required of a critic in matters so difficult and profound. Sympathy—a certain degree of sympathy—is essential to supply the links and concordances of thoughts, which were never reduced to a coherent system, but were scattered through the writings of many years, and stand much in need of a commentary—not by an opponent, but by an admiring and competent disciple. It is not less true of a philosophical system than of a religious creed, that to judge it competently one must first believe in it, and then, perhaps, cease to believe in it—at least lose the ardor of the disciple.

Although Mr. Mill is by no means so far removed in opinion from the school of philosophy which Hamilton represents as many of his own school are, he is none the less separated from it by that fundamental division which has maintained two great schools throughout the whole history of speculative thought; a division which is at bottom one of feeling and mental character, and one in which no love is lost. No philosopher has had the genius to arbitrate between them. Not even Mr. Mill, sagacious and just as he is, is generous enough to catch the spirit and point of view of his opponents in speculative matters.

We cannot give an adequate illustration of this defect from the topics of Mr. Mill’s book without exceeding the limits of this article. It may suffice to point out one misinterpretation of Hamilton’s doctrines, as we conceive them, which is fundamental, and plays an important part in the “Examination.” Mr. Mill attempts to prove that the doctrine of “the relativity of human knowledge as held by Sir William Hamilton” is in direct conflict with Hamilton’s doctrine of the perception of the primary qualities of matter, two doctrines on which his fame as a philosopher chiefly rests. Nothing could be more damaging to Hamilton’s reputation than this criticism, if it be true. Minor defects and inconsistencies in his writings might be accounted for on grounds not dishonorable to his character as a philosopher; but if the two principal doctrines, on which he has expended so much learning and labor, are incompatible with each other, then indeed his sagacity was much at fault.

After an introduction, in which Mr. Mill sets forth the scope of his work, he discusses in the second chapter the authentic meanings of the phrase “relativity of knowledge,” and the varieties of the doctrine as held by different philosophers. In its simplest form the doctrine is this, that we know only our sensations, and know not any other things save as existences which, in themselves unknown, produce sensations in us. Other things are only supposed, not known; and are only supposed as powers to produce sensations, not as reasons or inmost natures, which might explain the phenomena of sensation. They are as inmost natures inexplicable, and cannot be described in known terms, but only as the unknowable. This doctrine is fundamental in one of the two great systems of metaphysics, but can be understood in a less definite sense. If a philosopher should hold that some properties of things are not powers to produce sensations in us, but existences, which like our sensations are immediately known, he would not hold, our author thinks, to the relativity of knowledge in a perfectly definite sense. He might mean that all knowledge is a mixture of the relative and absolute kinds, but he ought not to affirm that all knowledge is relative.

The author then comes to the discussion of the meaning in which Hamilton taught the relativity of knowledge. Hamilton affirms the complete relativity of human knowledge, but in his doctrine of natural realism he appears to deny it. He affirms it of the secondary qualities of matter, such as colors, odors, tastes, etc., but denies it of the primary qualities, such as extension, figure, resistance, etc. The existence of matter as the cause of sensations can only be affirmed, Hamilton thinks, by being known immediately and in itself as extended. An extended something is immediately known, the property of extension not being a power to produce a sensation or a group of sensations, but an existence known as immediately as our sensations are. By “immediate” Hamilton does not mean non-relative to us, but without the intervention of a representative object or sensation. The knowledge is immediate, though the thing is related to us in the act of knowledge. But Mr. Mill enquires whether this knowledge is supposed to involve more than exists in this relation; that is, whether this immediate knowledge is of anything non-relative to us. Hamilton appears to think that it is, and he therefore appears to hold that the knowledge is not wholly relative to us. Hamilton asserts in the plainest terms, says Mr. Mill, that this immediate knowledge of things “is a knowledge of somewhat in the thing ulterior to any effect on us;” but in his doctrine of the relativity of knowledge he asserts that neither matter nor mind are known in themselves as substances or subjects of the phenomena. Matter is known “only in its effects.” “The existence of an unknown substance is only an inference we are compelled to make from the existence of known phenomena.” In such words Hamilton lays down the doctrine of the relativity of human knowledge in an exposition which, Mr. Mills says, “would have satisfied Hartley, Brown, and even Comte.” The doctrine that we know matter “only in its effects,” and that “its existence is only an inference we are compelled to make” from phenomena, is the doctrine, however, says Mr. Mill, “which, under the name of cosmothetic idealism, is elsewhere the object of some of Hamilton’s most cutting attacks.”

We have dwelt somewhat at length on this topic, since it illustrates very completely how much a philosopher’s comprehension may be limited by his creed. Even with the words before his eyes, Mr. Mill appears to have overlooked, or else rejected as trivial, a distinction of great consequence in Hamilton’s philosophy—the distinction between “effects on us” and effects in general, or those relative phenomenal existences of which unknown substances, matter or mind, are the causes. In this is all the difference between Hamilton’s doctrine of the relativity of knowledge, and that doctrine of cosmothetic idealism which he attacks. That a knowledge should be of effects, and yet not of effects on us, does not appear to have occurred to Mr. Mill; but this is briefly Hamilton’s doctrine. Mr. Mill and Sir William Hamilton (in his metaphysics) use the words “cause and effect,” however, in different senses; but Mr. Mill does, not appear to be aware of this, else his chapter on Hamilton’s “Theory of Causation” would, we think, have been made less severe.

The division of existences into phenomenal and real (the always becoming, the never being, and permanent real existences) is made in the school to which Hamilton belongs, irrespective of any theory of perception. This Platonic distinction is as fundamental in the older metaphysics as the simpler doctrine of relative knowledge is in Mr. Mill’s, but has no reference to the distinction of subject and object in knowledge. Draw the line where we will between the ego and the non-ego; include all cognizable being in the ego, or exclude a part—whether all cognizable modes of existences are sensations and groups of sensation in us, or whether other modes of existence form a part of the phenomena of knowledge—it is in either case true that particular and passing modes of existence, not their substances, are the objects of knowledge. All that Hamilton in his “Theory of Perception” contends for is, that we have a knowledge of modes of the non-ego as immediate as our knowledge of our own sensations; that our consciousness in presentative knowledge is composed of phenomena or modes, which are referable immediately some to a substance ego and some to a non-ego; but that it is only through these phenomena that either ego or non-ego is known, and the knowledge of both is therefore relative. The subjects of phenomena are still unknown in themselves, though the primary qualities of matter be as immediately known as sensations are. The relations involved in the phenomena of. knowledge are, according to Hamilton, sui generis, and cannot be explained, he thinks, as relations of attributes to a single subject, but they are explained to the common sense of mankind by the doctrine which Hamilton calls natural dualism. According to this, a real or immediate knowledge is no more a mode of the ego than of the non-ego, but is a phenomenon, a mode of being, by which two substances manifest themselves equally and in contrast as two substances. When Hamilton speaks of our “knowing nothing absolute, nothing existing absolutely, that is, in and for itself, and without relation to us and to our faculties,” he does not contradict his doctrine of real presentationism. Though things do produce effects on us—namely, sensations—it is not these which constitute knowledge of things. Real knowledge, as a phenomenon, is the joint result of two real causes, neither of which is known in itself, but both are equally known as the necessary substrata of the phenomenal elements of knowledge. Those elements which are immediately referred to the non-ego are not “a knowledge of somewhat in the thing ulterior to any effect on us,” as Mr. Mill interprets them, but at the same time they are no mere modes of the self. They are

the modes of a self and a not-self in union and equipoise. When Hamilton contends that we know the primary qualities of matter as they exist in things, he does not assert that we know things in themselves—that is, the noumena or things independently of us. We only know them as independent of any affections of us. We know them by affections of themselves on the occasions of their mysterious union with us in our intuitions of them.

That this doctrine is a genuine product of the old metaphysical mode of philosophizing, and is exposed to the gravest objections, we willingly admit. It is really an attempt to explain a phenomenon by describing it in terms which imply that it is ultimate and inexplicable. Like much beside in metaphysical philosophy, this doctrine attempts to justify the common opinions and natural prejudices of the undisciplined mind, instead of attempting to account for them. Very profound in appearance, it rests on the most superficial evidence, and does not bear examination. But while we admit all this, we are unwilling that the really strong points of Hamilton’s metaphysical genius should be underestimated. His theories really fit each other much better than they do the more recondite facts of experience. Between this doctrine and the psychological explanations which Mr. Mill gives in Chapter XI. and the two following ones, there is a difference as important as that between the astronomical theories of Plato and those of Newton. We regard Mr. Mill’s definition of substances as “the permanent possibilities of sensation,” and the interpretations of the facts of consciousness which he makes in accordance with it, as among the most important contributions to psychology which have been made in modern times. The chapters devoted to his psychological theory of the belief in an external world, in matter and mind as substances, and the psychological theory of the primary qualities of matter, are the most valuable in the book, and comprise the maturest and most defensible views on these difficult subjects which have been reached.

In the chapter on Sir William Hamilton’s theory of causation, Mr. Mill retorts with great effect the criticism of Hamilton on Brown, but, as we have intimated, this severity could have been spared, if instead of aiming at a polemical success our author had attempted to realize what the metaphysical idea of cause is, and what precisely Hamilton meant in his charge against Brown that “he professes to explain the phenomena of causality, but previously to explanation, evacuates the phenomenon of all that desiderates explanation.” Misled, we suppose, by what must be allowed to be a very faulty account of the principle of causality, in which Hamilton gives a precise scientific explanation of the metaphysical idea of cause, while in fact the idea has only a vague unprecise import, Mr. Mill thinks that Hamilton has confounded the notion of efficient cause with that of substance, the causa efficiens with the materia, and that when Hamilton speaks of the complement of existence always remaining unchanged, and of the impossibility of conceiving any change in it, he has in mind the permanence of material substances, which, as Mr. Mill justly says, is not a necessary conception, such as the principle of causality is supposed to be. Doubtless this conception furnished Hamilton the faulty metaphor under which he describes the principle of causality, but it should have been interpreted like Plato’s archetypal world—that permanent existence which is supposed necessary to account for the changes as well as the apparent permanences in the world of phenomena. Mr. Mill, following Brown, is quite as far from defining, in his law of causation, the metaphysical efficiens as he supposes Hamilton to be. His idea of cause is the scientific one, which is more properly named physical cause. It is the most general law of the successions of phenomena, and is derived from the total results of experience, whereas the principle of causality is supposed to be implied in the very beginnings and elements of experience. The law affirms that all successions are made up of invariable and unconditional sequences, but the metaphysical cause is the supposed real substratum of the unconditionality of a sequence. This principle is a genuine product of the metaphysical mode of philosophizing, and on close examination does not yield much meaning, but such as it is was Hamilton’s meaning. Phenomena change. What makes them change? Not themselves. Not their regularity, which is expressed by the law of causation. “That which can produce changes must itself be permanent” is the metaphysical postulate called the principle of causality. For if it also changes, then something else must make it change, and this something else must either be permanent or the effect of some still more remote unchangeable existence. Such we conceive to be the notion of causality as held by Sir William Hamilton. Doubtless, if Mr. Mill had so comprehended it, and applied to its explanation his psychological method, he would have resolved it into a mere crudity of undisciplined thought—into anything but a necessary principle. This, however, would have been better than misunderstanding it, to the apparent detriment of his author’s reputation.

In respect to one of the principal topics of Mr. Mill’s book, the position of Sir William Hamilton is quite anomalous. Though belonging to the school to which Mr. Mill is opposed, Hamilton, it is well known, agrees in one of his most important opinions with his opponents. This has caused a great quarrel in the family. The absolutists and the quasi absolutists among religious thinkers have found in him a formidable antagonist; but this wins for him no sympathy from his critic of the opposite school, but rather subjects him to a severer condemnation. He is discovered in his lion’s skin. He is not genuinely unorthodox, but, by what appears to his critic to be a subterfuge, retreats from his position on the incognizable and inconceivable character of the infinite and the absolute, by affirming that, though these cannot be known or conceived, they may yet be believed in. “What is rejected as knowledge by Sir William Hamilton, brought back under the name of belief,” is the topic of Chapter V., in which Mr. Mill disposes somewhat summarily of a distinction of great consequence with theological writers, and one which also plays so important a part in Hamilton’s philosophy, that a more careful and sympathetic study of it would have saved Mr. Mill, we think, much perplexity in his interpretations of Hamilton’s opinions, especially in a later chapter on the doctrine of Judgment.

“Belief without knowledge” seems to our author an absurdity, and though the antithesis and the frequent antagonism of faith and science have rendered the distinction a familiar one, it must be confessed that there are few psychological matters more difficult than the discrimination of a faculty of faith from our general faculties of knowledge. But that there is more than a simple difference of degree between knowledge and belief, even in the common acceptation of the terms, seems to us obvious. Hamilton uses the word “belief” in a somewhat technical sense, to express a simple and elementary form of consciousness, which he supposes to underlie every cognitive act, and to take part in the formation of notions as well as of judgments and reasonings. That Mr. Mill is not fully apprized of this use of the word appears when he says that, “according to Sir William Hamilton, we believe premises, but know the conclusions from them,” and adds, “but if we know the theorems of Euclid, and do not know the definitions and axioms on which they rest, the word knowledge, thus singularly applied, must be taken in a merely technical sense.” But really, according to Sir William Hamilton, we not only know these theorems by means of the axioms and definitions, but we also know the axioms, though in a different manner. Though proposed in the form of cognitions, they rest, he thinks, on an instinctive apprehension of certain universal facts, which may govern our actions and even our judgments without passing themselves into the distinct consciousness of knowledge. Expressed in language they may be known, but independently of this they are believed and acted on. They exist and are originally given in the form of “simple feelings or beliefs.” Mr. Mill, of course, gives a different and, we think, a better account of the origin of universal truths, but this is no reason why he should not comprehend and correctly state the real opinions of his author, though it may serve to explain why he does not do so. His own opinions are so different from Hamilton’s that he is very likely to mistake him.

Among the many confusions, real and apparent, which Mr. Mill finds in Hamilton’s writings, the most perplexing belong to this subject. Hamilton appears to our author to propose, at a distance of exactly three pages, two different theories of judgment “without the smallest suspicion on his part that they are not one and the same.” But, in reality, though Mr. Mill does not appear to be aware of it, the first of these theories is a definition of the act of judging in its simplest form the element, which, according to Hamilton, is common to all the products of the understanding or the elaborative faculty, while the second theory defines the special product called specifically a judgment, in which, in addition to the common principle of comparison, there is apprehended and expressed the relation of subject and predicate. It is this relation which, according to Hamilton, distinguishes the logical judgment from a complex concept, and not the element of belief, which, according to Mr. Mill and others, belongs only to the judgment. This difference of opinion and nomenclature occasions Mr. Mill much perplexity. His author seems to him to reach in this matter “the very crown of the self-contradictions which we have found to be sown so thickly in Sir William Hamilton’s speculations. Coming from a writer of such ability, it almost makes one despair,” he adds, “of one’s own intellect and that of mankind, and feel as if the attainment of truth on any of the more complicated subjects of thought were impossible.”

Mr. Mill makes small account, as we have said, of the distinction of knowledge and belief. They differ, he thinks, only in the degree of the conviction with which they are held, or else in the degree of simplicity and directness in the evidence on which they rest. But if we examine them through their correlative ignorance and doubt, an important difference in kind becomes apparent, at least in their psychological relations. Knowledge and

ignorance are wholly beyond the immediate influence of the will. They depend only indirectly on feelings and motives. Belief and doubt, on the other hand, involve volition and depend on feelings and motives. That which Hamilton calls belief, the simple elementary sense we have—from whatever source—of a congruence or conflict among objects and ideas, is that which governs our attention and determines our cognitive acts. Such beliefs control one another like other motives to action, so long as any conflict can arise among them, and it is only when such conflict ceases or is supposed to cease that we attain to knowledge, or suppose ourselves to have attained to it; for much which is called knowledge is only supposed, not real—is a contingent knowledge, held without any actual doubt, but not without a recognized possibility of doubt. Knowledge, then, according to this theory, is not a single simple act of our cognitive faculties, but a harmonious action of all concerned, in which no opposing motive to action exists or is operative; so that what we know, we know without consciousness of choice. In the same way we are ignorant without choice. Conflicting beliefs are not only absent, but all beliefs are absent. Conflict among our elementary beliefs or judgments of agreement and disagreement ceases in two ways, by the discipline of our cognitive objective experiences, and by the discipline of our wills in the formation of character—by submitting our thoughts to the influence of scientific studies, and by submitting them to the control of a restraining culture. Hence the antithesis of the results, science and faith.

This account of the distinction between knowledge and belief is independent of the doctrine, which Hamilton holds in common with his school, that some of our universal beliefs are original and independent of experience; and it is perfectly consistent with what we regard as the truer doctrine of the other school, namely, that there are no postulates in real science—nothing requiring to be admitted beforehand. It is a doctrine, however, associated so strongly with the à priori theory, that it appears to have prejudiced Mr. Mill against it.

In Mr. Mill’s examination of Hamilton’s review of Cousin, in spite of certain important agreements in opinion with his author, he is not disposed, as we have said, to grant him any favor. He even seems inclined to charge him with the absurdities involved in “the senseless abstractions,” “the infinite,” and “the absolute,” and to make out as good a case as possible for those who think they attach significance to them. He goes so far as to say that though “the infinite” (what is infinite in all respects) is not merely, a “fasciculus of negations,” but, what is worse, a “fasciculus of contradictions,” yet if in place of “the infinite” we put the idea of something infinite, Hamilton’s idea collapses at once. “Something infinite is a conception, which, like most of our complex ideas, contains a negative element, but which contains positive elements also. Infinite space, for instance; is there nothing positive in that? The negative part of this conception is the absence of bounds. The positive are, the idea of space, and of space greater than any finite space. So of infinite duration; so far as it signifies ‘without end’ it is only known or conceived negatively; but in so far as it means time, and time longer than any given time, the conception is positive. The existence of a negative element in a conception does not make the conception itself negative, and a nonentity.” True, if “infinite space” be a conception, and not a mere juxtaposition of words or incompatible ideas, then space is a positive part of it. But the question is whether the judgment, “Space is infinite,” can be made, so as to bring the ideas together. Mr. Mill simply assumes that it can, and this too by a mistake of the meaning of the term “infinite,” which Hamilton took much pains to guard against. He confounds the “infinite” of the metaphysician with the improper use of the word by mathematicians. In itself and with the metaphysician, this word is simply the negative of the finite; and as such is entirely incomparable with the finite in respect to magnitude or in any other respect. How does Mr. Mill know that the infinite is greater than any finite? Only by substituting for it a false representation of it. “True,” he says, “we cannot have an adequate conception of space or duration as infinite, but between a conception which, though inadequate, is real, and correct as far as it goes, and the impossibility of any conception, there is a wide difference.” But the conception which Mr. Mill puts forward as the “infinite” is not only inadequate, it is a false conception; arising very naturally, it is true, from an association in our minds between the indefinite and the incognizable. Very large magnitudes are the least definitely or adequately conceived, and we therefore attempt, but wrongly and confusedly, to represent infinite space by putting for it an indefinitely great extension. But this indefinitely great does not contradict or exclude the finite. “Greater than any finite” does exclude the finite, it is true, but so does “less than any finite” exclude it, and both are equally entitled to be called the infinite, yet neither of them is conceivable—neither can be judged to exist.

Mr. Mill appeals for the reality of the conception of the infinite to the results of mathematical calculations. “Considering,” he says, “how many recondite laws of physical nature, afterwards verified by experience, have been arrived at by trains of mathematical reasoning, grounded on what, if Sir William Hamilton’s doctrine be correct, is a non-existent conception, one would be obliged to suppose that conjuring is a highly successful mode of the investigation of nature.” When we consider the reproaches which our author heaps upon Hamilton in a later chapter on the “Study of Mathematics” for his presuming to write about a subject of which he knew so little, we are tempted to respond in the same kind. Hamilton was at least fortunate in not knowing just enough of mathematics to be misled by a loose technical term, or else in knowing enough to be aware that mathematicians can afford to be careless about the etymologies and the strict connotations of the terms they employ. Mr. Mill is not given to superstitions, but if he supposes that mathematicians ever drew any conclusions in regard to physical nature involving in the premises a negation of the finite, he should look again to the works of his philosophical mathematician, Mr. De Morgan, for a correction of his error. The conclusions of the calculus are founded, not on a consideration of quantities really infinite, but of those which by the conditions of its problems may be regarded as indefinitely great—or, more correctly, incalculably great and incalculably small; and the conclusions drawn with their aid are proved to differ from the truth by incalculably small amounts—that is, by as little as we please. This is all that mathematicians have to do with the infinite, and this is just nothing at all.

Of the metaphysical infinite and absolute, and the simple feeling or belief, and the religious sentiment through which Sir William Hamilton and Mr. Mansel think these can be regarded as existing, Mr. Mill washes his hands. Rather than worship a being such as Mr. Mansel presents, of which no real conception, however inadequate, can be formed, he is ready to suffer the worst possible fate. Perhaps those among Mr. Mill’s opponents who are more familiar than he with religious æsthetics, would deny the name of worship to the sentiment he is capable of feeling toward a being whose government of the world receives his unqualified support and approbation, with the sanction of “the highest human morality which we are capable of conceiving.”

In spite, however, of Mr. Mill’s incapacity to enter into a requisite degree of sympathy with his opponent’s point of view, his eminent justness of thought and feeling give his criticisms great weight and value. There is much of interest in his book which we cannot even mention in this brief notice, but we earnestly recommend the whole to our philosophical readers.

Review of Draper's Thoughts on the Future Civil Policy of America.

Thoughts on the Future Civil Policy of America. By John William Draper, M. D., LL. D. New York: Harper and Brothers. 1865. 8vo. pp. 317. [From North American Review 101.2 (October 1865): 589-597.] ²⁰

The object of this book is to show the application to America of the principles set forth by the author in his work on “The Intellectual Development of Europe,” in which he endeavored to show “that the historical progress of the nations of that continent illustrates the fact that social advancement is as completely under the control of natural law as is the bodily growth of an individual.” The present work is founded on four lectures delivered before the New York Historical Society for the purpose of showing this application.

Encouraged by the popularity of his principal work, the author deems it advisable to give these lectures a more permanent form. This appears the more desirable, since “at the present moment, when the Republic has reached one of those epochs at which it must experience important transformations, it may not be inopportune to direct attention to the effects of physical agents and laws on the advancement of nations.” “We are too prone,” he adds, “to depreciate their influence.”

Dr. Draper more than atones, however, for the neglect which the workings of physical agents have suffered at the hands of the philosophical historian, at least in his appreciation of them. The possibility of historical foresight from a knowledge of physical science is much insisted on; but if ever the movements of society come to be traced scientifically to the workings of physical agencies, the merit of the discovery will hardly be Dr. Draper’s. Like two other recent and popular writers, Mr. Buckle and Mr. Spencer, he begins at the end of this possible future science, asserting roundly and in most unqualified terms conclusions of which the demonstration would require a knowledge amounting almost to omniscience, as compared with any conceivable attainments of science. These conclusions may be correct, at any rate they cannot be refuted; but the practical importance of insisting on them does not consist in any use that can be made of them so long as the science exists in the undeveloped state in which Dr. Draper leaves it. For he contributes little or nothing to filling up the void which exists between the problem and its solution. The historian who deals with the more particular and proximate causes and the empirical laws of historical events will be more successful, we think, and of much greater service to the statesman.

The connection between remote physical causes and their effects on the character and movements of society and the individual will, though we may be easily persuaded of its reality, is one which we can hardly

hope to bring within the compass of exact science, or to employ for the practical purposes of historical foresight; and the only motive we can conceive for insisting on its reality is a polemical desire to dogmatize in opposition to those who ignore or deny its existence.

To avoid the imputation of such a motive, Dr. Draper affects a practical object. He proposes to offer principles for the guidance of the American statesman. The only practical lesson of the book occupies, however, but little space for its development. The author advises American statesmen to prevent the division of the country into separate nationalities, and to counteract the modifying effects of climate by encouraging constant emigration and intercommunication.

“It is not enough,” he says, “that there should be free movement for thought; free movement for the people themselves is of equal importance. That is the true method for combating climate effects, — preventing communities from falling into Asiatic torpor, and contracting senseless antipathies against each other. Had the Southern States for the last ten years been pervaded by an unceasing stream of Northern travel in every direction, the civil war would not have occurred.”

Three pages back the author exempts the great empire of China from this description of “Asiatic torpor,” and recommends it as an example for us. To the question, “Can we not neutralize those climate differences, which, if unchecked, must transmute us into different nations?” he says: —

“In two words, I think, we find an answer, — Education and Intercommunication. Nor is this the suggestion of mere theorists. Under that formula four hundred millions of men — one third of the human race — have found stability for their institutions in China. By their public school system they have organized their national intellect; by their canal system they have made themselves, though living in a climate as diversified as ours, essentially one people. The principle on which their political system is thus founded has for many thousand years confronted successfully all human variations, and has outlived all revolutions.”

The practical statesman might object, however, that restrictions on “free movement for thought” in the Southern States have been for the last ten years among the most serious obstacles to that “unceasing stream of Northern travel” which the author thinks so desirable.

It is doubtless true, that commerce and free intercommunication are among the most valuable means of maintaining civilizations and nationalities, whether by counteracting climate effects, or by those obvious utilities which will more readily occur to the unscientific observer of human nature. But our Professor of Physiology is haunted with the idea that there is a peculiar fatality in climates. These can change the

color of the skin, the habitual employments, and the objects of familiar contemplation, and hence the habits of thought; hence the mental character; hence the development of the brain, and, finally, the shape of the skull; and lo! we have a new race of men, no longer fitted to live with each other in peace and amity! The fatal, inevitable character of these changes so fills his imagination, that he appears to ascribe to them a celerity equal to their certainty, apparently forgetting that throughout the whole length of recorded history, and during the rise and fall of all known nations and empires, the physical features of the human races have undergone very slight, if any, material modifications. But our author builds national differences on very slight physical changes due to climate. Speaking of the zone of the Northern States, he says: —

“Follow that zone with a prophetic eye, as it becomes peopled to the shores of the Pacific Ocean, and tell me, as those busy hordes extend over the vast sandy desert, climb up the threatening ridges of the mountain chains, descend through the moaning forests of enormous pines beyond, how many are the vicissitudes through which life must be maintained, and I will tell you how many distinct families of men there must be.”

The view which is most acceptable to philosophical naturalists of the present day represents race-variation as the effect, primarily, of geographical separation and isolation, and the cumulative effects of many and obscure causes, most of which are as likely to be of a very special character as to be dependent on general conditions such as climates. But the immense sweep of the causes which our author delights to contemplate — their simple and irresistible character, their fatality — obscure his vision of all those intermediate proximate causes to which men ordinarily ascribe the actions and peculiarities of their species. Hence we have such specimens of aphoristical wisdom as this: “The absence of summer is the absence of taste and genius; where there is no winter, loyalty is unknown.” Again, we are told that “without the Gulf Stream Newton would never have written his Principia, nor Milton Paradise Lost.” What a comprehensive view of causation we have in these facts! It impresses “the control of universal law” very forcibly upon our author. Those so-called Special Providences, long trains of trivial events and apparent accidents, on which the lives of the poet and philosopher depended, which are the fittest to excite surprise in the unsophisticated heart, are as nothing compared with the long reach of the causes through which the productions of genius are made to depend on the facts of physical geography and meteorology, and astronomical events to work out their own science.

A fatalistic view of causation is presented throughout the book, — not dogmatically, but rather in the rhetorical figures in which the

author’s imagination delights to revel. He is most profoundly impressed with “the existence of controlling law.” He discovers that animals and plants change “helplessly” under physical influences, and he therefore regards them as illustrations of “the control of universal law.” The empirical laws, disclosed in the statistics of crime, are quoted from the same motives, “for the purpose of bringing into clearer relief the cardinal doctrine that in individual life, in social life, in national life, everything is influenced by physical agents, and is therefore under the control of law. Far from denying,” he adds, “the operation of man’s free will, I give to that great truth all the weight that can be desired; but then I affirm there is something that overrides, that forever keeps it in check.” Then follows this curious illustration of his meaning: —

“If the reader will try a very simple physiological experiment upon himself, he will probably come to a clearer understanding of what is here meant. Let him execute with his right hand the motion he would resort to in winding a thread upon a reel. Then let him do the same thing with his left hand, only winding the opposite way. Are not these two contrary motions which he thus consecutively accomplishes thoroughly under his control? He wills to do either, and forthwith either is done. Both illustrate his voluntary power. But next let him try to do both, not successively, but simultaneously. Let him put forth all the strength of his determination. A free-will actor, he has now the opportunity of giving an illustration of his power. In the failure of repeated trials, he may discern what his voluntary determinations come to, and what they are really worth. He may learn from this simple experiment that there is something that over-controls him, and puts a limit to his power.”

Certain important considerations are overlooked in this remarkable example, which materially affect its value. The compound motion which, according to the author, baffles the free will of man, is something more than the sum of the other two. To perform either simple act of which it is apparently composed requires the guidance of the sight or the imagination. Now, although men have two hands, they have only one imagination, and the difficulty of this double motion is in the action of this guiding faculty. It is a difficulty, however, which is not insurmountable. A little practice will overcome this “something that overrides” the free will, “that forever keeps it in check.” More familiar though less imposing illustrations might have shown our author’s meaning more clearly. Indeed, examples of the limitations of human agency, whether free or otherwise, are not infrequent in human experience.

But our author’s salvo in favor of the “great truth” of free agency is not exempt from more weighty objections. If we can correctly interpret his meaning independently of his illustration, his doctrine of free

agency does not rise in dignity a whit above the barbaric fatalism which pervades the volume. This free will is one of the “resistances” to the “force” of universal law; “overridden,” it is true, and “forever kept in check.” Thus, if climate induce a man to fan himself or seek the shade, it is his free will that is coerced, not his indolence. The idea comports well with the doctrine that plants and animals are “compelled” to change their forms and habits to meet the variations of climate and other circumstances; that they “yield helplessly” to physical influences. Writers like Dr. Draper and Mr. Spencer, who closely resembles him both in style and doctrine, though they disclaim alike the dogmas of Free Agency and Necessity, or any hostility to either, yet present in their philosophies what is far more prejudicial to a clear scientific philosophy or a healthy moral nature. It is not the dogma that hurts. It is in its influence on the imagination, and, through this, on our scientific conceptions and moral feelings, that fatalism is mischievous; and in this manner the language and conceptions of fatalism are quite as efficacious as the dogma itself. We have said, that the author does not present his fatalistic views dogmatically. It is difficult, however, to distinguish, in a style luxuriant in vague paradoxical illustrations, what is meant to impress the reader and what to instruct him, but the moral tendency of the figure or doctrine is illustrated in the following passage: —

“And here I cannot help making the remark, that whoever accepts these principles as true, and bears in mind how physical circumstances control the deeds of men, as it may be said, in spite of themselves, will have a disposition to look with generosity on the acts of political enemies. Even when in madness they have rushed to the dread arbitrament of civil war, — a crime in the face of which all other crimes are as nothing, — and brought upon their country immeasurable woes, he will distinguish the instrument from the cause, and, when he has overpowered, will forgive.”

There may be good reasons why our moral feelings, in view of the crimes of the late Rebellion, should yield to higher motives; but the reason Dr. Draper gives would, if logically insisted on, suppress moral feeling altogether. He distinguishes only by the names between a crime and a physical evil. Men of sense punish the one, and prevent or overcome the other, if they can; and if they do not punish crimes, it is not because physical circumstances have produced them, but only because punishment will not prevent them.

The real search of science is for the laws of physical and other forces; but the lesson our author and similar writers seek to draw from the facts of science is the doctrine that there is force in physical laws. Between these two aims there is all the difference of the most enlightened

modern philosophy of science from the Manicheism of a barbarous theology. Under the formulas of matter and force, power and resistance, agent and patient, nature and circumstance, we still preserve the old duality of principles. Science still finds these phrases convenient; but scientific philosophy has at length emancipated itself from their doctrinal import and their influence on the imagination. They have degenerated into merely technical, abstract terms, expressive of nothing specifically real, though still useful in representing phenomena. The dogmas implied in these terms are like the old doctrine of Optimism, the doctrine that the world was created the best, the simplest, the most perfect which devising skill could make. The conception of a potential obstacle or hindrance to creative power, some hostile power or an intractable material, lurked under the doctrine, since otherwise there could be no question of better or worse, more or less perfect. In the same manner, the dominion of law, the control of physical forces, “the existence of controlling law,” plants and animals and the human will “yielding helplessly” to physical influences, suggest that there might be something to hinder, some lawlessness or some perverseness in the nature of things and in the human will which required to be overcome.

The law of causation, the highest principle of positive science, which teaches that law or regularity is everywhere to be found even in the determinations of the human will, is guilty of no such fatalism as this. True scientific philosophy finds no compulsion in the laws it investigates, because it finds no opposition to them. Opposing laws and opposing forces are not found in real nature. The notions are used in the abstract scientific analyses and representations of nature, but only where no ambiguity or misconception can arise. They are concretely propounded only in such barbarous philosophies as this we are noticing, and in similar popular works. The fascination of such crudities constitutes one of the chief attractions of these books to the general reader, whose imagination is pleased to drive the round of the sciences with a tight rein, all the forces under control and well in the traces.

Another secret of their popularity is in their frequent resort to entertainments of really valuable and interesting scientific and historical facts, ostensibly given to furnish illustrations of the dreary platitudes which they really serve to relieve. Many digressions of this sort adorn Dr. Draper’s pages. His scientific facts are, however, too frequently obscured by paradox, and his historical facts by doubtful theories. Well-ascertained facts and scientific guesses are given with equal positiveness. Facts, irrelevant to the illustrations in which they occur, find place in his pages, if they are only interesting and connected with the others. But the reader will not complain of this, nor ought we to find fault with

it. Abstracts of physiology and physical geography, historical monographs, facts of social and industrial science, biblical history and criticism, are scattered through the book. A complete treatise on the physical sciences is sketched, to “illustrate” man’s conquest of nature, the great idea which will hereafter compete with the climates of North America in the development of our nation. This treatise gives us information on gases, meteorology, acoustics, the sea, the steam-engine, electricity, magnetism, and the wonders of science. “But,” he concludes, “it is vain to go on. I remarked a few pages back that the facts of science exceed the capacity of any book.”

This principal digression is intended “to give emphasis to the proposition that a nation which is preparing itself for sovereignty among the powers of the earth, must shake off the traditions of obsolete policy, and stand forth the defender and protector of free thought.”

The following is, perhaps, the most impressive passage in this “illustration”: —

“Who could have believed that the twitching of a frog’s leg, in the experiments of Galvani, would give rise in a very few years to the establishment beyond all question of the compound nature of water, separating its constituents from one another, — would lead to the deflagration and dissipation in a vapor of metals that can hardly be melted in a furnace, — would show that the solid earth we tread upon is an oxide, — yield new metals, light enough to swim upon water, and even seem to set it on fire, — produce the most brilliant of all artificial lights, rivalling, if not excelling, in its intolerable splendor the noontide sun, — would occasion a complete revolution in chemistry, compelling that science to accept new ideas and even a new nomenclature, — that it would give us the power of making magnets capable of lifting more than a ton, cast a light on that riddle of ages, the pointing of the mariner’s compass north and south, and explain the mutual attraction or repulsion of magnetic needles, — that it would enable us to form exquisitely in metal casts of all kinds of objects of art, and give workmen a means of performing gilding and silvering without risk to their health, — that it would suggest to the evil-disposed the forging of bank-notes, the sophisticating of jewelry, and be invaluable in the uttering of false coinage,— that it would carry the messages of commerce and friendship instantaneously across continents, or under oceans, and ‘waft a sigh from Indus to the Pole ’!”

It is indeed surprising that the twitching of a frog’s leg should have given rise to all this, and were it not that many other causes conspired with it, we should be disposed to regard the occurrence as little less than miraculous.

Two historical “illustrations” are intended to show the political force of ideas, for the agency of which there is still opportunity in spite of climate. Two ideas, a sane and a crazy one, coming into the

disturbed brain of Mohammed, produce from our author the sketch of a treatise on the “causes of mental delusions,” and other consequences as numerous and important as those to which the twitchings of Galvani’s frog gave rise. Arabian history is made to give “a most striking instance of the impelling power of an idea.” Jewish history, on the other hand, is made to furnish an example of the resisting power of an idea, and many interesting facts and discussions are elicited in connection with the history, though they have nothing to do with the idea illustrated by it. Indeed, the general reader will be much impressed by the author’s great and various learning, though it consists for the most part of information which the press has already disseminated in encyclopedias, gazetteers, and elementary works on science and history.

No work of this sort could be complete, without basing itself on the two great cardinal doctrines of modern science, — the imperishable nature of matter and force, and the order of organic development. These are presented in the vague, paradoxical terms which fit them for the “illustrative” uses they are made to serve. In place of the precise physical facts which these doctrines express, we have vague analogical extensions of them to phenomena of which our knowledge is as unprecise as possible. One of these doctrines is incorrectly illustrated, even within the sphere of its proper and well-ascertained application. We are told that plants are nothing more than condensations of the air, extracts from an invisible and noxious gas, “their parts being held together by force that has been derived from the sun, — force that, as it were, is imprisoned in them, but ever ready to reappear.” But really only a small part of the force which the sun expends in vegetation is represented by the forces that hold the parts of an organism together and in their organic order. This force is chiefly expended in separating the main elements of organic compounds from oxygen; and it is represented by the conditions which keep them sundered from this element, for which they have so powerful an attraction. This attraction represents the intense heat of combustion, and a much greater quantity of force than is developed by the chemical separation of the parts of the plant. Poetical imagery comes in place when the facts of the case are not obscured by it. It might be poetically correct to describe the power of an avalanche as bound, Prometheus-like, to the mountain-side; but to present unfamiliar scientific facts in such images is neither poetically nor scientifically correct. This is, however, of little consequence to the use which our author makes of the abstract ideas and general laws of science. He hastens, like Mr. Spencer, to apply them not so much to a clear elucidation of known phenomena as to a vague description of what he fancies certain phenomena ought

to be, but which exact science is still very far from having adequately investigated.

In spite of the serious defects of thought and style with which this book is marred, it will generally be well received. Dr. Draper, like Mr. Spencer, is a popular writer, and interests us by nearly the same means which have heretofore entertained us in treatises on Natural Theology. The pious or the impressive applications which serve as convenient transitions to new topics of a scientific character, rest the understanding from its pleasant rambles among the wonders of science. The interest is nearly the same, whether the lesson be on Divine Providence or on the force of an inscrutable and irresistible fate. The main interest is in the facts of science and the narratives of history.

Mill on Comte. “The Positive Philosophy of Auguste Comte. By John Stuart Mill.” Boston: William V. Spencer. 1866. 8vo, pp. 182. ²¹ [From The Nation 2.27 (4 January 1966): 20-21.] ²²

This book consists of two essays reprinted from recent numbers of “The Westminster Review,” in which Mr. Mill, as one of the early English admirers of M. Comte, passes in review the two careers of this distinguished philosopher, re stating and vindicating the fundamental doctrines of M. Comte’s earlier work, the “Philosophie Positive,” and breaking, for the first time, the long silence which his English admirers have maintained concerning his later performances.

Mr. Mill’s judgment in regard to the “Philosophie Positive” is that, while it contains a few capital errors, its fundamental positions are essentially sound, and form a valuable original contribution to philosophy; but on the later speculations of M. Comte this judgment is reversed. These are regarded as in the main false and misleading, though filled with valuable thoughts and suggestions of thought in detail.

In Mr. Mill’s first essay we have a very interesting discussion of the doctrines of positivism, both in the larger sense which this word has acquired since its introduction by M. Comte, and in the special sense in which it denotes what was original with M. Comte himself. The foundation of positivism was laid by M. Comte’s predecessors in the school to which Mr. Mill himself professes allegiance, and, though now often referred to under the name of positivism, does not belong exclusively to M. Comte or his followers. This foundation is the doctrine of the relativity of human knowledge, which denies to human intelligence the power to know anything except phenomena and their orders of co-existence and sequence; which denies any other knowledge of causation than the facts of observed invariable and unconditional sequences in the orders of phenomena; and denies any other knowledge of substance than observed permanences in the groupings of phenomena. But M. Comte made this doctrine peculiarly his own by the use he made of it, and by the complete definition he gave of it in relation to older doctrines. This was done in his famous historical law, by which he traced the growth of the clear scientific or positive intelligence out of those earlier forms of philosophic belief which he called the theological and metaphysical philosophies.

Instead of using the term “theological,” Mr. Mill would prefer to speak of the personal or volitional explanation of nature, touching those beliefs which ascribed the events of nature to the volitions of supernatural beings, and he prefers the term abstractional, or ontological, to the term metaphysical, used by M. Comte to designate' those beliefs which ascribe the events of nature to the agency of essences, powers, forces, natures, and occult qualities, or, in a word, to “realized abstractions.” And, instead of the term positive, Mr. Mill prefers phenomenal for its objective aspect, and for its

subjective the word experiential. But while he deems these changes of nomenclature desirable, he recognizes the right of an author to have his thoughts set forth by his critic in the terms, he has chosen. Accordingly, in his further expositions, Mr. Mill adheres to M. Comte’s nomenclature, but proceeds to set free the doctrine from certain misconceptions, which these terms have tended to confirm, not merely in the opponents of positivism, but in M. Comte himself.

Positivism is opposed to the theological conceptions of causation, not because these are proved false, but because they are neither self-evident nor capable of proof, and do not, therefore, involve in them any real knowledge. The volitional explanation of nature, whether in the form of fetichism, or under the more advanced conceptions of polytheism, or even under the final form of monotheism, must ever stand on conjecture and doubtful analogies, and can admit of nothing like proof or verification; and such conceptions are destined, M. Comte thinks, to die out with the advance and diffusion of positive science. With this latter opinion his critic does not agree, but, on the contrary, is anxious to free the essential positions of positivism from any such implication. In his inability to remain on the neutral ground of positivism, M. Comte lacked one of the virtues of a true philosopher, which his critic possesses in a marked degree—the power to maintain that commonly painful mental attitude, a suspended judgment. To entertain open questions was wholly opposed to M. Comte’s tendencies as a thinker, and, accordingly, in his later speculations he does not hesitate to substitute a refined kind of fetichism in place of the current theism, not, indeed, as a true doctrine of science, but as a view of nature which we ought to entertain in our poetical and religious contemplations of it. The barrenness of science, its inability to satisfy the emotional side of our nature, is M. Comte’s apology for the religious speculations to which he devoted his second career; but he is betrayed into calling his religious poetical views of nature by the name of “beliefs,” thus sacrificing, at least in his language, the fundamental position of positivism.

In condemning the metaphysical or realistic explanations of nature, M. Comte excluded from legitimate science much that is called metaphysics, but which ought not to be regarded as such in M. Comte’s use of the word. The science of logic considered as method, and the theory of association in psychology, are omitted from his classification of the sciences, though they do not fall under his description of metaphysical philosophy; that is, they do not suppose any abstract entities or independent realized abstractions as their foundation. Allowance being made for these omissions, his critic accepts his classification of the sciences, and defends its principle from the strictures of his opponents; this principle being to exhibit the sciences in the order of their dependence in their progress towards the positive or purely scientific state. Misconceptions of this classification have arisen, because this dependence does not exist while the sciences are in their empirical stages, and before they possess demonstrable truths.

The most admirable portions of M. Comte’s earlier work, according to his critic, are those which trace out the historical development of society and philosophy. M. Comte’s powers as an historian are second only to his philosophical powers as a systematizer. “Whoever disbelieves,” says Mr. Mill, “that the philosophy of history can be made a science, should suspend his judgment until he has read these volumes of M. Comte. We do not affirm that they would certainly change his opinion; but we would strongly advise him to give them a chance.”

But Mr. Mill “fails to see any scientific connection between M. Comte’s theoretical explanation of the past progress of society and his proposals for future improvement.” Excepting his analysis of history, “he has done nothing in sociology which does not require to be done over again, and better.” M, Comte’s attempts at a reformation of society belong chiefly to his second career, “in which the savant, historian, and philosopher of his former treatise came forth transfigured as the high priest of the religion of humanity.” The essay in which Mr. Mill treats of this portion of M. Comte’s speculations is one of the most admirable of his many admirable writings, and we earnestly recommend it to the serious attention of our readers. As keenly alive as any opponent could be to the ridiculous character in which M. Comte here appears, and really as much opposed to the general aims of his speculations, Mr. Mill does not, therefore, condemn or desert him; but, by an admirably just and discriminating analysis of his writings, seeks to trace his errors to their source, and to disengage from them the substantial merits of his views of social progress and religion.

A peculiar discipline, “hygiène cérébrate,” by which M. Comte kept his mind isolated from the influence of other thinkers in this later career, and a “gigantic self-confidence” in which M. Comte surpassed even those philosophers whom he most nearly resembled, and another circumstance of a personal nature, his passion for Madame Clotilde de Vaux, and her influence in producing in him a “moral regeneration,” explain in part the difference between his second career and his first. But the chief causes of his aberrations were philosophic. He fundamentally misconceived the proper office of a rule of life, an “error which is often but falsely charged against the whole class of utilitarian moralists; he required that the test of conduct should also, be the exclusive motive to it;” that the good of others should be the sole aim as well as the supreme guide of conduct. This error arose from his passion for “unity,” and his belief that all perfection consists in “unity” and “system;” and that the object of all morality is to reduce human life to a system in which there should be nothing arbitrary. All individualism was therefore to be sunk in duty, which should consist of complete self-devotion to the happiness of others; or, in M. Comte’s language, egoism should give place to altruism. The Golden Rule was not enough for him. To do as we would be done by had, with him, the nature of a personal calculation. His morality had, therefore, all the austerity of asceticism, was as rigid as the Calvinism which teaches that “whatever is not a duty is a sin.” Though adopting most of the features of his religious ceremonials from Catholicism, his morality was Protestant in its austerity, with no middle ground between salvation and saintship, no room for conduct which, without being obligatory, might be meritorious.

It is difficult to conceive how a religion which renounces all the common motives and incentives to a virtuous life could be efficacious in realizing any morality, even one less severe than M. Comte’s; “but this is exactly the point,” says Mr. Mill, “on which a doubt can hardly remain in an intelligent reader of M. Comte; and we join with him in contemning, as equally irrational and mean, the conception of human nature as incapable of giving its love and devoting its existence to any object which cannot afford in exchange an eternity of personal enjoyment.”

The later portions of this essay are devoted to an account of the details of M. Comte’s religious observances and rules of life. His love of “unity” and “systematization” and his “frenzy for regulation” carry him to the absurdest lengths; but, in spite of all this, Mr. Mill is willing to allow M. Comte’s own estimate of his rank as a philosopher:

“M. Comte was accustomed to consider Descartes and Leibnitz as his principal precursors and the only great philosophers (among many thinkers of high philosophic capacity) in modern times. It was to their minds that he considered his own to bear the strongest resemblance. Though we have not so lofty an opinion of any of the three as M. Comte had, we think the assimilation just: these were, of all recorded thinkers, the two who bore most resemblance to M. Comte. They were like him in earnestness, like him, though scarcely equal to him, in confidence in themselves; they had the same extraordinary power of concatenation and co-ordination; they enriched human knowledge with great truths and great conceptions of method; they were, of all great scientific thinkers, the most consistent, and, for that reason, often the most absurd, because they shrank from no consequences, however contrary to common sense, to which their premises appeared to lead. Accordingly their names have come down to us associated with grand thoughts, with most important discoveries, and also with some of the most extravagantly wild and ludicrously absurd conceptions and theories which ever were solemnly propounded by thoughtful men. We think M. Comte as great as either of these philosophers, and hardly more extravagant. Were we to speak our whole mind, we should call him superior to them, not intrinsically, but by the exertion of equal intellectual power in a more advanced state of human preparation, but also in an age less tolerant of palpable absurdities, and to which those he has committed, if not in themselves greater, at least appear more ridiculous.”

Spencer's Biology “The Principles of Biology. By Herbert Spencer. Vol. I.” New York: D. Appleton & Co. 1866. ²³. [From The Nation 2.55 (8 June 1866): 724-725.] ²⁴

“The aim of this work is to set forth the general truths of biology as illustrative of, and as interpreted by, the laws of evolution; the special truths being introduced only so far as is needful for elucidation of the general truths.” This first volume consists of three parts; the first, called the “Data of Biology,” treats of the elements, the materials, and their properties which enter into the processes of life, and the ideas which determine its definition. The second, called the “Inductions of Biology,” treats of the various fundamental facts and classes of facts observed in organic life in general, including the main principles of biology as an inductive science. The third part, called the “Evolution of Life,” is a discussion of the bearing of the general facts of biology on the question of the origin of species. In his second volume Mr. Spencer will “pass to the more special phenomena of development as displayed in the structures and functions of individual organisms.” Two other works, the “Principles of Psychology” and the “Principles of Sociology,” will complete the labor which Mr. Spencer1 has proposed for himself, namely, the survey of the sciences for the purpose’ of including all human knowledge under the conception's set forth in his “First Principles,” and for establishing a universal science or philosophical

system on the basis of the inductive sciences, interpreted by certain forms or laws of thought which Mr. Spencer assumes to have an à priori validity and a universal application. These forms are given in the mechanical conceptions of matter, motion, and force, and the à priori truths supposed to he implicated in them. Every fact of science is to be represented in such mechanic terms.

As a philosophical theory this system has also, of course, a theological as well as a scientific side. It proposes a cosmological theory of the dependence of the world of phenomena on its unknown cause. The unknowable, hitherto represented as the Creator producing the world from a non-phenomenal existence, or from nothing; or pictured as the Great Artificer building an order out of chaos, is by Mr. Spencer represented as the cause, the unknown cause, of evolution, continuously producing the worlds and all the forms of life. Evolution is regarded as the profoundest conception which the human mind can compass of the divine agency in creation. The first existence, or the chaos whence the world and its order arise; is the homogeneous or undifferentiated matter of the universe, with its primitive forces and their necessary laws. Creation, or the connection between the first cause of things and the last effects of nature, consists of the processes by which the world passes from the homogeneous to the heterogeneous. This is the direction in which creative power is exerted. It is the unfolding of the properties of matter and force. These terms, matter and force, must he understood, however, in a sense broad enough to include all first existences which are cognizable, and to exclude the antithesis between the metaphysical and incomprehensible entities “matter” and “mind.” The phenomena of mind are also to be formulated in terms of matter, motion, and force; but it is matter in a generalized mechanical sense that Mr. Spencer takes as his type of the first cognizable existence.

If we must have a cosmology—if we cannot restrain our speculative faculties to a less ambitious exercise—then that theory of the universe in its totality which agrees best with the facts of science and the ideas with which science has familiarized instructed minds in modern times, is the one most likely to gain credence. But science itself stands in no need of such illumination. The leading idea of Mr. Spencer’s system, the thread on which he displays a mine of scientific lore, with unsurpassed abilities in scientific speculation, is too weak to sustain its load. Not that his facts in any degree militate against his thesis: they only fail to prove what is peculiar to it. They simply “illustrate” what Mr. Spencer means by his law.

Different portions of Mr. Spencer’s writings have very unequal merit. It is his ambition to produce a philosophy; but his strength lies in his clear summary expositions of the widely various departments of scientific facts and generalizations, with which he has most industriously and laboriously made himself acquainted, and in the ingenuity he displays in the very suggestive and instructive generalizations and colligations of the facts which he presents. In such portions of his writings he is clear and strong, though somewhat too easily impressed by a mere analogy, and sometimes mistaking a figure of speech for a matter of fact. But when called upon to rise into the region of pure abstractions in setting forth his system, and dealing with the ideas to the illustration of which he has devoted so much study, his writing becomes vague and weak. He is obviously not so able in the treatment of the higher abstractions as in the proximate generalizations of science. Where the philosopher would appear at his best, Mr. Spencer becomes very tedious. His grasp of the mechanical ideas by which he would interpret the facts of biology is quite unlike what the masters of mechanical philosophy have shown in the mechanical sciences. His application of mechanical ideas to the organic sciences very much resembles the use made of similar ideas in physics before the time of Galileo. His principle of the “Persistence of Force,” which in his book of “First Principles” he supposes to be the same as the mechanical doctrine of the conservation of force— only a better name for it—has none of the technical precision and definiteness which belong to this doctrine; and the important conclusions, which he deduces somewhat summarily from it, really flow, so far as they are facts, from the more general philosophical doctrine, “the Law of Causation.” Mr. Spencer’s “Persistence of Force” is in fact only a mechanical name for this fundamental postulate of science. In the same way, to suit his system, he renames other principles of science. Mr. Darwin’s law of “Natural Selection” he designedly translates “Indirect Equilibration,” while the principle of the improvements of adaptation by use he calls “Direct Equilibration.”

If this mechanical terminology really added anything to the resources of science; if Mr. Spencer could deduce anything from his mechanical principles which could confirm any inductive conclusion or direct any inductive enquiry, which are not already confirmed or determined by philosophical principles without a mechanical dress, we should welcome his philosophy most cordially. As it is, this mechanical dress seems to us superfluous.

But to return to Mr. Spencer’s lucid expositions of science. No account of the argument for the transmutation hypothesis has appeared to us abler or clearer than part third of this volume. Not even Mr. Darwin’s remarkable hook presents the evidence so conclusively. But Mr. Spencer appears to value this part of his hook and, indeed, all his disquisitions on the “special truths” of science “only in so far as they “illustrate the general truths” of his philosophy. He evidently prides himself on his weakness, and is quite .unconscious of his real strength. All that his studies prove, or tend to prove, is “that the groups within groups” of related races, “which constitute the animal and vegetal kingdoms, have arisen by direct descent, multiplication, and divergence—that is,” he adds, “by evolution.” But evolution implies more in Mr. Spencer’s philosophy than the transmutation hypothesis postulates. It implies and necessitates progress, a progress which is inherent in the order of things, and is more than the continuity and community of causation which the physical sciences postulate. It borrows an idea from the moral sciences, the idea of an end. Mr. Spencer’s philosophy is not teleological in the narrower sense of the word; that is, it does not postulate specific ends—like the conditions of human happiness—as determining the order in nature; but it is none the less as a cosmological theory—or a theory of the universe in its totality—charged with a mission. It contemplates the universe in its totality as having an intelligible order, a relation of beginning and end—a development. All that the transmutation hypothesis presupposes is continuity and uniformity in the temporal order of nature. Mr. Spencer admits that paleontology, the only inductive science which can testify directly on the subject, is inconclusive. So far as inductive evidence is concerned, it is doubtful whether there has been any progress in the types of organic life. That the present forms of life are derived from comparatively few forms living in the remote past, is probable from the argument from classification; but that these forms were the only types of life then in existence, or that the extinction of species has not kept pace with their multiplication, cannot he concluded from the geological record. Transmutation, then, is as well fitted as any word to express all that the evidence of paleontology, the geographical distribution, or the classification of animals and plants tends to prove. The argument, for progressive development from embryology is merely analogical. To be valid it requires a much closer resemblance in essential points between the terms of comparison, namely, between the individual life with its limits and definite steps of progress, and the indeterminate continuity of life in a race. Evolution expresses more than the evidence warrants, and more than many transmutationists are disposed to admit. “It may be thought paradoxical,” says Lyell, “that writers who are most in favor of transmutation.(Mr. C. Darwin and Dr. J. Hooker, for example) are nevertheless among those who are most cautious, and one would say timid, in their mode of espousing the doctrine of progression; while, on the other hand, the most zealous advocates of progression are oftener than not very vehement opponents of transmutation.” . . “The true explanation of the seeming anomaly is this, that no one can believe in transmutation who is not profoundly convinced that all we know in paleontology is as nothing compared to what we have yet to learn, and they who regard the record as too fragmentary, and our acquaintance with the fragments which are extant as so rudimentary, are apt to be astounded at the confidence placed by the progressionists in data which must be defective in the extreme.”

Mr. Spencer is both a transmutationist and a progressionist, but he is the latter on à priori grounds chiefly. No one has set forth and illustrated the imperfections of the geological record more forcibly; but, instead of following the cautious naturalists, and suspending his judgment in the lack of evidence, he takes advantage, as it were, of this lack to reach his conclusion by the “high priori road.”

A philosophy like Mr. Spencer's is doubtless a great desideratum to many, nay, to most minds, to enable them to receive the facts and hypotheses of modern science hospitably. A philosophy once received is a potent source of credence, and makes it easy to admit asserted facts and to entertain hypotheses. That the general belief in supernatural agencies has proved the miracles, and filled the world with fairies, devils, and witches, cannot be doubted. That a general doctrine which excludes all supernatural agency will enable the inductions and hypotheses of science to take a firmer hold on the faith of mankind, is equally certain; but this is not the method in which the facts and - theories of science have been established. An Intellectual virtue, very rare and difficult to attain, the power to go out from all philosophies and preconceptions into the world of observation and fact—the power to suspend the judgment and to scrutinize facts on their own merits—this is the virtue of the scientific, philosopher, and the potent cause of the great change in the intellectual life of modern times.

Review of Martineau’s Essays. “Essays, Philosophical and Theological. By James Martineau.” Boston: Wm. V. Spencer, 1866. ²⁵, [From The Nation 2.60 (26 June 1866): 804-805.] ²⁶

MARTINEAU’S ESSAYS.

Professor Martineau’s essays are remarkable not so much for presenting any new phases of philosophical or theological doctrine, or even of new arguments for the positions of his school, as for the tact and sound practical judgment with which he has measured modern movements of thought and the tendencies of modern discussions, and signalized the principles on which that phase of Protestant Christianity which he represents must make its stand.

To speak with authority—to testify at the same time against ecclesiastical assumption in matters of religious belief, and to meet, on the other hand, the doubts and objections of the current scientific philosophy, it is clear that the theological teacher must, to a great extent, be his own prophet. A reforming religion, which is still a religion, must appeal from one authority to another. As the older Protestantism appealed from the Church to the Fathers and the canonical Scriptures, so the modern extreme of Protestantism appeals from the literal Scriptures to the reason and conscience of instructed and disciplined Christian men and women, as depositories of sacred truth not less authoritative than the historical documents themselves.

But a reason and a conscience that can be thus authoritative, even to the criticism of the sacred Scriptures, must be more than merely receptive or instructed representatives of revealed truth. They must be capable of reproducing it; not, indeed, at once and in the perfection which the truth has attained in the growth of centuries, but still by the instincts which the truth has only quickened and by a power which the truth does not create. Hence an essential philosophical position of that liberal Christianity which would still speak with authority, is that the native and original powers of the mind hold potentially the key to all divine knowledge; that every doctrine which can rightly claim the believer’s assent must find its voucher in the believer’s own instincts; that faith is the most certain kind of knowledge to those who have found their religious instincts answered in their creed. The credo ut intelligam of all religious philosophies means in this philosophy the yielding of the proud and wilful thought to the willing heart—not the trying on of creeds. This philosophy represents the reason as a native power of absolute knowledge, which cannot, however, possess itself of its inheritance save by repeated struggles and by the aid of outward and historical appliances.

Such being the ultimate ground of the religions authority which extreme Protestantism can exercise, it behooves our author, as he clearly sees, to vindicate against all opponents the philosophical doctrine of rationalism. His essays are accordingly directed chiefly against the experiential philosophy, as set forth in its several aspects by Comte, Mill, Bain, and Spencer. In Hamilton’s “Philosophy of the Conditioned,” as applied by Mr. Mansel to religious ideas, he meets his opponents on the theological side, who have come, as it were, by a flank movement over from the phenomenal philosophy into the camp of the ecclesiastics. With this power on its own grounds he does not feel called upon to deal very vigorously; but he battles most manfully against the tenets of positivism, with no loss of faith or courage from being apparently on the losing Bide.

Saving the merit we have mentioned, the excellences of these essays are mainly personal. With a style of most persuasive eloquence and with the sincerity of a clear and open-eyed faith, Mr. Martineau overwhelms by irresistible assault all spiritual opposition, and fails to win the battle only because the doubt he lays siege to is not the doubt of dull or faltering spirits, nor one which can be dissipated, like a mist, with the warmth of zeal and trust. Dealing, as he really does, with philosophers not less clear and earnest in their opinions than himself, his rhetoric is often misplaced. In the midst of keen discussion his meaning vanishes into a cloud, which is none the less obscuring for its brilliant and alluring colors.

The leading essay on “Comte’s Life and Philosophy” has until lately been one of the chief sources of the general English reader’s ideas of the religious character of positivism. Exhibiting great fairness of spirit and as much fairness of understanding as could be expected from a deeply interested opposition, this review yet fails to discriminate the really earnest beliefs of this school from the dogmatic atheism of the theologian's traditional and imaginary opponent.

It appears to be beyond the author’s power of conception and credulity to believe that real excellences of character can be hoped for, and earnestly sought for, without a belief in their actual and present realization in an object of religious veneration. He takes offence at the pretension that the positivist can believe in any object worth his life’s devotion, or that he can aim at the happiness of unselfish pursuits unless he renounces his scepticism and adopts the positions or “constants” of a religious philosophy. On the positivist’s “type of real perfection, below which we must still remain, though it invites our persevering efforts to continual approximation,” he observes: “May we not ask, Where, then, do you find this ‘ type of real perfection above us?’ Is it indeed real to you? Or is it ideal, and that in the poor sense of being merely imaginary?” To this the positivist might answer, “Why is it necessary that we should ‘ find ’ this perfection realized in order practically to believe in its possibility, and to strive for it? Are the savant in his search for a more and more perfect knowledge, and the artist in his efforts to reach a more perfect ideal of expression and beauty—are they necessarily platonists, believers in the supersensible reality of ideals? Religions alone, or rather religious philosophies, postulate as essential to progress an actual contemplation of its end; but to every one who believes in a better than has been attained, the evidence of its possibility lies within the limits of his common human experience. Every man’s sagacity outstrips his understanding, his purposes, and his performance; but does it on that account deserve apotheosis—to be called the reason, and be made participant of the absolutely true and beautiful and good? Or is it on that account evident that the sagacity is not informed like the understanding by experience?”

To the poetical representation of the phenomenon of progress as a growth or an effort to grow in a formative plastic power within us, there can be no exception taken on grounds of poetical truth; but to stake the moral culture and aspirations of the human race on the dogmatic truth of platonism, as our author does, is to limit the highest human interests by the conditions of a personal peculiarity.

Mr. Martineau is platonic in his temperament, like his master the poet-philosopher Coleridge, but his gifts have a more practical turn, and he exerts himself in defence of the à priori philosophy not merely from a poetical instinct, but as the sagacious leader in a school of theology. He grants his opponents large latitude at the outset. All the world of physical science, all phenomena and their laws, are allowed to the experience philosophy. Inductive methods must deal with all these; but then inductive methods cannot take a step without starting from the unprogressive “ideas of causality, of soul, of God, of substance.” If, on account of the unprogressive character of these ideas, the name of knowledge be denied them, the author does not object, “provided it be understood that they are, if not knowledge, the conditions of knowledge; if not the object seen, the light by which we see them.” From these “constants” of religious philosophy he allows no abatement. They are essential articles of faith, and faith is knowledge. At least faith has all the certainty of knowledge, and only differs from it in not being acquired. It is almost a moral offence with our author to regard the principles of causality and substance as empirical generalizations of our experience of the connections of phenomena, or as hypotheses to account for these connections; and it is a sad moral delinquency not to see that these principles are recognitions by the reason à priori of the necessity of such connections. Power as well as phenomena—power as opposed to phenomena—belongs to the province of intuitive knowledge. And there are two distinct sources of knowledge, and both are concerned with all that we know. Physical as well as moral science has its postulate of pure reason. In short, Mr. Martineau lays down the à priori theory in all its purity, and holds to it on practical as well as theoretical grounds as essential not only to a religious philosophy, but also to a religious life; essential, that is, to every nobility of character and to every form of devotion. By those who have not studied metaphysics, these articles of faith are, of course, implicitly assented to, though the disciple may not be aware of possessing two independent sources of knowledge, or be on his guard against the wiles of the experiential philosophy.

It is, of course, important for the author to make out that the apostles of this philosophy are not very admirable men. With Comte the case was not very difficult; but when he comes to the great English champion of this school he speaks with some obscurity and hesitation. He experiences in the tone of Mill’s writings “a singular impression of melancholy and unrest.” But “a certain air of suppression” is the “greatest fault” he finds in him, “and the shade which it passes across his face is sometimes so strong” to our author’s vision “as almost to darken the philosopher into the mystagogue,” as if he regarded the world as unprepared for his lessons. No greater misinterpretation of a most natural and courteous reserve could be imagined; but it is a very instructive illustration of a deficiency of sympathy or insight, which is not uncommon with thinkers of Mr. Martineau’s type of mind. Capable of infinite degrees of the love or the sympathy which looks upwards or downwards in reverent devotion or in tender pity, this temper admits of little real sympathy with what is around it but is not of its own household. Liberal to an extreme towards the opinions of students in science and in Biblical criticism, our author withholds his toleration from whatever interests him “from the moral side,” if it be beyond the pale of the à priori philosophy.

Review of Alden's Elements of Intellectual Philosophy [From North American Review 103.2 (July 1866): 260-269.] ²⁷

Elements of Intellectual Philosophy, By Rev. Joseph Alden, D. D., LL. D., late President of Jefferson College. New York: D. Appleton and Company. 1866. 12mo. pp. 292.

“In an experience of more than a quarter of a century as a college teacher, the author,” as he tells us in his Preface, “found that he was successful just in proportion as he was elementary in his instructions”; and he adds, “If men become familiar with the alphabet of thinking, they are prepared for progress toward profoundness.” But he does not tell us whether his success consisted in awakening a genuine interest in the problems of philosophy, or, as appears more probable from his book, in destroying all the attraction such problems have for the unwearied mind of youth. His book is indeed too elementary, — in fact chaotic, — altogether preliminary to any serious consideration of the problems of mental science. It goes over much ground, and professes to treat no topic exhaustively, but claims that “no topic has received superficial consideration.”

One would naturally expect, from such a mode of treatment, that many questions would be raised for the future consideration of the pupil who was thus inducted into philosophy. But no. There are no questions left for his consideration. Everything is settled by short and easy methods. It is the author’s intention, if this book is received with favor, “to prepare, for the benefit of those who have entered upon a course of philosophy under his guidance, a volume embracing additional topics and more extended investigations.” This volume will illustrate, we suppose, the kind of “progress towards profoundness” which those who have had the benefit of the author’s guidance might be expected to make. Until this appears, we cannot, of course, judge of it; but we gather from the present volume that it will settle some minor details, and allay some subsidiary questionings which a perverse ingenuity might raise, in spite of an elementary discipline in habits of dogmatizing.

The author’s idea of philosophy has the merit of not being new or

original with him. It is a very old and respectable one indeed, and is associated with great reputations; but it is none the less, in our estimation, deserving of reprobation. It would appear from most standard works on mental philosophy, that the science of mind contemplates only the avoidance of dangerous opinions, and the establishment of sound and wholesome ones, — that the questions of philosophy are nuisances, which must be counteracted by those hygienic prescriptions commonly called the elements of mental philosophy. These elements are, in fact, certain dogmas, which owe their existence and importance to the fact that some minds have the insane or uncommon propensity, and sometimes the ingenuity, to transcend, in their inquiries about themselves, the bounds of common sense. Such elements are therefore laid down for the purpose of keeping thought within these bounds, and giving the coup de grace to impertinent problems.

So urgent does this practical side of mental philosophy appear to writers like our author, that they do not stop to inquire whether the problems they settle so summarily are really in contravention of an enlightened common sense: it is enough if they appear to be. And so it happens that mental science comes to consist, in these books, of such facts as the mind already knows about itself and its processes, or can easily ascertain by direct inquiry, but which have for their principle or for the ground of their pre-eminent importance in philosophy the very questions which they set aside. We may, therefore, define the mental philosophy treated of by our author, and many writers like him, to be the art of settling the questions of mental science in an easy and summary manner. This is the alphabet by which the pupil is to be “prepared for progress towards profoundness.”

The author himself gives us no definition of his subject, but introduces it thus: —

“Numerous definitions of philosophy have been given. It would be of no advantage to repeat them. We have a field to explore. It is of comparatively little importance what name we give to the field, or to the process of exploration.

“A perfect definition of a science must include all that belongs to it, and exclude all that does not belong to it. It marks, therefore, the completion, not the commencement, of the science.”

The first of these paragraphs identifies definition with naming, and the second identifies it with exposition; and between the two the author fails to give what is all that is required, sufficient directions about the “field” we have “to explore,” and some notion of “the process of exploration.” These he leaves, perhaps wisely, for the reader to gather. We do not conceive it to be very important to the reader to

be told beforehand what precisely the scope of a treatise is to be; but it is important that the author should know, and we can see no reasons why he could not, in this case, have made an intelligible statement of it, in place of confounding the names, definitions, and expositions of his subject all together in two short paragraphs.

It would be unfair to our author to suppose that he is original in treating mental science as having no problems but such as a perverse ingenuity has raised, and which a sound mind will answer by an immediate reference to what it already knows. This view of the matter has come down traditionally in the school of philosophy to which the author belongs. Traditional misrepresentations of the opinions of the opposite school, put in the form of questions which nobody ever seriously asked, are refuted by virtually showing that the questions are idle and foolish. These refutations, and the discussions and definitions of the terms in which the questions are stated, together with a simple classification of the mental powers, make up the matter of orthodox common-sense philosophy, as presented by Dr. Alden, following in the wake of Hamilton and McCosh.

We will begin our illustrations of this philosophy with the great central question of the cognition of objects external to the mind. On this our author says: —

“Some say we are conscious of the state of mind termed cognition or perception, and of nothing else. We see an external object. The seeing, cognizing, is confessedly a mental act. Of its existence, it is said, we are certain; but we are not certain of anything else. We are not certain that there is anything external corresponding to this state of mind, which alone is the object of consciousness. Thus we have no certainty of the existence of external objects.

“The error contained in the above statement consists in not taking the whole of the conscious state of mind into view. That of which we are conscious is this: we are conscious that we cognize the object. When we say we are conscious that we have a cognition, — a subjective state of mind, — we have not stated the whole truth. Our consciousness embraces the cognition of the object. We are as certain that we cognize the object, as we are that we have a mental state.” — p. 34.

What a satisfactory state of certainty is this, which precludes, of course, the possibility of hallucination, or deception by our senses! But this, though personally convenient, is of little philosophical worth. It omits to take account of the only real philosophical question. This is not whether we have an adequate feeling of certainty in our judgments of external existence, but it is the scientific question, why this feeling can be opposed by a doubt, such as we cannot feel or entertain in regard to our judgments of the internal states of the mind. It is

enough for philosophy that a doubt can be entertained in the one case, though only arbitrarily, which cannot be entertained, even arbitrarily, in the other. This fundamental problem in philosophy our author entirely overlooks, or rather misinterprets, probably through the misrepresentations of it received from other writers. He appears to suppose that the doubt in question is one for the mind to decide upon as to its legitimacy; whereas this doubt, or the possibility of it, is a point to be explained as to its significance, since it lies at the foundation of the distinction between mental states and the existence of external objects.

Philosophy does not begin with a doubt for the purpose of testing its legitimacy; but upon recognizing the possibility of a doubt, its business is to study the significance or the grounds of this possibility. A possibility of doubt in regard to a judgment of externality is the one characteristic which all true philosophers allow as its distinguishing mark, however differently they may interpret the meaning of this mark in their theories of perception. The thorough-going idealist interprets its meaning to be, that there is no certainty, besides the mind’s cognizance of its own states; but the interpretation of most philosophers is, that there is no intuitive certainty except of these states. Even Sir William Hamilton, so far from denying that the possibility of doubt is a discriminating mark of external cognition, has insisted more than any other philosopher on its importance; and he discriminates by means of it between the testimony of consciousness concerning the reality of an external world, and the certainty we have about our own mental states. But our author has removed all cause of contention among philosophers, not by criticising their solutions of this problem, but by sweeping away the problem itself.

The appeal to consciousness for what is ultimate in it is legitimate in philosophy only when made critically, that is, by such rational procedures as will enable us to distinguish between what is really simple and what is apparently so, like those effects of constant association which resemble ultimate elements of knowledge. Sir William Hamilton has laid down rules, though inadequate ones, for such criticism; and even Dr. McCosh, many of whose opinions our author adopts, proposes what may be regarded as tests for determining the ultimate facts of consciousness, which are, however, of little philosophical worth. But our author does not appear to be aware that any discussion is required in criticism of the natural dogmas of the undisciplined mind. He simply dismisses the real problems of philosophy, and adheres to the crude dogmas of common sense.

With the main problem, which we have noticed, he dismisses, of course, all the subsidiary ones. Thus he says: —

“Some philosophers have labored hard to discover how the idea of externality — of something external — is first acquired. It is acquired when the mind cognizes an external object. Whenever the mind cognizes an object out of the mind, it cognizes it as out of the mind. No one in cognizing a material object by means of sight or touch ever cognized it as a modification of his own mind, or as existing within his mind.” — p. 35.

This is carrying common sense in philosophy to an extreme. We doubt if its most ardent advocates would claim much authority for its judgments on a question in philosophy, when it so far mistakes the purport of the question as to propose the complete realization of an idea as an explanation of its origin. Nobody ever questioned that the idea of externality is already acquired, when the mind discriminates from its own states any existence as an external object. But though “no one in cognizing a material object by means of sight or touch ever cognized it as a modification of his own mind,” yet it is contended that the elements of which such cognition consists may, nay, must, at one time have been indistinguishable from mere mental states, and that they become what they are simply by their combinations and their relations to other mental states. “Suppose,” says the author, “a person destitute of all the senses except hearing. Let a violin be sounded near him. What would be the effect on his mind? He would cognize a sound; and he would cognize it as external to his own mind.” This would depend, we imagine, on his previous experience of sounds, — on whether they had generally occurred in connection with other and previous mental states, just as anger and fear do,—or had always arisen from bodily conditions, like hunger and thirst, — or, thirdly, had remained dissociated from any of these, and had generally occurred without any reference to them. These are the ways, we suppose, in which sensations get referred to their classes, and finally, in the development of perception, come to lose their importance as sensations or as pleasures and pains in their greater importance as the signs of external or foreign sources of other pleasures and pains. For the idea of externality involves the function of sensations as signs, either in their simplest state, or more commonly in combinations, in which they become inseparably associated; and their proper function as signs is to produce a state of expectation with reference to the things signified, without being themselves the objects of any expectation. A sign must occur inconsequently; else it is more properly called a cause or an antecedent merely. In being as a sign unexpected, the idea has the mark of externality in it; and by producing a state of expectation it possesses the mark of reality, and is thus the sign of an external reality.

The test of the idealist’s sincerity which has been derisively proposed,

namely, that he should run against the objects in whose absolute existence he does not believe, and learn by the pain they will cause him the error of his creed, is indeed the very test the idealist allows of that external reality in which alone he does believe. For bodily pains and pleasures are real, — simply real; and their causes or antecedents, when known in perception, make this perception real also. Simple sensations are real, and so arc invariable sequences, and hence a knowledge of their antecedents must be a real knowledge. If such cognitions, while happening in no constant relations to antecedent states of the mind, are yet found to have an order among themselves, the mind soon comes to apprehend this order in the course of experience under the form of the general laws and ideas of external nature. But what is the external object, and how is it distinguishable from the group of sensations which constitute the cognition of it? In most systems of idealistic philosophy, this object is regarded as an external something, of which the idea or the group of sensations is regarded as the sign. This we believe to be an inadequate account, since, so far as an idea is a sign at all in a cognition, it is the sign of the unknown cause, not of itself, but of other actual or possible sensations, the existence of which as pleasures or pains constitutes the reality and the efficiency of the cognition; and the general expectation of these sensations is our general sense of an external reality. The idea is not a sign of an external existence numerically distinct from itself and a counterpart of itself, but only a sign of the sources of those other mental states which as real pleasures and pains can be expected as concomitants or consequences of it. In this consists the difference between the occurrence of an idea in a real cognition, and its recurrence in the representations of memory or imagination. In the latter form the idea loses its real externality, since it is no longer the sign of real pleasures or pains, present or inferable as consequent upon it. The idea in this form is also in itself less distinct as a group of sensations, so that relative distinctness becomes a secondary mark of reality. But reality essentially consists in the connection of an idea with concomitant or consequent pleasures and pains. In dreams the secondary mark is present, though the essential one is absent, and this discrepancy is the source of the surprise which we often feel in dreams in not suffering the consequences which our apparent cognitions lead us to expect. There are thus two marks of reality in a real cognition, —distinctness and real significance; and there are two corresponding objects, — the mental one, or the cognition itself as a state of the mind, and the existence of the external source of what it really signifies or reveals. Of the first we are immediately conscious, and cannot doubt its existence, since it is presented in itself as a state of the mind; but of the second object there may be a doubt, as in dreams or hallucinations.

The question of philosophy in regard to this doubt is not whether it is as legitimate in our waking moments as it is in our dreams; and our author answers no real question in philosophy by his assertion that “we are as certain that we cognize the object, as we are that we have a mental state.” What he really does is to overlook one of the most indisputable facts which philosophy has to consider, namely, that there is a difference in respect to our capacity to doubt between the external and internal objects of cognitions.

The next problem which he proceeds to suppress is the more special question of the origin and ultimate elements of the ideas of extension and space. “We get the idea of externality through all our senses; but not in all cases the idea of extended externality. A distinction is to be made between externality extended and unextended.” (p. 36.) This is the best that he has to say on this question. What follows in the next chapter, instead of being an explanation of the mode in which we get the idea of extended externality, or any account of the distinction between extended and unextended externality, is only an appeal to consciousness for facts which have no bearing on the subject. It is no explanation of the origin of the idea of extension to say, “that the mind cognizes extension and form by means of the eye, that is, cognizes extended and figured objects by means of the eye.” (p. 38.) But this is all that the author offers in the way of positive science on the subject. He objects, on the flimsiest grounds, to the several attempts at explanation which have been made. To the doctrine “that we get the idea of extension and figure by the sense of touch, and that those ideas are, by association, transferred to our visual perceptions,” he says: “So far is this from being clear, it is doubtful whether any accurate idea of figure could be gained by the sense of touch alone. Let one be blindfolded, and then let an object different from any object previously seen and handled be presented to the sense of touch, and he will form a very inaccurate idea of its figure.” It is surprising that the author should have overlooked the accuracy with which the blind discriminate forms by touch; but tactual determinations of figures should not be confounded with their visual representations, and the author misrepresents the theory he is criticising if he supposes that the sense of touch was ever regarded as competent to give by itself anything like visual images to the mind, or to do more than inform the vision of the tactual significance of visual marks. The author appears to conclude, because an untrained touch alone is inadequate to take the place of trained vision in a blindfolded man, that therefore the touch could have been of no service in training the eye to produce visual images of extension.

On the more probable doctrine, that the notion of extension is the joint product of sight and touch, (including, we should add, muscular sensations,) the author cites the following argument: —

“Some admit that we can cognize extension by the eye, but deny that we can cognize figure, that is, solidity, length, breadth, and thickness. That we now acquire a knowledge of solidity by the eye is, it is said, the result of inference from our experience gained by the sense of touch. It is admitted that we seem to cognize solidity by means of sight, and, in reply, it is said that we seem to cognize distance by the sense of sight, whereas our cognition of distance is an inference or judgment.”

To this the author replies, “Now we affirm that we do cognize distance by means of the eye.” By which he means, of course, that the cognizance is by means, of the eye alone, and that it is an immediate, simple, inexplicable act; else his statement would be an irrelevant and trifling one. He does not tell us, however, whether this immediacy is known on the authority of consciousness, or in some other way; but he obviously thinks that he has a right to affirm it, and that the burden of proof rests on those who deny it. For he says, “Those who deny this assume that in all our primary perceptions by sight all objects appear equally near”; and adds, “This is a mere assumption. Memory does not reveal to us our primary perceptions.” There is so much of truth and significance in this last remark, that we are surprised that the author did not make a better use of it. It is, indeed, a mere assumption to assert that at any time, in the development of vision, objects should have appeared equally near; but as an assertion essential to the theory which the author is criticising, it is an assumption of his own. And the opposite assertion, that at all times, in the growth of our visual powers, objects must have appeared at unequal distances, is also a mere assumption, concerning which memory does not inform us. There is, indeed, a third alternative more probable than either, namely, that antecedently to our conjunct experiences of light and tactual and muscular sensations no notions of extension or even of externality were attached to them. There is no presumption, therefore, or burden of proof in the matter, and the author’s dictum, “that we do cognize distance by means of the eye,” is of no authority on the question. The only direct authority is in a memory which is silent on the subject, and hence the question is one for science and indirect inference to deal with. The facts of physiological and optical science, together with the psychological doctrines of association, are thus the real foundation of the doctrines which our author proposes to reject in his summary way by a dictum of consciousness.

That the eye by itself, that is, the optical apparatus and the retina,

independently of muscular sensations and movements and tactual perceptions, cannot give the means of discriminating what we do discriminate in vision, and cannot afford the ground for inferring relations of distance, or even externality, from the sensations of light, is a position in mental science which must he regarded as demonstrated. And we further believe that, with these auxiliary sensations, movements, and perceptions, all the mental phenomena of vision can be adequately accounted for. This is one of the problems of mental science. The following is the author’s way of disposing of it: —

“It is asked, How, since the image on the retina is inverted, do we see objects upright? The reply is, we do see them upright. This we know. Why the physical conditions of perception are as they are, we do not know. A similar answer may be given to the question, why, when there is an image of the object in each eye, we see but one object. Some recent discoveries in optics reveal in a measure the connection between binocular vision and the cognition of form.” — p. 39.

This reply, that “we do see objects upright,” is in fact no answer at all to the question the author proposes. Who has ever doubted this? The question is not one of fact, but it is a demand for the explanation of a fact. Equally irrelevant is the remark, that “ we do not know why the physical conditions of perception are as they are.” The question is not one of final causes, but it is the scientific inquiry concerning the mode in which these physical conditions are conditions, in consequence of which, and not in spite of which, the perception is realized; and this explanation is not so very far to seek as the author appears to think. Indeed, the only difficulty in the problem comes from the mistake, often made, of supposing that the images on the retina are cognized in themselves as extended objects, instead of being simply, in their several and ultimate parts, the means of cognizing the parts of the real external and extended objects.

In the last sentence which we have quoted, the author intimates that science has done something towards solving the problem of binocular vision. Some account of this would have been to the point, but the author is content to assure his pupils that their confidence in the fact itself of vision cannot be improved or impaired by any explanation, since the fact of seeing a single upright object, though it be by means of two inverted images, rests on the infallible testimony of consciousness. What sort of ideas of a true mental science can such an assurance communicate? None, we think, but the erroneous ones, that science undertakes to explain a fact by disputing it, and that we ought therefore to be contented to affirm the fact without trying to explain it.

Such is the elementary instruction which the author has found to be

the most successful by an experience of a quarter of a century, and now thinks worthy to be presented to the public. Our illustrations of his method, though taken from his earlier chapters, are sufficiently characteristic of the whole work, and make it unnecessary for us to say more.

Review of Mill on Hamilton [From North American Review 103.2 (July 1866): 250-260.] ²⁸

An Examination of Sir William Hamilton's Philosophy, and of the principal Philosophical Questions discussed in his Writings. By John Stuart Mill. Boston: William V. Spencer. 1865. 2 vols. 12mo. pp. 330 and 354.

The value of this most searching examination of Sir William Hamilton’s writings, and its enduring interest as a contribution to philosophy, separating it widely from the short-lived publications of the season, are sufficient apologies for calling our readers’ attention to it at this late day. In one respect, indeed, the work is a very timely publication, and in this it exhibits a literary skill of no ordinary merit. The position and present reputation both of the author and his subject are such, that the mere announcement of the work was sufficient to inspire with the liveliest curiosity every student of philosophy.

The writings of Sir William Hamilton have been so long published, that they have had a fair chance to gain a hearing, and to gain such prepossession of thinking minds, that their critic was sure of an intelligent and deeply interested attention, if not of an unprejudiced one; and his criticisms are the more effective, since they are not obliged to inform the

reader for the first time of the issues in question. They fall upon very widely known and popular opinions, which the influence of Sir William Hamilton has organized into a school of considerable extent, both in Great Britain and America. The recent prominent position of Mr. Mill in the political world has doubtless drawn the attention of many to this work who were not acquainted with his previous philosophical writings and his position among British philosophers.

Barely in the history of philosophy has so excellent an opportunity been so judiciously used. What will interest the reader most is, in fact, only incidental to the main object of the work, which is to define and justify the opinions of the school of philosophy usually accounted unorthodox, of which Mr. Mill is the principal adherent among living English thinkers. He has taken this occasion to develop his views on several fundamental questions in philosophy, which have only appeared incidentally in his previous works. “My subject,” he says, “is not Sir William Hamilton, but the questions which Sir William Hamilton discussed.” The reader will, however, retain most vividly the impression that the work is a masterly polemic against the opinions and the influence of the man whose acknowledged abilities as a teacher of philosophy have produced an erroneous impression of his powers as a thinker. In this his critic has wisely pursued a policy which is a secret of success in all controversies, as well in philosophy as in practical politics, — the policy of taking the offensive. On the critic’s success in discrediting an acknowledged authority in philosophy rest, in great measure, the chances of his own opinions to gain a hearing; and they have the additional chance in such a mode of presentation, by challenging comparison, to gain a fair hearing.

Such a course was the more desirable, because the philosophy of Sir William Hamilton, while it retains most of the positions essential to orthodoxy, appears to adopt from the opponents of his school their strong points, and to reconcile them with the authorized religious or orthodox philosophy. The principal doctrine which Sir William Hamilton thus seems to adopt from his opponents is the doctrine of the relativity of human knowledge. This doctrine teaches that knowledge, even in its highest exercise, is only a cognizance of states of the mind, and that our faculties can recognize these only as effects on us, produced, we know not how, by powers we know not what, — that any other natures than such mental states cannot be cognized at all, or recognized as other than the unknowable, which we may suppose to exist, but cannot suppose to be in any manner comprehensible. Idealism and sensationalism both postulate this doctrine; and Sir William Hamilton, apparently adopting it also, attempts nevertheless to refute these philosophies. This at least appears to be the main issue of Mr. Mill’s criticism.

It is certain that Hamilton adopts this doctrine to the extent of affirming that the known implies a something unknown, which is necessarily supposed as the ground of its reality, or as the unknown cause of the objects of knowledge; and he calls the knowable phenomenon an effect. The real difference between him and his critic appears to us to be, that, while both recognize the coexistence of a something known and a something unknown in every act of real knowledge, Mr. Mill, with the idealists, identifies this antithesis with the distinction of the ego and non-ego, the known effect being with him an effect on us by an unknown cause in the non-ego; while Hamilton does not regard the two distinctions as coextensive. That things in themselves as absolutely and necessarily existing or as uncaused cannot be known to us, is what we understand to be Hamilton’s doctrine of the relativity of knowledge; but this does not signify, with him, that the objects of knowledge are effects on us. On the contrary, he regards the evidence of our immediate cognizance of a non-ego to be quite independent of this doctrine, and by no means inconsistent with it. With Hamilton, the relativity of knowledge does not decide the fact of an immediate knowledge of a non-ego in a phenomenal external world, but only determines the character of this knowledge, as a phenomenal one, relatively, not to the ego, but to the real existence of the external world itself.

The difference between Hamilton and Mr. Mill may be reduced, we conceive, to a difference in the meanings they attach to the word “phenomenon.” With Hamilton it has an extended meaning; so that the phenomenal scarcely signifies more than that existence which necessarily implies some other, of which it is the manifestation, — some hidden existence necessarily inferred, though in itself unknown. But with Mr. Mill the word seems to signify more specifically a mental state, implying some cause which is not a mental state. The doctrine that all knowledge is only of phenomena will of course admit of two different interpretations, according to these two meanings of the word. With Mr. Mill’s or the idealist’s meaning of the word, it follows that an immediate knowledge of a non-ego is impossible. But if Hamilton’s more extended use of the word be admissible, then an existence non-ego may be immediately cognizable consistently with the doctrine of the relativity of knowledge, provided this non-ego be phenomenal, that is, necessarily dependent on some other incognizable existence among the real causes of things. Whether Mr. Mill has failed to discover the precise significance of Hamilton’s use of this word, or, regarding it as inadmissible, has chosen to hold him to the authentic meaning, does not appear. If the latter was the case, we conceive that the criticism might have been made more to the point. Mr. Mill takes issue, however, on what he conceives

to be an inconsistency between two portions of Hamilton’s writings, —bis theory of the perception of the primary qualities of matter in his notes to Reid, and his doctrine of the relativity of knowledge in his Lectures. This is the chief issue of the book; but if the meaning of the word “phenomenon” which we have attributed to Hamilton be a valid one, his philosophy escapes from this criticism by affirming that the primary qualities of matter, that is, the having extension, figure, etc., though not cognized as the effects of matter on us, are yet modes of existence implying an unknown substance, and are hence phenomenal in Hamilton’s meaning of the word.

We think it would have been proper enough to object to Hamilton’s description of these qualities as effects, in any other sense than as effects on us, — a description which confounds effects with attributes; but instead of discovering this confusion, Mr. Mill supposes that Hamilton meant to represent the primary qualities of matter as effects on us, while he inconsistently ascribed to them an existence independently of us. In the criticism on Hamilton’s theory of causation, Mr. Mill does indeed discover a confusion corresponding to this, but he misinterprets it. In this theory Hamilton confounds cause with substance, in a manner analogous to his confounding effects with qualities; but while Mr. Mill has clearly pointed out the fact of this confusion, he has failed, we think, to discover its significance or its origin in the point of view of Hamilton’s philosophy. Just as Hamilton extended the application of the word “phenomenon” beyond its use by the idealists, so did he with as little warning extend the word “cause” to denote, not merely one of the essential elements of an event, but also to mean any existence, whether known or unknown, without which neither a quality nor an event could be manifested. With Hamilton a cause signified more than the necessary antecedent of an event. It meant that which makes an antecedent necessary, and without which qualities neither appear nor change. While he denied that a cause in this sense could in itself be known, he maintained that, as implied in all phenomena, it is known as the unchangeable determinant of all changes, and as persisting through change and under all phenomena. The metaphorical phrases and the illustrations by which Hamilton set forth this view of causation, representing the constancy of cause by the law that an effect is equal to the sum of its causes, and that the sum of real existences in causation remains unchanged, are so far misinterpreted by Mr. Mill that he supposes not merely that Hamilton confounded cause with substance, but also the efficient cause with the material, or the cause of changes with the substance which is changed. On the contrary, Hamilton is far from confounding the existence which determines with that which is determined,

or the invariable attributes of the latter with the immutable substance of the former, or the physical law of the indestructibility of matter with the metaphysical law of immutable causes, — as Mr. Mill appears to think.

Perhaps in this case also Mr. Mill has chosen rather to hold his author to what he conceives to be an authentic use of terms, than to try to discover the consistent though metaphysical significations in which Hamilton used them. At any rate, in following the course he did, he has made Hamilton appear sufficiently contradictory and absurd, as if his aim were, as we have intimated, rather to discredit the authority of his author than to ascertain and criticise his real doctrines. Thus Mr. Mill says that,

“According to Sir William Hamilton, when we say that everything must have a cause, we mean that nothing begins to exist, but everything has always existed. I ask any one, either philosopher or common man, whether he does not mean the exact reverse; whether it is not because things do begin to exist, that a cause must be supposed for their existence. The very words in which the axiom of causation is commonly stated, and which our author in the first words of his exposition adopts, are, that everything which begins to exist must have a cause. Is it possible that this axiom can be grounded on the fact that we never suppose anything to begin to exist? Does not he who takes away a beginning of existence take away all causation and all need of a cause? Sir William Hamilton entirely mistakes what it is which causation is called in to explain.”

We think, rather, that Mr. Mill has entirely mistaken what it is that Sir William Hamilton calls in for this explanation. His problem was to explain the beginnings, the persistence, and the endings of things as phenomena, or as they are known to us, and in their relations in their orders of necessary sequence. This Sir William Hamilton proposes to explain by the doctrine that things, not as phenomena, but in themselves and in their real existence, do not change; and he grounds this doctrine on his law of the conditioned, the really central and characteristic position of his philosophy. With this law, and not by its own merits, must Hamilton’s doctrine of causation stand or fall. The unsoundness of this law, which Mr. Mill has sufficiently exposed, is in postulating judgments concerning what, by their very nature, cannot be the subjects of judgments, namely, things in themselves. But this will appear more clearly in what follows.

Mr. Mill’s criticism of Hamilton’s law of the conditioned, and of the methods followed by Hamilton and his school, are by far the most effective portions of the work. Kant had taught concerning things in themselves, that their existence in an intelligible world and the possibility

of an intuition of them as noumena, that is, independently of sensuous perception, could be held only as problematical. Such a possibility of knowledge could neither be asserted nor denied from the conditions of possible experience, and neither proved nor disproved from the data of intuition. Sir William Hamilton, holding substantially the same view of a knowledge of the absolute, but rejecting Kant’s analysis of the conditions of experience, and his ideal affirmation of ontological beliefs, attempts by a profounder classification of possible realities to prove, while refuting the positions of the absolutists, that we may legitimately hold for true what we can neither conceive as possible nor know by intuition; for logic itself compels us, he thinks, to assert one of two contradictory propositions, and to deny the other, concerning things in themselves, each of which alone might be merely problematical. Hence he held that there are possibilities, neither proved by the capacities of thought nor by those of intuition, which can yet be held for true. These he called the Unconditioned. Those possibilities which experience and its conditions determine he called the Conditioned. The laws of logic, disclosing the limits of the conditioned, make known, according to Hamilton, the existence of the unconditioned, or that of which the possibility cannot be conceived. But how does logic disclose these limits? By showing that of two contradictories, neither of which is contained within the conditioned or the thinkable, one must be true, and hence that truth transcends the thinkable.

Mr. Mill elsewhere, and on wholly different grounds, also rejects conceivability as a test of possibility, and so far agrees with his author. He was, therefore, concerned only with this point of difference, namely, Hamilton’s doctrine that, while truth may transcend the thinkable, belief may transcend it also. This he refutes, by showing that there is no validity in applying the laws of logic except to the thinkable. To the Unconditioned — to things in themselves — the laws of logic cannot be presumed to be applicable. Of phenomenal existences, it is true, the laws of logic cannot be denied; but the antinomies on which Hamilton’s doctrine of the Conditioned is founded are propositions about things in themselves, or else they are propositions which are not really inconceivable. Infinite space or duration, for example, may mean that space or time, as known or conceived by us, is without bounds or determinate magnitude. This is perfectly intelligible, and the contradiction of it is conceived as false. But about space and time in themselves, what does infinity, or limitation, or even magnitude, signify? Instead of being, as Hamilton represents them, inconceivable predicates, they are known predicates affirmed of inconceivable subjects. It is not the predicate infinity which it is impossible to conceive, but, according

to Mr. Mill, it is space in itself, since this cannot be made the subject of any judgment.

The extreme inadequacy of our conception of infinite space as a phenomenon is virtually the ground on which Hamilton affirms the inconceivability of infinity as predicated of space in itself, or of any other existence, whether noumenon or phenomenon. This inadequacy amounts to impossibility, according to Hamilton; and he consequently affirms that the conception of infinity is simply the notion of the impossibility of conceiving a magnitude without bounds, — that such a conception is only the negation of conceivability itself as applied to magnitude. But Mr. Mill contends that an infinite magnitude, since it is conceived as one greater than any finite one, implies more than the mere negation of conceivability. It is only partially inconceivable. To say that an infinite magnitude is greater than any other is a positive statement, though we can say or think no more about it. It excludes all we can think definitely and adequately, but it does so in a determinate manner, namely, by affirming that the infinite is greater than the finite. It affirms the direction of the exclusion; and this notion of the infinite is true, as far as it goes, of the space and time known to us. In other words, we know that the space and time of our apprehension exceed any measurable or assignable magnitudes. But how do we know this? Simply because we have found no limits, — not because we cannot conceive of any. The impossibility of conceiving a limit to space is, according to Mr. Mill, a psychological consequence of our experiences of spaces, and proves nothing save by representing these experiences, which are the real sources of all our knowledge of space. The affirmation of infinity is then only a denial of limits to the space of our experience; and it cannot, therefore, be made about what is by hypothesis beyond our capacities of experience, or about space in itself. On the other hand, the denial of infinity is an affirmation of limits; and since this is not given in our experience of space, or in its possibilities as determined by capacities acquired through experience, it is not conceivable at all, either of phenomenal space or space in itself. Space in itself cannot, therefore, be conceived as either limited or unlimited, since the subject is inconceivable. And, on the other hand, space either in itself, or in relation to us and our experience of it, cannot be conceived as limited, since this predication is inconceivable. But if both the propositions are about space in itself, the necessity of admitting one and denying the other, or the impossibility of any third inconceivable supposition, rests on no evidence of experience or acquired limitation of thought, such limitations being already transcended in the subjects of the propositions.

Hamilton holds, of course, that the unconditioned, the subject of his antinomies, is inconceivable, but he denies, in common with nearly all philosophers, that the laws of logic are determined or limited by experience; and with these premises, his main argument is irrefragable. But of these premises the absolutists deny the former, and Mr. Mill the latter. Against these extremes, therefore, his argument is inconclusive, but it follows from the premises of Cousin and many other philosophers. But Mr. Mill not only objects to Hamilton’s application of the ordinary rules of reasoning to propositions about things in themselves, but he joins, as we have seen, with the rest of Hamilton’s critics in opposing his subsidiary arguments, or those for the inconceivability of infinity in general as affirmed of anything. Hamilton attempts, in these arguments, to establish contradiction between inconceivables by an appeal to phenomenal experience itself. He asserts of space, as we know it, that limits and the absence of limits are equally inconceivable, and he therefore attempts a proof of the existence of the unconditioned from the facts and laws of the conditioned itself. The fallacy of this attempt Mr. Mill has sufficiently exposed. Either space, as we know it, has limits or it has no limits. In rejecting, in accordance with experience, the first supposition, we both affirm and conceive the last; but in attempting to realize this fully, we find our faculties inadequate. This inadequacy of conception does not amount, however, to impossibility, unless we attempt to transcend space as we know it, and to conceive of an absolute space, about which nothing whatever is knowable or conceivable. But about this we cannot, then, legitimately appeal to phenomenal experience.

Incidental to his discussion of the law of the Conditioned, the interesting distinction of knowledge and belief, which Mr. Mill does not regard as an important one, is briefly criticised. According to him, knowledge and belief differ only in the degrees of their certainty, or else in the degree of the simplicity and directness of the evidence on which they rest. We fully agree with him in rejecting Hamilton’s doctrine, that belief can rest on any other basis than one of knowledge; but we think it important to scrutinize more closely a distinction which has played so conspicuous a part in religious philosophy. While opinion, belief, and knowledge differ from each other in respect to the degrees of speculative certainty with which anything is held for true, yet these degrees are specifically distinguishable from each other in the philosophical uses of the words. There are, indeed, four distinguishable forms of holding for true, namely, opinion, belief, contingent knowledge, and perfect knowledge; though the limits between the second and third are not precisely fixed by usage. Perfect knowledge cannot be

questioned. It admits of no possible doubt. Contingent knowledge admits of a possible doubt, though not of any actual one. Belief, though not consistently distinguished from the latter, may be limited to what might be questioned on grounds of evidence, though it is practically unquestionable through restraints imposed on our speculative faculties by our moral or practical nature. Such beliefs can be held with an equal degree of certainty with knowledge, though with a certainty of a different kind; being indubitable on account of the limits imposed by the conditions of emotion and the determinations of the will, and not on account of limits from conditions of experience. Such are religious beliefs, which, though inferior to knowledge in speculative certainty, may equal it in practical certainty. And, lastly, opinion is distinguishable from a low degree of simple belief, since it is free from either of these restraints, and admits both of speculative and moral doubts.

The importance of these distinctions comes from the philosophical doctrines they embody; namely, the two orthodox positions, that the difference between science and faith, and the difference between experiential or contingent, and perfect or a priori knowledge, are fundamental ones. Both these positions Mr. Mill rejects, and he departs from orthodox philosophy on the issue, that any beliefs can rightly be held, except on grounds of positive experience, or with a confidence which these do not warrant.

Next in importance and in the order of treatment to the criticisms we have noticed comes Mr. Mill’s examination of Hamilton’s methods and arguments in treating the various topics of phenomenal psychology. The meaning and authority of consciousness, and the rules for its interpretation, are discussed in a manner as much superior to anything which has preceded it on method in psychology, as the philosophy of the modern physical sciences is to the Physics of Aristotle. The fundamental problem of psychology is to determine which of our knowledges are ultimate and which can be supposed to be derivable by intelligible mental processes; and to discriminate these is the object of method in mental science. “The Introspective Method,” by which Mr. Mill designates the method of Hamilton and his school, is a direct appeal to consciousness on this problem, regulated by certain precautions, by the use of which the philosopher is supposed to be superior to the vulgar. By the use of such precautions, Sir William Hamilton proposed to prove, against most philosophers, the vulgar opinion that the external world is an object of immediate perception; and he does this virtually on the ground that the opinion itself seems to a mature consciousness like an axiom, and that the supposition of its truth does not contradict any other fact of consciousness. This is the gist of Hamilton’s

argument. As well might the analogous fundamental question of astronomy, Which moves, the earth or the heavens? be decided, in like manner, by an appeal to the senses.

This comparison suggests a remarkable resemblance between the methods of modern physical science and the “Psychological Method” which Mr. Mill opposes to such an appeal to consciousness. A common characteristic of them is to employ hypotheses, that is, verifiable hypotheses, in order to supplement the facts of observation before deciding upon such questions as the rotation of the earth, or the ultimate simplicity of a fact in consciousness. If the question of psychology had been to determine which of our knowledges are ultimate and which are derived by such mental processes as are cognizable in the present operations of consciousness, the Introspective Method would have been complete. But then a further question would require answer. Are there not present states of consciousness apparently simple, but really the results of past and long-forgotten mental processes? Have not, for example, our present ideas of externality and extension such an origin? Introspection of present consciousness cannot decide this; but this is the real question between Sir William Hamilton and the idealists as represented by Mr. Mill. Just as the analogous question of astronomy was decided against the vulgar in the Copernican system, so a really scientific application of the ‘‘Psychological Method” decides against the vulgar on this question; and as the dynamical laws of matter placed the Copernican system on a firm, irrefragable basis, so the mental laws of association are made the foundation of idealistic psychology. For if the ideas of externality and extension can be shown to be derivable, though not by present or remembered processes, yet by intelligible ones, they cannot be regarded as simple merely on the authority of present consciousness. The only limit to the application of the law of inseparable association as an hypothesis to explain the origin of ideas from simple feelings, must be in its inability to make this genesis distinctly intelligible; and here is the weak point of associational psychology, and one in which, with its present attainments, it fails to resemble the science of astronomy with which we have compared it. But Mr. Mill and Mr. Bain (whom he quotes on several points of interest) have done much to show how this failure may in future be remedied, when psychology shall have come out completely from that region of dogmatic metaphysics in which Sir William Hamilton leaves it, to become one in the sisterhood of the modern sciences.

Mr. Mill’s criticisms of Hamilton’s logical doctrines are not less fundamental than those on his metaphysics and psychology. Very few indeed of the opinions which are original or essential to Sir William Hamilton

find acceptance with his critic. But this is not surprising, when we see how fundamentally their philosophies differ. What will surprise the reader most are the numerous contradictions and inconsistencies in Hamilton’s writings which his critic has pointed out. The principal of these we have tried to explain as arising from misinterpretations of his doctrines. There are enough remaining, however, to greatly impair his reputation, before unchallenged, for profundity and accuracy, and even for scholarship.

Review of The Workman and the Franchise [From North American Review 103.2 (July 1866): 241-250.] ²⁹

The Workman and the Franchise. Chapters from English History on the Representation and Education of the People. By Frederick Denison Maurice, M. A. London and New York: Alexander Strahan. 1866. 8vo. pp. 244.

The representation and education of the people, and what relations the House of Commons have borne in the past to the English people, are the questions which Mr. Maurice ponders in these lectures. No one could be better qualified for such a study, so far as sympathy with his subject and the heartiest devotion to the labor of regenerating the English working classes can avail. But Mr. Maurice is too much the clergyman, too little the scientific historian, to make his work of much value to any one who is not ready to accept his opinions from confidence in the excellence of his heart.

To decide a priori between political creeds, — to estimate the moral soundness of a watchword, party-cry, or political theory by the tests of sentiment, —this is to take part in history, to throw the weight of one’s personal influence into the one or the other scale, but it is not to weigh history. However broadly philanthropic and disinterested our motives may be, we cannot thus gain an insight of those real causes, grand utilities, inevitable necessities, which the actors of history feel rather than understand, and which only the perspective of history can disclose to scientific analysis.

Writers like Mr. Maurice deal only with the external phenomena and the proximate causes of historical events, with the reasons which were calculated to stimulate or control zeal and heated passions, with the maxims which have served to concentrate the attention of confused understandings, and with the personal characters of historical agents. The causes which produced these, or gave them historical prominence, lie deeply obscured in the most difficult of the subjects with which scientific methods will have to deal in real history.

The survey which Mr. Maurice gives us of English political history, while it is too rapid and sketchy to present the dramatic interests of this grand movement, is too much in the style of ordinary histories to give us any clear ideas of the causes that

determined it. The principal thesis of the lectures is, that the word “people” has always meant in English polities, not the “fragments” which Caius Martius, in Shakespeare’s Coriolanus sends to their homes, not the mere multitude, which has nothing but numbers, but the “organized” classes. Organization is, according to Mr. Maurice, the basis of the representation which has hitherto prevailed in the English political system. Manhood, it is true, is indirectly the ground of the right of representation, but it is not manhood displayed in the units. Individuals have a right to a voice in the government only as they and their fellows have the virtue, power, and manhood to organize themselves, and to become conscious of their true interests as a class. Mr. Maurice, therefore, so far as he favors the further extension of the suffrage at all, would limit it, not to classes arbitrarily determined by property qualifications, but to spontaneous organizations representing real interests, or to co-operative societies. The success of the English volunteer militia movement suggests to him the kind of organization to which he would be willing to extend the suffrage.

There is much significance in the general doctrine which Mr. Maurice sets forth, but not much, we think, in his special interpretations and application of it. Organization is a rather vague term. In one sense, no human society is unorganized. “Man is more political, than any bee or ant.” He is the political animal. What Mr. Maurice calls the “fragments” of society, the multitude which he thinks most dangerous to civil order, would, were they really unorganized, be in the aggregate the most inefficient of bodies. Each member, bent on his own individual aims, unconscious of co-operation, would be only one of the disorderly with whom the police have to deal. Divide et impera would be the method of dealing with them.

But such is not the character of the multitude from which the state has to guard itself, either by skilful legislation or by force. It is only so far as the multitude is organized, that it becomes at all formidable. This multitude has so often appeared in European politics to great disadvantage, has so often been the dupe of knaves or fools, that great folly and moral baseness have got to be associated with it. Mr. Maurice

ascribes these qualities to the majority. He exclaims against conforming to the will of a majority, “So help me God, I do not mean to follow the will of a majority; I hope never to follow it, always to set it at naught.” In the light of American politics we judge this character of baseness to be erroneously imputed to the majority as such. Not only the many who in England feel their unity and common cause in their misfortunes or wrongs, but any class of society, the lords, the knights of the shire, and the burgesses of the town, when similarly placed, have also exhibited folly and brutality, and have violated the public order to overthrow oppression or opposition. Why then has immorality been affixed to the multitude as an essential and permanent quality? It is because the many have nowhere, except in America, ever been allowed in an organized capacity to display any other traits. As a preacher, Mr. Maurice is, of course, predisposed to divide the world into good and bad, and classify mankind on ethical principles; and on no other ground can we account for his horror of a majority. He appears to think it impossible for the majority ever to be right and the minority wrong, else he would not have committed himself to a rule which in practice might easily involve him in the greatest immorality.

With such sentimentality is naturally associated an opposition to utilitarian ideas of morality; and, accordingly, our author goes on to say, “And for that expression about the ‘greatest happiness of the greatest number.’ I do not understand it. I have no measure of it. I cannot tell what happiness is, or how it is to be distributed among the greatest number, or how the greatest number is to be ascertained.” If Mr. Maurice could do all this, if he could understand and measure and discover all that this maxim demands, he would surpass all the prophets and lawgivers whose instructions have blessed mankind. But it is obvious that he does not understand how the maxim is meant to be applied, for he adds, “If it could be put to the vote of the greatest number what they would have for happiness, I have no security that they would not decide for something profoundly low and swinish.” This method of ascertaining the greatest good is not implied in the utilitarian’s maxim; nor, on the other hand, is it the object of

democratic governments to consult the majority as an oracle. The will of the majority and the good of the majority are confounded neither by the democrat nor by the utilitarian. Would Mr. Maurice contend that the will and judgment of a monarch are always right? Of course not; but would he deny then, that, imperfect as it is, the monarch’s legal exercise of his will and judgment is the best policy for the state? Majorities are only the monarchs of democracies, not their prophets.

The course of politics in America has been, on the whole, so much smoother than in Europe, real grievances and imperfections of government so much sooner remedied, and measures of reform so much more thoroughly and promptly tried, that political theories have had less opportunity to gain the character of moral or religious causes by a rankling repression in the moral consciousness. Governmental institutions have, therefore, gained with us more and more the character of expediences. Our revolutionary maxims are not held with such worshipful zeal that we cannot see in the course of our history the solid grounds of utility which have been the real though unseen motives of our political career.

That the actual causes of historical events should be sought for, not merely in the reasons assigned for them by the agents through whom they are brought to pass, or in the political creed which is given in justification of them as political measures, but should also be sought for in the special conditions and necessities by which the political society of the time finds itself constrained, is a proposition so obviously evident, when stated, that we do not conceive it to stand in need of any proof. Communities, like individuals, act from many motives, but assign as the reasons of their actions such considerations as are calculated to give dignity and moral weight to them.

It is natural and proper that motives should stand in our practical philosophies in the order of their moral dignity, whatever may be the order of their practical efficiency. Active benevolence is justly claimed, for example, as the motive of a beneficent action, though this may have been dependent also on some less dignified motive, — on some selfish impulse of temporary convenience. If, therefore, in history we seek for political causes in the conveniences and expediences of society, as well

as in its declarations of political principles, it is because the efficient causes of its action are not always or exclusively moral.

The more prominent or moral motives of political action assume a utilitarian character or a sentimental one, according as the action is in pursuance of conservative or of revolutionary measures. Revolutionary ethics always appeal to moral sentiment, and in the announcement of first principles are likely to put out of sight or to subordinate unduly the occasions which bring these principles to notice and secure for them the requisite attention. The discovery or the first clear appreciation of a principle of action is much more likely to be regarded as an inspiration, than as an historical effect of social antecedents; since it is by its force as a sentiment that a principle is efficacious at times when its force as a rule of expediency depends on the logic of events.

It is therefore only when a policy is in the course of a peaceful and normal development in human affairs that its foundation in the actual necessities and conveniences of society becomes prominent, or even distinctly apparent. In the storm of revolutionary passions, morality takes refuge in those sentiments to which religious and revolutionary ethics have ascribed the validity of its precepts. Utility becomes a mean consideration, and is impotent against the violence of passion; but its maxims are secured, in the absence of calm reason, by the force of moral feeling. Hence it is that revolutions bequeath maxims and first principles clothed in wit and eloquence, rather than in rational discussions or scientific explanations of political measures. In later times, in pursuance of these measures, men come to regard them more and more in the light of expedients, and to refer their validity and the conditions of their application to those exigencies of society which were their real though unseen origin.

The principle of universal suffrage, and the more general doctrines that the governed have a right to a voice in the administration of public affairs, and that just governments only exist by the consent of the governed, are maxims for which utilitarian reasons exist, though they are often regarded as first principles, sanctioned by a sense of justice or by enlightened moral sentiment. But those who regard them as fundamental

truths see clearly that they have never attained to that dignity in the practical workings of our political institutions. Any limitations of these principles, save by equally fundamental considerations of justice or necessity, are properly regarded as offences, if they have in truth the character which revolutionary ethics claim for them. Those who hold that the right of suffrage rests immediately on a moral basis urge consistently that the suffrage should be extended, not only to all male citizens, but also to women, and to whoever in fact is morally and mentally competent to exercise the function; and these theorists also appeal consistently to the professions of political faith with which our history and political documents abound. But if we waive the reasons assigned by our Revolutionary statesmen, and interpret their wisdom by their acts in relation to the exigencies of their times, we shall find in these a sufficient justification of the existing extension of the suffrage, and reasons also for its further extension, with proper limitations, without the necessity of admitting the doctrine which would condemn our present short-comings as moral offences.

The non-existence of a governing class sufficiently self-conscious and united, and sufficiently powerful in its command of the moral and physical forces necessary to keep in subjection other classes of society, is the condition either of social anarchy, or else of the intervention of that enlightened, public-spirited good-sense and capacity for self-government which our forefathers showed in their Colonial history.

This capacity for self-government in every class of citizens, and a command of the last resort, the war power, by small communities in their militia organizations, which were first required for self-defence against hostile neighbors in the border life of new settlements, and, more than all, the fact that few representatives of the governing class were among the earlier settlers, and soon lost whatever prestige they may have brought from the mother country, — these facts were the conditions which made democracy a feasible scheme of government in America. But these conditions were compelled to assume a new aspect when the Colonies began their quarrel with the mother country. The possibility of such a form of government, or even its actual existence, was powerless against the

moral force of prescriptive rights and long-sanctioned usages, when fairly brought in conflict with them. These conditions required a moral force sufficiently powerful to cope with the sentiments of loyalty and respect for the past. The right of self-government in every class of citizens, and the right to use the war power which they actually possessed, and, above all, the rightful equality of all citizens before the law, had to be asserted, not merely as desirable political results, which the Colonists had substantially realized, but as morally binding principles, to which all mankind owed obedience. And this was a fair issue; for so long as conservatism and prescription rely on sentiment, so long must revolutionists be prophets. To “Thus saith the law,” the only answer is, “Thus saith the Lord.” The divine right of the people exists so long as the divine right of kings has any power in the world. The utilitarian grounds by which both rights might be justified under their proper conditions, and by the philosophical historian, were not inspiring considerations, and required calmer thought than passion permits.

The success of the Colonists in arms secured the conditions of the existence of democracy in America, which had come to be regarded, however, by the dominant party with the feelings that the Revolution engendered, that is, in the light of moral principles. The demonstrated capacity for self-government in the American people was interpreted as a right to self-government in all classes of mankind; but this principle was not consistently carried out, as we have said. What was really pursued were the two ends, to abolish a governing class proper, or one whose interests could be opposed permanently and systematically to the interests of the governed, and to incorporate into the body politic every possible class whose interest might be dangerously opposed to good order and the stability of the government. American politics sought to shun two opposite dangers, — dangers to the governed from the supremacy of any class, and dangers to the government by the exclusion of any class which might have sufficient unity, self-conscious power, and independent interest to attempt the same kind of revolution which the Colonists had themselves sanctioned, and which other American republics have repeated without end.

This was not indeed the view which successful democracy took of its new responsibilities. It did not profess to aim at strengthening a government inherently weak by conciliating all possible hostile classes and disaffected subjects with participation in the government, nor to prevent political power from falling into the hands of a class whose just right to govern could be denied only on the ground of its inability to govern justly. This would have been to confess weakness and distrust, which, though real and efficient motives, were not so worthy or inspiring as those of the new political ethics. The right of mankind to self-government, though practically signifying only the right of white male adults to hold office and take part in elections, was a broad, positive moral ground of action; and, so far as applied, tended to the same results as the inferior motives. As a moral principle it was doubtless essential to the success of the great experiment, and was a far truer doctrine than the equally sentimental conservatism which it defeated. But the inferior motives were satisfied with the limits to the extension of the suffrage which have actually obtained, and which are in direct conflict with the higher principle. Honest and uncompromising believers in this principle are justly scandalized at the inconsistent disfranchisement of women in all our States, and of negroes in most of them. It has been a sufficient consideration, however, in practical American politics, that women, though a natural class, could never become a political one with distinct interests to be defended, or with a possible ability to defend them for themselves. Nay, it has hitherto been a sufficient consideration with the greater number of the United States, that the negro, though standing in urgent need of protection from the cupidity and prejudice of the white citizen, was unable to help himself or injure the state.

But while our people have thus disregarded the integrity of the maxims of their political creed, have they therefore acted wholly from selfish motives, and without reference to moral ends? Or is it not true, rather, that their faith in this creed has never been so entire and uncompromising as some political orators would have us believe? The peaceful and normal pursuit of politics tends, as we have said, to give to principles of

action more and more the character of rules of expediency; but it does not necessarily convert them into maxims of a narrow, short-sighted, or selfish expediency. Utilitarianism has its unselfish principles as well as sentimental ethics. The distinction is, that these principles are not rules or commandments or maxims of conduct. They are rather the objects which rules subserve and by which a maxim must be justified. The greatest good to the greatest number, or the greatest sum of human happiness, or by whatever phrase we seek to generalize these ends, are not rules of conduct, but tests of rules: they are not sources of moral maxims, but criterions of them. But utilitarianism does not forego the sanctions of moral sentiment. It removes the sanction from the rule or commandment to the reasons for them; and these reasons are not the more general principles from which practical maxims may be deduced, but are the ends, in various forms of human excellence, for the accomplishment of which the rule must be contrived, and with reference to which it may be altered or disregarded. In considering how far rules may thus be dealt with consistently with a sound morality, a source of great confusion in the discussions of moral philosophy should be noticed. This is in the fact that one of the greatest of human excellences is in the having rules of conduct, and in pursuing them steadfastly; this being the essential condition of the realization of any higher good. The twofold error has been committed by those who distrust the utilitarian spirit, of attributing to it an omission or denial of this excellence, and of assuming, in opposition to it, that morality consists essentially in what is only a condition of its realization, namely, in conscientiousness or fidelity to principles. Fidelity to bad principles makes one a “man of principle,” no less than fidelity to good ones. This fidelity is not a source of enlightenment, but at best is only a condition of receiving enlightenment, and fidelity is the better condition in proportion as the ends which rules subserve are made its objects, rather than the rules themselves.

American politics have not ceased to aim at the benefit of mankind and the greatest good of the greatest number, however lamely these ends may have been pursued, and in spite of our want of faith in the political creed of the last century.

This creed is indeed a thing of the past, beyond recall, but with it political morality has not perished. This survives under a new and more enlightened form. The right to have a good government, and to secure to the machinery of government all the conditions necessary to this end, takes the place of the asserted fundamental right of self-government, except so far as this is seen to be one of these conditions. The value of self-government, when possible, is more truly appreciated now than ever before, since it is prized for what it is worth; namely, for that degree of good sense, public spirit, and self-restraint in any people which makes self-government possible, and thus makes it a means of educating the people to higher degrees of these good qualities.

It is upon such considerations as these that the question of the suffrage ought to be discussed, for it is upon such grounds that it must be decided.

Review of The Differential Calculus [From North American Review 103.2 (July 1866):233.] ³⁰

The Differential Calculus: with Unusual and Particular Analysis of its Elementary Principles, and Copious Illustrations of its Practical Application. By John Spare, A. M., M. D. Boston: Bradley, Dayton, &Co. 1865. 12mo. pp. xix., 244.

An eccentric work, written in execrable English, and meant to help the tyro over the elementary difficulties of the Calculus by a profusion of practical problems, in which “the work aims at cultivating and prolonging the enthusiasm of the student, by clothing his conceptions of quantity in the garb of romance, or something of a supposable human experience. These conceptions may, with the more interest, be erratic and fanciful as to economical life, without ever filling or exhausting the generality of pure mathematical conception.”

The difficulties which this work is fitted to overcome are so idiosyncratic, that it will fail, we think, to meet the common needs of the student, who will find superadded to the difficulties of “pure mathematical conception” the perplexities of the author’s practical problems.

“The present treatise on the Differential Calculus is believed to be the first, of any character, that has been written and published in America as the special topic of a volume; and the first, so far as known to the author, ever published, that professes the character of the present one.” It must be conceded that there is a sort of negative merit in the self-restraint which has saved the Integral Calculus from the author’s romantic explanations. We can imagine no other reason why the limits of the work should be mentioned, but for the purpose of apologizing for them.

The author thinks he has proved that several American treatises are at fault in their treatment of certain elementary problems in the Calculus; but he is generous enough not to expose them by name.

Ennis on the Origin of the Stars. “The Origin of the Stars, and the Causes of their Motions and their Light. By Jacob Ennis.” New York: D. Appleton &Co. 1867. 12mo, pp. 385. ³¹, [From The Nation 4.90 (21 March 1867): 231-232.] ³²

The author of this book has undertaken to explain the origin of the motions of the universe without having qualified himself for so great a task by so much as even making himself acquainted with one of' the simplest and most elementary of the laws of motion. He may have read in the course of his somewhat extensive researches that “action and reaction are equal” in all the known causes of changes in motion; but he has signally failed to understand what this law of motion truly signifies. And of the more recondite mathematical deductions from this and the two other laws of motion he appears to be quite unconscious.

That the mutual actions by attraction, repulsion, collision, and friction between the parts of a body or a system of bodies cannot change the motion of the centre of gravity of the body or system, or change the average movements of revolution about this centre as measured by the description of areas; or, to take concrete examples—the facts that a body cannot be raised from the earth by any terrestrial force without a depression of the earth by the same amount; that a body cannot be moved along the surface of the earth or around its centre of gravity without pushing the earth backwards by the same amount; that a railway train, whether moved by traction or by its own weight on a downward grade, cannot bring its freight to its destination without also turning the earth backwards by as many tons per mile; that a bird rises on the air only by forcing downward the air and the earth, and can only move forward by forcing the air backward by as many ounces per foot; that a sparrow cannot fall to the ground without raising the earth by an equal amount—these facts are elementary examples of laws of motion which, though we cannot presume the general reader to be familiar with them, ought to be known to any one who should undertake to discuss the mechanical problems of the “nebular hypothesis.” Yet the author of this book has attempted, in utter defiance of the laws of the “conservation of areas,” to account for the origin of the movements of revolution in the

solar system and in sidereal systems as results of the mutual gravitation of the parts of the nebulous masses, which he does not hesitate to believe were the primitive forms of these systems. And he has done this not only in defiance of the elementary principles of motion, but also against the authority of all the best writers on the subject with whose judgments on this question he is acquainted. He appears to regard these judgments as mere opinions, or as confessions on the part of the writers of their own inability to account on the nebular hypothesis for the origination of these movements; and ho therefore proposes by his contributions to remedy what he justly regards as a great deficiency in the hypothesis. But unluckily, instead of accomplishing what previous writers have failed to do, he has failed to see what previous writers have really accomplished, namely, the demonstration that the movements of revolution in the solar system could not have originated, as the author believes, in the interactions of the parts of the system, whatever may have been the original form of the system, and whatever the nature of forces of interaction, provided these have obeyed from the beginning the universal laws of motion.

Nothing further, therefore, requires to bo said about this part of our author’s treatise. But this is not the only thesis on which he has opposed himself to the world of living scientific authority as well as to scientific demonstrations. He proposes to go backward and revive the antiquated doctrine that chemical action is the cause of the light and heat of the sun and the stars; and to this doctrine, and its various relations, he devotes the greater part of his volume.

As in his other doctrine he attempts to do away with an insurmountable defect in the nebular hypothesis, so here he proposes a theory in opposition to its only demonstrated sufficiency. Though gravity cannot account for the motions of revolution in a system of bodies, it is able to account for the light and heat of the heavier masses like the sun, and this by the strictest of physical demonstrations, in which nothing is hypothetical except what the author regards as established—the nebular genesis of the sun and the stars. Once grant the author's premise, the nebular hypothesis, and by the strictest reasonings on mechanical principles, as extended by recent researches in physics, it is shown that the falling forces of the matter of the contracting sun are sufficient, or at least vastly more competent than any known chemical action, to account for its light and heat. As he reasons in one of his theories in contravention of the principle of the “conservation of areas,” so in the other he is at issue with the principle of the “conservation of power,” a principle which, though not so universal in its applications to the phenomena of visible motion as the former, has become, by the extension given it in the modern “mechanical theory of heat,” of equal validity and extent.

Of this principle the author has at least learned the name, though it is evident he does not understand it. By a confusion of the two things expressed by the word force, namely, a tendency to produce or arrest motion, and the special conditions, including the tendency, by which the production or arrest of motion is rendered possible, our author has arrived at the conclusion, in opposition to the “law of power,” that “force may be annihilated.” The force of gravity is nullified, he thinks, when a body rests on the ground and is prevented by the earth's surface from falling further. But in this confusion our author does not stand alone. Several eminent physicists have failed to comprehend, on account of this ambiguity in the word force, the application of the “law of power” to the phenomena of gravity. The law that no “power” can be extinguished except by being replaced by an equivalent “power,” whether in the form of a motion or as a special new condition for the production of an equivalent motion, does not apply, it is true, to gravity as mere weight in a body and irrespective of the body’s position. The position of the body, its height above the earth’s surface, is a factor in the measure of the “force” of gravity, as the word is used in this law. In view of this ambiguity Dr. Mayer has proposed to limit the use of the word “force,” and to define gravity or the simple weight of bodies not as a “force” but as a “property” of matter; and he proposes the name “falling force” for the “forces” into which gravity enters as a factor, as in the “force” exhibited by a body when placed unsupported at a height above the ground. Not only the weight but the height of the body enters into the conception of “force” thus limited and defined. But, in spite of Dr. Mayer’s clear exposition of this principle, our author has totally misconceived him. He says: “Mayer regards gravity as a property of matter, and not as one of the forces capable of conversion and reconversion.” In fact, Mayer proposes “falling force” as the name of the conditions for the production of motion into which gravity enters as a factor, and he does this simply to avoid an ambiguity of language, and not on account of any difficulty in the theory.

But the author says “the theory of the conservation of force is yet in its infancy.” He cannot, then, be aware that, so far as the relations of “falling forces” to the “living forces” of motion are concerned, the doctrine is almost as old as the theory of gravity; or that, by the recent extension of the doctrine to the force of heat, it is made equally extensive in all astronomical problems with the principles of the “conservation of the centre of gravity” and the “conservation of areas,” and is thus sufficiently mature to have inherited the problems which the author proposes to solve without its aid and in defiance of it. It is at least sufficiently mature in the minds of the most eminent modern physicists to discredit the “chemical theory,” which, in his ignorance of the doctrine, the author has attempted to revive.

Review of Ennis' Origin of the Stars [From North American Review 104.2 (April 1867): 618-626.] ³³

4. — The Origin of the Stars, and the Causes of their Motions and their Light. By Jacob Ennis. New York: D. Appleton &Co. 1867. 12mo. pp. 385.

This book is full of errors of fact and fallacies of reasoning, and yet will probably not be challenged by one in ten of its readers for either of these defects. The author appears sufficiently well informed and sufficiently well disciplined in the matters he discusses to avoid the criticisms of common-sense and ordinary information on scientific subjects. But this is all. The questions he discusses require for a competent handling an expert’s discipline and knowledge, in both of which the author shows deficiencies which would be surprising were they not so common in writers and lecturers on such subjects.

The implicit confidence with which statements of scientific facts and arguments are received by the readers of popular scientific books and by popular audiences now-a-days, is like that which was once accorded to the assumptions and argumentations of theological writers and speakers. Such trust was then, as it is now, creditable to those who entertained it, inasmuch as the statements and arguments were opposed by nothing in the listener’s own experience, and no motive was apparent which could induce his instructor to mislead him, or to state with confidence facts which are not really known, or to offer arguments which are not really valid. On the contrary, the seeming motive both in theology and science is a genuine love of truth, uncorrupted by selfish ends. But how often is the real motive an egotistical love of opinion instead of truth, and a narrow advocacy of prejudices!

With, a pleasing naïveté our author confesses himself a believer in the “nebular hypothesis.” He entertains no doubts on the subject, and is confident that no doubt will remain in the minds of his readers, especially on those features of the theory which are original with himself. But a clear, open, enthusiastic advocacy of a scientific position, especially of one which is generally discredited, affords to the more cautious students of science a prima facie presumption against an inquirer’s competency. Advocacy is a method adapted peculiarly to practical questions, in the discussion of which truth is not the only, or even the main object; since some decision, authoritative at least, if not true, is often demanded for the occasions of future conduct in practical matters. Not so in science. Its questions can afford to wait and forego the dubious advantage of one-sided discussions, since no practical issues follow from the facts of science until they are ascertained beyond dispute. An enthusiastic defence of a belief, though often admirable in practical matters, since it is often a defence of truth against authority in practice, has no place in positive science, and dwindles to the proportions of a narrow, often obstinate, advocacy of mere opinion.

Accordingly, the better sort of writers on the “nebular hypothesis ” love rather to discuss it for what it is really worth as a means of concatenating and co-ordinating certain facts of science, which otherwise in the present state of our knowledge would remain outstanding problems. So unsatisfactorily, however, has this function been fulfilled by the nebular hypothesis, that the best later writers regard it as an hypothesis of which the best that can be said is, that it is not likely soon to be supplanted by any other. Our author quotes a long list of writers who have acknowledged one of the most serious defects of this hypothesis, namely, that the mutual gravitation of the parts of the supposed original nebulae could not have caused the motions of rotation and revolution which exist in our solar system and in some of the compound stars, and that these motions or their equivalents in rotation must have existed in the supposed original nebulous masses. It is upon the characters and relations of these motions in the solar system, and among the members of sidereal systems, that the main argument for the nebular hypothesis is based; namely, that the characters and relations of these motions imply a common origin. To get beyond this first step, the hypothesis has been obliged to assume, not only that all the matter of the solar system, but also the resultant of its motions of revolution about its common centre of gravity, existed in the supposed diffused mass of the nebula;

since it is one of the fundamental principles of mathematical mechanics, — the principle of the “conservation of areas,” — that no “rotation area” can be added to or subtracted from the amount existing in any independent body or system of bodies through the mutual actions of its parts, whether these actions arise from gravitation, collision, or friction. This principle is an immediate deduction from the primary laws of motion, and especially from the third, the law of the equality of action and reaction in all mechanical phenomena.

It would, therefore, naturally be supposed that our author quotes this list of authorities in proof of the position that the total “rotation area” of the solar system existed entire in the supposed original nebula. But this is not at all his object, which appears rather to be self-glorification, — to show what an array of scientific genius he has triumphed over, by solving the problem which has baffled them all! He has proved to his entire satisfaction that the mutual gravitation of the parts of an irregularly shaped but originally quiescent nebula will result in its rotation, and his argument deserves a place among the curious paradoxes with which inventors of perpetual motion, anti-Newtonian heretics, and squarers of the circle have enriched the literature of science. Though not so palpably absurd, it is still of the same character as the efforts of the man who should essay to lift himself by the straps of his boots.

That the weight of a gravitating body can be converted into a motion around the centre of gravity of the system to which it belongs, is clear to the author from certain familiar examples on the earth. Sliding down an inclined plane, the motion forward and around the earth’s centre which a train of cars, for example, acquires by its own weight on a downward grade of a railway, or the forward motion of a bird descending on the air, — are not these cases of the conversion of falling forces into motion around the centre of gravity? Such is the author’s argument. That he should have overlooked the fact, patent in the most elementary analysis of so simple a problem as the inclined plane, that one component of gravity in the sliding body urges the inclined plane, or the masses on which it rests, by the same amount backward, as the other component urges the body forward, is truly surprising in a teacher of the natural sciences.

By no such movement can a surplus of motion be produced in any direction about the centre of gravity of a system, or indeed about any other fixed point in space. This follows almost immediately from the law that action and reaction are equal in all kinds of mechanical phenomena, — in attractions, repulsions, collisions, and frictions. The “conservation of areas” and the “conservation of the centre of gravity” are twin doctrines of mechanical philosophy, equally fundamental,

precise, and extensive in their applications, and are among the most certain of the laws of nature. Equally proper would it have been for the author to argue that an irregular shape in the original nebula could have transferred it en masse to a new position, or caused a motion in its centre of gravity, as to argue that such a shape could have set it spinning on its axis.

We are aware that a majority of readers are as much “in the fog” as he on the subjects of our author’s speculation, and this is our apology for taking so much space in noticing a book which otherwise would scarcely deserve a notice. We desire to warn the reader against fallacies which would greatly intensify the fog. Let us suppose, then, since mechanical principles experienced in the actions of our own muscles are best brought home to our common sense, — let us suppose that a living human body could be placed at rest in the midst of the stars, removed from any sensible influence from other bodies. Let the muscles play as they may, let the man writhe and plunge, contract and expand his limbs as much as he can, he will find, on assuming any fixed posture, that he has not changed his position one iota, nor acquired any continuous motion; and on relaxing his muscles, he will find that he still faces in the same direction, and that his head and feet still point to the same invariable poles. Action and reaction have always and everywhere been equal. No more can a nebulous mass acquire a motion of translation or rotation by the mutual actions of its parts. The motions produced by the falling in of its parts on the contraction of the nebula must always balance each other by current and counter-current, or be converted by friction and collision into heat, which is only another form of balanced motions, the minute molecular vibrations of bodies. But the “areas of rotation” must in the aggregate forever remain unchanged.

If we could suppose two living bodies, instead of one, placed as we have supposed, but within reach of each other, these two could turn each other round in opposite directions, and push each other apart or draw each other nearer to their common centre of gravity, but no unbalanced rotation around this centre and no motion of this centre could be produced by their mutual action. In the same way, if two nebulæ, instead of parting company, as is commonly supposed, should continue to act on each other, they might by supposable forces or supposable conditions of gravitative action set each other into opposite rotations, like opposite vortices in water; or one nebulous mass might acquire opposite and balancing vortical movements in its internal and external parts. We throw out this hint for the benefit of our author and others who may be disposed to pursue the subject further.

Having staked his reputation on the mechanical thesis which we have examined, our author omits to consider, if indeed he is aware of, the several other mechanical difficulties which recent and more careful investigations of its mechanical conditions have found to beset the nebular hypothesis; such as the facts that the nebulous rings of this hypothesis could not have equal angular velocities or rates of revolution on their external and internal parts, and that, if broken at all, they would most likely be broken into many parts; and the fact that the planets or planetoids so formed would revolve on their axes in directions opposite the actual rotations of the real planets.

The author sacrifices the only real triumph, the most satisfactory result, of the nebular hypothesis, to another of his pet theories, in which at the present day he almost stands alone, namely, the theory that the origin of the heat and light of the sun and the stars is “chemical action.” The “establishment” of this theory occupies the first part of his volume. The one triumph of the nebular hypothesis is the explanation it has afforded, in the hands of modern physicists, of the constant and almost unlimited production of light and heat by the sun, which the geological periods would appear to demand. If the sun can be regarded as at present in a state analogous to its supposed parent, the nebula, and to be still contracting, the falling force thus brought into action — which cannot, as our author erroneously supposes, be converted into rotation, but which must be exhibited by counter-currents or balanced motions about the centre, and finally be converted into heat — this falling force would be sufficient to supply all the energy expended by the sun’s radiations if the contraction of the sun’s diameter should only amount to one part in twenty millions in a year, a rate so slow as to be insensible in its effects on the sun’s apparent diameter from the earliest observations to the present day. This conclusion is not a matter of conjecture or opinion, but matter of demonstration. All that is hypothetical about it is the supposed present contraction of the sun at the given rate. The rest follows according to the best ascertained and most universal of the laws of nature. But while holding to the hypothetical nebulous part of the proposition, as matter of certainty, our author ignores or is ignorant of its unavoidable conclusion; and holds to the “chemical theory” of the origin of cosmical light and heat, as the only adequate one, the only objections to which are “unfounded assumptions.” He is confident of his readers’ assent to this position, when they have duly weighed his arguments. Throughout he argues as if the subject were not, as it really is, involved in the densest obscurity. All that appears to him requisite for the establishment of the “chemical theory” is the removal of the objection which he discovers

to rest on “ three unfounded assumptions.” This objection is, that the chemical theory is inadequate, — that there is not fuel enough in the sun to support combustion for so long a period as the sun is known to have shone. This appears, first, from the known amounts of heat given out in combustion by known chemical elements and compounds; secondly, from the known conditions which modify these amounts; and thirdly, from the known limits of the matter of the sun which can be supposed to be combustible. The author sums up his answer as follows: —

“I have shown that this objection — the want of fuel in the sun — is unfounded; for it proceeds on the three unwarrantable assumptions. In opposition to the first assumption I have shown that it is possible, and even probable, that the materials of the sun, pound for pound, give out far more heat than those of the earth. In opposition to the second assumption I have shown that it is possible, and even probable, that, in the vastly different conditions of chemical action in the great central orb of our system, more heat may be given out by the very same materials than in our small furnaces. In opposition to the third assumption I have shown that it is possible, and even probable, that by the action of the physical forces at work in the process of chemical action and condensation, new fuel may be constantly prepared to keep alive the burning of the sun.” — p. 205.

In other words, to the positions which are assumed in accordance with all that is certainly known of combustion, the author replies by assuming a great deal of which we know and can know nothing with certainty; and he calls this demonstration!

If we reason at all from science about the origin of things or about phenomena beyond the reach of scientific tests, we should confine ourselves to what we know most pertinent to the matter. If we may call in ad libitum what is “possible,” or “even probable,” on vague analogies, because we have not yet arrived, or cannot arrive, at any certainty, then we may as well free ourselves altogether from the limitations of science, and build as widely and freely as fancy may choose.

The author appears throughout his argument to regard the “objection” he combats as one supposed to disprove, instead of one which merely discredits, his theory. There is no question of absolute proof or disproof involved in the matter, and the real objection to his theory is untouched by his discussion. It is this. Chemical forces as we know them are not only inadequate, but vastly more inadequate for the production of cosmical light and heat than two other known sources of heat, under the conditions presented by the sun and similar cosmical masses. One of these sources would exist in the contraction of the sun’s mass supposed by the nebular hypothesis, through the enormous falling force which would thus be brought into action; and the other

would have effect in the supposed fall to the sun of meteoric masses. Both of these, when tested mathematically in accordance with known laws of nature, are found to exceed vastly the known resources of combustion, even if we modify these as much as we can, in accordance with conditions known to affect them. Indeed, there is no real alternative between the chemical and the mechanical theories of cosmical light and heat. There is only a question of priority; and this should be decided, if decided at all, by what we know, and not by what we may be ignorant of.

We have no space to illustrate adequately the author’s numerous and curious misstatements and errors in science; but one instance pertinent to the case in hand may suffice. He says: —

“The idea that by chemical action a pound of matter of any kind all over the universe, and under all possible physical conditions, must give only the same amount of heat as a pound of our charcoal burned in the open air, has been a very pleasing idea; but it it is rashly theoretical,” &c. — p. 180.

This idea is not only rashly theoretical, but in direct contradiction to well-known and long-known determinations in chemical physics. Certainly no chemist could be pleased with it, and all that any one would venture to maintain at all resembling it is, that given quantities of given kinds of matter, of given densities and forms of aggregation, will under all known variations of other conditions produce in combustion determinate quantities of heat. And these are of such an order of magnitude as to discredit our author’s theory, if speculation on such subjects be limited, as it should be, to reasonings from what we know, and in analogy with what we know.

But our author’s positive grounds for his “chemical theory” are in reality theological. He says: —

“If there be any truth more plain than all others, it is that God, in creating, upholding, and governing the world, works by agencies and according to law, and that his process is invariably from the simple to the complex. [!] .... The chain of dependencies from the body of a man back through plants and compound minerals to the simple elements is a large one, interlinking many agencies and laws; and it is most irrational to say that in the original creation God began somewhere in the middle of this chain, — say with compound minerals. No! He began with the beginning; this is ‘ the way of the Lord.’ He began with the simple elements, and combined them according to his ordained and combining laws!”— p. 62.

Again: —

“The simple elements were formed separately, and afterwards combined; because God has created a special agency called ‘Chemical Force,’ acting according to a complicated system of laws, whose object is to unite or combine these elements.” — p. 63.

A few pages further on he says: —

“The simple elements were originally created separate, and afterwards combined by laws, because their creation in a compound state would have involved an infinite number of miracles, without any object for such miracles. .... To form a compound mineral otherwise than by the laws above given would be a miracle without any assignable object. It would be a miracle in mere idleness, the very thought of which is an impiety.” — p. 65.

To our mind there is a much greater impiety in the confident manner in which the author thus pretends to a knowledge of God’s ways and designs, and imputes his theory to the Almighty. We would not accuse him of a conscious impiety. Indeed, we are convinced that he is not the less pious, because his love of his theory is so much greater than his caution or his regard for the simple truths of fact. But one would naturally infer from his statements that he regards the great “reducing” processes of nature, and the processes by which chemists have discovered the “ultimate elements,” as magical and diabolical ones, and analytical chemistry as still one of the “black arts.” It would seem also, that heat, which decomposes many chemical compounds, and is probably able to decompose them all, works contrary to “the way of the Lord.”

But in sober truth “the way of the Lord,” so far as it can be known by the laws of physical science, is always and everywhere equally by process and counter-process. No chemical compound, known to be such, can exist, which is not decomposable by processes as natural and as much the ways of the Lord as those which our author regards as peculiarly divine. Moreover, the laws of mechanical and chemical physics point to no such simple beginning, and to no such progressive development of the universe as a whole, as are assumed, without warrant from science, in the nebular hypothesis. In one respect this hypothesis is legitimate and worthy of serious attention. In so far as it attempts to account, however inadequately in our present state of knowledge, for effects which are obviously of a physical origin, its claims to respect are clear. But as ordinarily presented and discussed, this hypothesis involves a problem and an assumption which are entirely foreign to science. Physical science knows no beginning, and from its own principles it has no right to presume one; and it is quite out of its element when employed to simplify the universe “at the beginning,” — to lessen the labor of Omnipotence! — to reduce to its lowest terms the miracle of creation! But this use of natural laws is an unconscious testimony to the aversion to miracles which scientific conceptions have engendered. In the merely physical explanations which the nebular hypothesis suggests, cosmologists like our author and Mr. Herbert

Spencer have little or no interest. They welcome it rather on account of its fancied solutions of problems quite foreign to science.

One other remarkable feature of our author’s method deserves notice, a feature not unprecedented in efforts of the same sort, namely, the putting of a scientific question to a vote of “facts,” on the principle, apparently, of free and impartial suffrage and numerical majorities. The “facts” which various theories “account for” are duly marshalled, paragraphed, and numbered by the author. Forty-seven facts prove the resemblance of the earth to the planets; twenty-three, that the fixed stars are suns; twenty-eight, the author’s theory that the earth was once self-luminous like the sun. “Eight facts or classes of facts” prove his theory that the chemical elements were “formed during the period of nebular condensation.” The chemical theory “accounts for” seventy-one facts, and gravity “accounts for” fifty-three free and independent facts in the solar system.

It must be confessed that the magnitude of these numbers is in many cases due to a want of entire independence among the “facts,” and oftener to the circumstance that many of them are only interpretations of fact in accordance with theory. Some of the facts, moreover, need qualification, others confirmation, and nearly all lack that power of demonstration which the author attributes to them. Their strength lies in their numbers, but the genuine truths of science do not depend on such crude numerical inductions. One fact as well ascertained as the law of gravity might be sufficient to rout the whole seventy which the author’s chemical theory “accounts for,” without injury to the substantial merits of a single one; though it would hardly be able to do so if it depended on evidence no more cogent than the fifty-three which gravity accounts for, according to the author. In reality, gravity accounts with mathematical precision for as many thousands of facts, — facts of particular and direct observation. And this is the only kind of evidence which ought to be considered as a basis of physical demonstration.

The Reign of Law “The Reign of Law. By the Duke of Argyll. Fifth Edition.” Alexander Strahan London. 1867. 8vo, pp. 435. ³⁴. [From The Nation 4.102 (13 June 1867): 470.] ³⁵

We think that it would he a profitable enterprise for some American publisher to reprint this book. It is one of the best of its class published in recent times. Popular treatises on natural theology and the theological bearings of modern scientific ideas have degenerated to such merely sermonical discourses, or else into partisan treatments of scientific questions (which seek to gain support from religious ideas rather than to give support to them), that a genuinely philosophical work of the olden stamp—showing power of thought and an earnest purpose, at least—has a peculiar claim to respect, even if it be not entirely successful in removing the difficulties which religious philosophy has encountered in the changed aspects of modern science.

That these difficulties are great it would be prejudice to deny. The idea of the “supernatural,” which is still the prevailing one, as a power of operating independently of orderly or natural causes—as one which interferes with them or sets them aside—such a supernatural power finds little favor with thinkers most advanced in scientific culture. To such thinkers the willingness to believe in an arbitrary exercise of creative power appears to indicate not so much the ripest discipline of faith as a defective discipline in science; and though miracles are not thereby excluded from a scientific conception of nature, yet their definition demands amendment. Miracles, as conceived by our author, involve not less than natural events the operation of natural causes, the use of natural means, and an observance of natural laws. To make an event miraculous it should involve, he thinks, a supermaterial instrumentality—that is, it should involve a special design or thought or have a purpose—and it should be superhuman either in its designs or in its command of means, though this command is not manifested by changing the laws of the means employed. It consists rather in a power which is not in its nature superhuman, a power to combine causes and make them means to an end through an observance of their laws. Interfering with laws thus signifies, according to this view, the power to convert them to use by combining them and turning their courses instead of arresting their operations. This implies, however, the existence of free causes which can so turn to use the forces of nature. But the human will is not, according to our author, a pure type of such a power, though the higher sentiments of the human heart appear to him to present such types. By the freedom of the will he does not mean freedom from motives. The reign of law which extends throughout nature, which requires that creation itself should be by means and according to the laws of already existing things, extends also over the “realm of mind.” “By freedom,” the author says, “we do not mean that any of the phenomena of mind, any more than any of the phenomena of matter, can arise without ‘ an antecedent,’” and he expresses his idea of the manner in which man is subject to the law of causation by these words from Mill’s “Examination” of Hamilton: “That his (man’s) volitions are not self-caused, but determined by spiritual antecedents in such sort that when the antecedents are the same the volitions will always be the same.” “But,” the author adds, “this word ‘ antecedent ’ is one of the many vain words in which metaphysicians delight. The highest antecedents which we can trace as determining conduct are to be found in the constitution of the mind itself. Love is an antecedent; so is reverence, so is gratitude, so is the hunger after knowledge, so is the desire of truth. Higher than these—further up the chain of cause and effect—we cannot go” (p. 811).

This passage discloses one of the most curious of the misunderstandings which are so common between the two great schools of philosophy. Our author obviously understands the words “spiritual antecedents” as if synonymous with the “spiritually antecedent”—that is, higher up in the hierarchy of moral worth and power—an interpretation natural enough to one versed in the conceptions of the ancient metaphysics. But if our author had been equally familiar with the tenets of positivism, he would hardly have chosen Mr. Mill’s words as expressing his idea of law in the “realm of mind,” for from the context and the general tenor of Mr. Mill’s writings it would have been evident to him that by spiritual antecedent Mr. Mill meant that state of the spirit—that is, of the mind and the character—which is immediately antecedent in time to an act of volition. The vagueness of the expression is not so much in Mr. Mill’s use of the word antecedent as in our author’s understanding of the word spiritual. He would also have known that the sentiments of love, reverence, gratitude are regarded by this school as also effects, the effects of inheritance, education, and the circumstances of life, and that the chain of cause and effect which this school contemplates reaches backwards and forwards in time indefinitely, not upwards and downward in the “spiritual” hierarchy.

This want of familiarity with the doctrines of the modern scientific philosophy has led our author into other still more curious misunderstandings in his criticisms of Mill and Comte, which we have not space to notice. We have commended his book in spite, therefore, of many serious blunders, because in this respect he is not much inferior to the best of the writers of his school, and because in freshness, liberality, and originality his book surpasses most similar recent treatises.

He allows to Mr. Darwin’s “Law of Natural Selection” some share in the origination of the adaptations in the organic world—a power, at least, to preserve and perfect the adaptations and contrivances of designing skill. He is also cautious not to ascribe intentions to nature in the sense of final causes or ultimate intentions. He contends, nevertheless, that immediate intention is shown in the structures and functions of organic beings, in contrivances and adaptations, which he appears, however, to ascribe to nature as a whole, rather than to the mental or tentative and contriving powers in the lives of the several races of animals and plants which these contrivances benefit.

With our author, as with all writers on natural theology, the natural evidences are read in the light of a metaphysical tenet, namely, that design is (or involves) a free power, is something more than taking advantage of circumstances in their empirical combinations. It is supposed to involve the power of making the combinations in the first instance, and independently of an empirical knowledge of causes or of acquired powers of combination in thought. And it is upon this tenet rather than upon the facts of natural science that the issue of the debate really turns; and the debate, it should be borne in mind, is not upon the tenableness of the positions meant to be established by these arguments, but rather on the validity of the proofs adduced.

Of the scientific merits of the book, we have but a word to say. The author contributes to the illustrations of design in nature an interesting discussion of the “machinery of flight” in the wings of birds, and by this and other scientific matters makes his book a very readable one.

Mathematics in Court. [Letter to the Editor, signed as "V. X." The Nation 5.116 (19 September 1867): 238.] ³⁶

To the Editor of The Nation:

The question of forgery is involved in the “Howland Will Case,” and it is contended that two signatures must have been traced.

Mr. Crosman was engaged in examining different signatures of various individuals with reference to the question of signatures repeating themselves. He “stated at great length the result of the comparison of these signatures; that he found many of them to cover much better than the signatures of Miss Howland to the second pages and to the will; that in one case both lines, ‘ Tour obedient servant ’ and ‘ Joseph B. Spear,’ covered much better than the two signatures of Miss Howland.”

The whole case was closed by the testimony of Prof. Benjamin Peirce upon the doctrine of chances. I quote from this testimony as follows:

“In the case of Sylvia Ann Howland, this phenomenon could occur only once in the number of times expressed by the thirtieth power of five or more—exactly, it is once in two thousand six hundred and sixty-six millions of millions of millions of times, or 2,666,000,000,000,000,000,000. This number far transcends human experience. So vast an improbability is practically an impossibility.” How then to account for “Your obedient servant, Joseph B. Spear,” and other duplicate signatures?

Now, I would ask if all this testimony of Prof. Peirce’s is not irrelevant? The signatures that do correspond, and are not forgeries, are facts, and by the side of this doctrine of chance they seem to prove that figures cannot always be trusted. It appears to me that the case in question is not amenable to the laws of chance. It is always a person’s intention to make the signature similar to others as nearly so as possible every time. The elements of will and desire unfit it for judgment by such laws. Figures can be prostituted to prove almost anything, and were it not for Prof. Peirce’s high position, one might be led to think his evidence nothing more than a special plea. And the tone of his testimony is arrogant and positive, as if he were charging the judges.

I doubt very much whether “all the mathematicians of the world” will instantly recognize the correctness and applicability of this doctrine.

V. X.

[Mr. Crosman’s testimony does not in any way conflict with Professor Peirce’s, for the conclusion of the professor’s testimony is not that there may not or do not occur exact coincidences in the signatures of certain persons, but that in the case of Sylvia Howland such a coincidence would be a most extraordinary event, unless designedly produced by tracing or other form of forgery. The evidence on which this conclusion is founded is a minute comparison of about fifty signatures of Miss Howland each with all the others. So irregular were the signatures found to be that a coincidence so close as that of the alleged forgery ought not to be expected more than once in 2,666,000,000,000,000,000,000 cases of comparison. This calculation is not affected by the fact that other people write more regularly than she; it is based simply on an investigation of her habits of writing. This investigation might be called in question as being in the nature of things somewhat arbitrary so far as determining what are and what are not cases of coincidence. No two individuals of any species whatever could be found exactly alike if examined with sufficient minuteness. It was accordingly necessary to resort to the practical judgment of common sense to determine the data for this calculation; and the value of the calculation, which is a very simple one, depends wholly on the judgment used in observation, and is not a mathematical question at all. The procedure was substantially this: The thirty down-strokes of Miss Howland’s signature were chosen as test objects. In comparing any two signatures, as many of these lines were made to coincide with corresponding ones as in the judgment of the observer could be made to do so. The coincidences, or what in the judgment of the observer were deemed coincidences, were counted, and the whole number of coincidences in the 1,250 comparisons was found to be to the number of non-coincidences as one to four nearly, or to be about one-fifth of the whole. The relative frequency of the occurrence of different numbers of coincidences in single comparisons followed the law of chance very closely, showing that the several coincidences were independent, accidental events, and hence, for the whole thirty to occur (the independent chance of each being one-fifth), there is only the chance measured by one-fifth to the thirtieth power. This conclusion is not invalidated by the fact that in the signatures of other persons exact coincidences do happen, unless it can also be shown that these persons generally write as irregularly as Miss Howland did. The effect of a person’s intention to make all signatures alike, which “V. X.” refers to, is fully taken account of in the investigations of the person’s habits. There is nothing whatever in what “V. X.” says about the “elements of will and desire.” His comment on the tone of Professor Peirce’s testimony is hardly just. Mr. Peirce has a not very wise way of putting his testimony in the most paradoxical and at the same time positive form he can devise, thereby making it very much less effective on the minds of common folks. If he appears arrogant, it is probably from a desire to make up in the earnestness of his statements the lack of convincing clearness—to supply his audience with a lively faith in default of a clear understanding. He is a little too much given to impute a certainty to the results of mathematical computation which only belongs to the processes and not to the data of the computation. The value of the present testimony depends wholly on the judgment of his son in estimating coincidences, and does not depend on the judgment of either father or son as mathematical experts.—Ed. Nation.]

Review of A. P. Peabody's Positive Philosophy [From North American Review 106.1 (January 1868): 285-294.] ³⁷

2. — The Positive Philosophy. An Oration delivered before the Phi Beta Kappa Society of Amherst College, July 9, 1867, and before the Phi Beta Kappa Society of the University of Vermont, August 6, 1867. By A. P. Peabody, D.D., LL. D., Preacher to the University, and Plummer Professor of Christian Morals in Harvard College. Boston: Gould and Lincoln. 1867. 8vo pamphlet.

Under the comprehensive name of positivism, a great variety of philosophical opinions are popularly designated at the present day. Authors who differ as fundamentally as Mill and Spencer, neither professing to be a follower of M. Comte, and one, Mr. Spencer, differing from Comte in almost every essential of doctrine, and openly repudiating the name, are now commonly called “positivists.” It is this enlarged and now generally adopted meaning of “positivism,” as synonymous

with one of the two fundamental divisions of the philosophical world, that our author appears to propose as the subject of his discourse. He discriminates none of its varieties, and imputes some opinions to all positivists which only a few really hold, and some which are held by none of them.

The process by which the word “positivism” has acquired its present signification is in itself an instructive lesson in philosophy. At first assumed as the distinctive name of the philosophy of M. Comte, it has since degenerated, through the vagueness of apprehension and the ignorance of its opponents, into a general appellation, as truly applicable to M. Comte’s predecessors as to his followers, or to any later thinkers of a similar mental character.

But though this name specifically belongs only to M. Comte and his few avowed followers, and is usually applied to other thinkers only by their opponents, yet, as thus generalized, it has a well-accredited and important significance. All positivists, so called, are agreed in regarding the methods of discovering truth exemplified in the maturest of the modern sciences, as the methods of all true knowledge, namely, the methods of induction from the facts of particular observations, and are agreed in ignoring all problems as idle and foolish which cannot receive such solutions.

Among these problems is that of metaphysical causation, the question of those real connections between phenomena as causes and effects which are independent of our experiences, and the invariable and unconditional sequences among them. To those who have reached the positive mode of thought, the word “cause” simply signifies the phenomena, or the state of facts which precede the event to be explained, — which make it exist, in the only sense in which an event can clearly be supposed to be made to exist, namely, by affording the conditions of the rule of its occurrence. But with those who have not yet attained to this clear and simple conception of cause a vague but familiar feeling prevails, which makes this conception seem very inadequate to express their idea of the reality of causation. Such thinkers feel that they know something more in causation than the mere succession, however simple and invariable this may be. The real efficiency of a cause, that which makes its effect to exist absolutely, seems, at least in regard to their own volitions, to be known to them immediately. Causation, among such remote and unfamiliar phenomena as the positions and movements of the heavenly bodies, may be only known by observation and the discovery of the rules of their simple and invariable sequences; yet the mind inevitably imputes to such successions real though unobserved connections, like those it believes itself to know absolutely and immediately in its own volitions.

Not only the positive philosophy, in its widest sense, but also the critical philosophy of Kant, and all so-called sceptical philosophies, deny such an immediate knowledge by the mind of the causal efficiency of its own volitions. That certain mental states of thought, feeling, and desire, of which we are conscious, are followed by certain external effects, which we observe, is to the sceptical schools a simple fact of observation. These thinkers extend the method of the more precisely known to the interpretation of what is less precisely known, interpreting the phenomena of self-consciousness by the methods of physical science, instead of interpreting physical phenomena by the crudities of the least perfect, though most familiar of all observations, the phenomena of volition. So obviously unphilosophical is the latter course, that the acutest of orthodox thinkers (Mr. Mansel, for example) regard the efficiency of cause to be immediately known, not between the internal motive and the external act of volition, but between the will, pure and simple, and its special determinations of the strengths of motives to action, which alone are properly ascribed to the will as an absolutely known cause. That u the strongest motive prevails in volition” is not merely true, but a truism, say these thinkers; “but the strength of the motive is an effect, not the cause of volition. Motives are phenomena of willing, not the efficient Will itself. The connection between the strongest or prevailing motive and its external effect may be merely one of sequence in observation, but this only removes the immediate intuition of causation one step farther back. The real nisus, immediately known, is between the Will and the motives through which it determines external actions. That the same motives, acting under the same external circumstances, are followed by the same external actions may be a matter of mere observation, and may afford no immediate evidence of real causal efficiency. The analogy which makes us infer real efficiency wherever phenomenal regularity is observed is not, consequently, invalidated by the fact that we do not immediately know the real connections between our desires and our muscular movements.”

All this the positivist may readily admit, and yet validly deny the force of this analogy. Regularity is the essential characteristic of what he regards as causal connections. The invariability of the sequences of phenomena has no point of analogy with the relation of an undetermined, undefined, unclassified, real efficiency to a determinate, definite kind of effect. So long as the will is not phenomenally known as so and so determined to action by definable motives, it bears no analogy whatever to observed causes, or to the relation of regular antecedents to their consequents. If it be said that, in one case the connection between cause and effect is known independently of any regularity, while

in the other case it is known only by regularity; or that in the first case the connection is known immediately to be real or causal, and in the other is inferred to be real or causal by analogy; the cogency of the reasoning will depend on whether the connections compared be alike in other respects, except the methods by which they are known. If phenomena succeeding one another, apparently at random, without rule or reason, can be known to be really connected, then analogy ought to infer that all such successions, the most irregular in nature, are connected by causation. But science discovers causation only in regularity. The exact application of the analogy would justify, indeed, what science condemns,— superstitious beliefs concerning signs and portents, the post hoc ergo propter hoc mode of reasoning of the unscientific mind. Either, then, the use of the word “cause” with which science has familiarized the positive philosopher is a complete misnomer, or else the vague notion of cause as a relation between an undefined, undetermined reality, the will, and a definite determinate effect, the motive, is wholly unphilosophical. In either case, there is no analogy between the laws of nature, as known by science, and free volition.

On account of this ambiguity in the use of the word “cause,” the word itself was reprobated and discarded by Comte, though by a wholly too generous concession to the abuses of the term. Mr. Mill reinstated the word, as validly signifying what science understands by it, namely, the sum of the conditions or antecedent phenomena, which by the laws of nature, material and spiritual, are followed by a determinate effect. If human volitions cannot be included under this formula, then, either we know nothing about their causes, or else the word is used in such a different sense, that there is no analogy between such causes and those causes in nature of which science treats. We are not, “therefore,” as our author says, “by a simple process of generalization, or, as a positivist might say, of classification on the ground of resemblance, compelled to infer that, in the changes which have taken place in the universe, in creation, in paroxysmal revolutions, in the annual and [other] periodical sequences of phenomena, will has been and is the efficient cause.” There is not only no analogy, but a direct contradiction, between a cause which is a determinate phenomenal antecedent, regularly preceding its effect, and the “cause” of changes which conform to no rule, — such as our author’s “paroxysmal revolutions.” Both may exist for aught the positivist pretends to know, but he can discover evidence of only one sort of causes. From observation of his own volitions, he finds that he himself, or his will (the name of the internal unity of thought, feeling, and desiring), is a cause, since certain determinate states of this self are followed regularly by determinate

actions or classes of actions. In this kind of phenomena he finds his earliest and most familiar types of causation, but not the best or clearest; for it is only with vague, ill-defined classes of effects that our earliest knowledge of causation makes us acquainted; and in fact we at length discover that the most familiar cases of causation, the phenomena of volition, are among the most complicated and difficult to analyze of all the phenomena of nature, and must be the latest to be reduced to scientific precision of knowledge.

To this extent thinkers like Comte, Mill, Grote, Buckle, Powell, and Spencer may be said to agree, however widely they may differ on other topics. “In all the natural sciences,” the author says, “an alarmingly large proportion of the younger adepts — many of them men of commanding ability in research and generalization — are already pronounced positivists, and are doing all that man can do to legislate God out of his creation”; for such is our author’s interpretation of the scientific doctrine of universal causation. Not to believe that God is capricious, or to believe that there is no valid evidence of capricious agency in the known universe, or any ground for supposing it, appears to be, according to the view presented in this discourse, legislating God out of his creation! As if the will of God were not as essential to the order of nature as to any supposable disorders, miracles, or “paroxysmal revolutions.” To the scientific apprehension, “will,” in the metaphysical sense of the word, is equally essential, or non-essential, to the existence of all phenomena, regular or irregular, and is equally unknown in all. It would seem, from various expressions of our author, that he believes it is only by the manifestation of a capricious will that God makes himself known and felt, like a froward child.

If the author were opposing the opinions of M. Comte and his most subservient followers merely, his statements of the positions he controverts might be accepted as sufficiently correct; but his expositions of what positivism is are given as the opinions of all who are commonly included under the name of “positivists.” In an account of the “foundation-principles” of positivism, he states as one of them, that “the unbroken series of physical antecedents and consequents embraces all nature and all being, so that there is no room for the action of moral or spiritual causes.” It is surprising that the author can seriously believe that he is here fairly stating the real belief of any one of those he has classed among positivists. Unbroken threads of causation are, it is true, the stuff of which the web of phenomena is woven, but these are not exclusively composed of physical antecedents and consequents, as distinguished from moral or spiritual causes and effects. Principles of conduct, moral and spiritual phenomena, our dispositions and emotions, are

not excluded by any positivist from the threads of causation. But it is possible that the author means by the “action of moral or spiritual causes” their metaphysical efficiency, not merely their regular phenomenal successions; yet equally in this case does he fail to represent the opinion he opposes. For the phenomenal regularity inherent equally in physical, mental, and moral phenomena does no more exclude the real causal efficiency of spiritual powers than it does of material forces. It excludes neither from a possible reality, but includes neither in actual knowledge. When, therefore, Dr. Peabody states next as a tenet of positivism, “that human history could have been written in advance, for all nations and for every individual man, by one who, in the remote past, could have comprehended all the material [!] phenomena then in existence, and have followed each out through its series of inevitable consequents”; and when he adds, that “Materialism and Necessity are then the two exponential words of the positive philosophy,” he misinterprets the doctrine he proposes to criticise. The truth is, that neither Materialism nor Necessity (in the sense which the author attaches to this word) are doctrines of positivism; for the one affects to know that spiritual consequents, thoughts, feelings, and desires may follow from antecedents purely material; and the other professes to know the absolute efficiency of causes. But positivism professes to know neither of these. Both transcend its sphere. Within this sphere of observation foreknowledge is believed by the positivist to be possible just in proportion as the mind can attain to a knowledge of the laws and special conditions of phenomena, even to the limit of perfect foreknowledge for all time. But this is not dogmatically asserting the doctrine of Materialism, or that mental phenomena could follow from purely material antecedents. It is a wholly distinct thesis.

Dr. Peabody closes his summary exposition of the “foundation-principles” of positive philosophy with these words: “Its only God is collective humanity; its only allegiance and worship are due to this abstraction, — the sole abstraction admitted in the dreary realm of phenomena.” Humanity is indeed an abstract term, though frequently used to denote the concrete manifold object, “all human beings,” and it is apparently used above in this concrete sense. If not, it would have been more correct to say that the God of the positivists (meaning only Comte and the professors of his religion) is the whole human race, including its past, its present, and its future. Now this is very far from being an abstraction, — is quite concrete.

Our author makes one exception to his sweeping imputations of opinion. He says: “I ought, however, to say that Mill, at this point dissenting from Comte, superciliously permits God to be, nay, grants

that he may possibly have originated the order of nature; but the Supreme Being is left in existence only with the proviso that he abdicate his sceptre, adhere to fixed laws, and abjure the right of providentially modifying those laws, — a God shorn of his godhead, otiose, powerless, — a mute and motionless figure-head, erected by philosophy to save itself from the stigma of atheism.” It is almost needless for us to say to the intelligent reader, that nothing could be conceived more remote than this from the spirit of Mr. Mill’s real opinions. The true positivist regards the existence of regularity — even the universality of causation—in the phenomena of nature as no proof whatever of Necessity or Fate. He knows nothing of what must be absolutely and in all possible worlds, for his principles are all derived from experience of this actual one. No more can he suppose, as our author does, that an apparent absence of law is a proof of free-will. Either hypothesis is perfectly consistent with the constitution of the universe, which science presumes and has in great measure disclosed. Either an immovable Fate or an unvarying Will is consistent with the discovered laws, and the presumed universal order of nature. The inmost nature of neither can be known to human faculties; nor, indeed, whether they are really unlike, except in their phenomenal manifestations. Will is manifested by thought, feeling, and desire, and their truly distinctive external effects. Fate, if there be such a nature, would be manifested, not by an unchanging, but by an unchangeable order in phenomena, both material and spiritual. Positivism, therefore, holds that science, in discovering the orders of phenomena, and even in presuming that such orders are universal, does not decide anything as to their inmost nature, but only as to what they are in external fact. This is very far from requiring that God “abdicate his sceptre, adhere to fixed laws, and abjure the right,” &c. It is simply and humbly discovering what is, instead of dictating what must be. But by Will our author understands Free-Will, and by Free-Will, caprice.

In opposition to the Comtean doctrine that consciousness cannot be an object to itself, and that self-consciousness means only the consciousness of the effects of the self, which are properly external objects, our author resorts to an argument which, since Kant, has been almost universally discarded. He says: “I believe in the relation of an antecedent and a consequent phenomenon only because I, who perceive the consequent, know that I am the same being who observed the antecedent.” More explicitly the theory is this: I know myself as perceiving the antecedent; I know myself as perceiving the consequent; and I connect the two only by knowing myself independently of them as continuing to exist between them. The simple fact is, that only by the representation

of the remembered antecedent, in conjunction with the observed consequent, am I conscious of myself at all. The word “I” is a meaningless subject, without “content.” Only with the predicates, “I think,” “I feel,” “I will or desire,” or synonymous and cognate ones, does it refer to any fact of experience or observation. The union of the antecedent and the consequent of experience in thought through representation is that “unity of apperception” expressed by “I think.” Our author discards, in his discussion of such points, the technical terms of philosophy, and thereby, we think, misses the facts of the case which these terms were devised to express. He proceeds in this way to a summary discovery of his own free-agency, and then gives further characterizations of the views he opposes. “I indeed act not without motives; and, according to the positive philosophy, motives are always [!] from without,— appreciable material forces, the resultant of which determines my action in this or that direction.” And again: “According to the positive philosophy, however, if I do not yield to what seems the strongest motive, it is because of the presence of still stronger, but less patent motives of the same order, — material forces exterior to myself, — which I do not take into account.” This is not the doctrine of any real necessitarian, or positivist. It is simply the fatuous fancy of ignorant barbarians, those Oriental visionaries who call themselves Fatalists. The author objects to it chiefly on account of “the clear consciousness of merit or demerit connected with my action.” Most other writers object to it for the palpable folly there is in supposing that feelings and desires, the causes of volition, (however regularly determined,) can be “material forces exterior to myself.”

Mr. Mill, in his “System of Logic,” distinctly and emphatically disavows that interpretation of the necessitarian’s doctrine, which our author here charges against him in common with all positivists.

We will give but one other instance of our author’s philosophy. He says: —

“Geology leaves us no reason to doubt that, in the earlier history of our planet, the most momentous paroxysmal changes have occurred. It carries us back to epochs at which there were no traces of organized being, and thus renders it certain that there has been creation, — if not creation out of nothing, the shaping, in time, of pre-existent materials. We have prima facie reasons for believing that there has been creation of separate species. Especially is the positivist bound on his own principles to maintain this; for it is not pretended that the transmutation of one species into another, still less of one order into another, has ever been observed or proved in a single instance.”

But is it pretended, as it should be to complete this argument, that

separate creation “has ever been observed or proved in a single instance”? A beginning of life on the earth, recent compared to the earth’s own duration, has perhaps been proved by geology, though hardly so conclusively as our author imagines, most of the evidence being merely negative. But, granting this beginning of organic life as a reasonable hypothesis, how does this prove the “creation of separate species”? And why may not the positivist be allowed the transmutation theory in lieu of this uncertainty, even though he cannot make out a complete case of the transmutation of one species into another? Partial, even very considerable, changes are effected in species by selective breeding and horticulture; and it is upon such facts of observation that the later transmutationists base their hypothesis by one of the best instances, in all scientific speculation, of the application of the positivists’ rules of legitimate hypothesis. Besides, this hypothesis does not profess to explain the absolute origin of life, but only those changes in its manifestations revealed by the geological record. No one is “bound” (least of all, a positivist) “to maintain” any hypothesis to the exclusion of any other, until it is proved to be true; whether it be the hypothesis of the separate creation, or of the transmutation of species. But here our author abruptly shifts his ground. He says: —

“But, in addition to, and often in modification of, the avowed fundamental maxim of the positive philosophy, — ‘Observed phenomena are the only objects of knowledge,’ — its disciples recognize another maxim, — a lex non scripta, yet none the less imperative, — ‘Whatever is impious is true,’ — whatever tends to chase the conception of God from the universe is so antecedently probable that it may be affirmed, even independently of observation.”

It would appear to be our author’s belief, many times indicated in this discourse, though nowhere explicitly laid down, that whatever conforms to law, or is regular and according to the general analogy of nature, “tends to chase the conception of God from the universe”; so that, as science understands truth, the converse of the above lex non scripta would appear to be its just rendering; namely, that “Whatever is true is impious.” Indeed, history affords many notable particular confirmations of this rule in the judgments of religious teachers on true hypotheses in science. Our author appears to base Theism on exceedingly narrow and precarious grounds in experience, and we could easily imagine a positivist with a much more rational faith in it.

The conception of a Being with a nature akin to our own, but perfect in all that we aspire to be; infinite in power, with perfect goodness and knowledge; who does not “providentially modify” the laws of his universe, since no laws can be supposed more wisely adapted to his own highest ends; whose will is just as immediately manifested in the

order of nature as in any supposable miracle, — such a conception is to many thinkers, who are called positivists, a most cheering and inspiring one, and is not inconsistent with anything which hitman science has yet disclosed, or is ever likely to discover.

Enlightened faith in the truth of such a conception is founded on the sentiments it appeals to. It does not demand as the condition of assent the force of irresistible demonstration; nor does it deceive itself with fallacious arguments.

Review of Bledsoe's The Philosophy of Mathematics. [From The Nation 4.148 (30 April 1868): 355-356.] ³⁸

The Philosophy of Mathematics, with Special Reference to the Elements of Geometry and the Infinitesimal Method. By Professor A. T. Bledsoe, A.M., LL.D., late of the University of Virginia. (Philadelphia: J. B. Lippincott &Co. 1868.)

This work is mainly devoted to the rationale of the various infinitesimal methods, and to a succinct and interesting discussion of the essential logic of these methods. We have discovered nothing of value essentially original in the philosophical exposition of these methods,

unless in a realistic and uncompromising application of the “method of limits” to their philosophy.

One English author, Mr. Todhunter, who ventures to ignore the question whether a variable actually reaches its limits or not, appears to be regarded by the author as an arch-heretic, because he purposely omits from the definition of a limit the words “that value which the function never actually attains.” Realism would seem quite out of place in matters so technical and abstract; and to us it seems quite unimportant in the “method of limits” to consider whether an actual infinity of steps are continuously passed over in “passing” to the limit of a ratio, or whether the limits of value in the ratios of infinitesimals he only substituted (or understood to be substituted) for their actual ratios. Either would fully justify that neglect of infinitesimal terms in sums and differences which the method explains.

The author is undoubtedly correct in regarding the “method of limits” as the only complete rationale of the exactness of the infinitesimal calculus, but he appears to us in his discussion of this method to be more a metaphysician than a mathematician, more concerned and interested in collateral considerations on the theory than in the practice of mathematical research; and we especially dissent from his views on the causes of the difficulties which students find in the common presentations of fundamental mathematical principles. The “axioms” of mathematics are properly only axioms of an art, and only claim to be the simplest, direct, practical maxims for mathematical deductions, not necessarily the most obvious of truths philosophically considered; though they are the most extensive and useful in the art of mathematical investigation. This is especially true of modern mathematics, which lack and forego the rigor of the ancient geometry, because they do not so much aim at a clear philosophical comprehension of what we already know as at a trustworthy and expeditious method of discovering what we are still ignorant of. No mathematician at all familiar with the infinitesimal calculus can doubt of its rigorous exactness in dealing with abstract hypothetical problems; even though he can render no clear account of its logic. As an abstract instrument of scientific research it may be better known through its technical axioms than in its philosophical foundations.

But our author appears to have chiefly in view in his work the difficulties of the mathematical teacher, the difficulties of making the principles of the calculus understood by the student. That he greatly over-estimates the philosophical difficulties to which his work is mainly devoted we attribute to his own admirable idiosyncrasy. He clearly knows and recounts his own difficulties rather than those of students in general. Simple algebra, which involves none of these difficulties, is a stumbling-block to the very sort of minds for which he has written his book. He knows much better what he is talking about than what he is talking to. The main difficulty is not metaphysical. It does not so much consist in a lack of the evidences, for the reception of which the human reason is especially apt, as in that want of disposition and attention to which the human will, since the fall, is especially prone. We would not be understood, however, as depreciating the importance of clear philosophical views in the study of an art either in mathematics or in politics, and we believe that this most interesting account of the controversy which has engaged the attention of metaphysicians since the origin of modern mathematical analysis will be instructive as well as interesting to most mathematical readers.

Notes on Peirce on Berkeley. [Note about Charles S. Peirce's review of A.C. Fraser, The Works of George Berkeley. The Nation 13.335 (30 November 1871): 355-356.] ³⁹

— Mr. Charles S. Peirce, in his review of Berkeley in the last North American, to which we promised to return, takes the occasion to trace out in the history of philosophical thought in Great Britain the sources of Berkeley’s doctrines and of later developments in English philosophy. These he traces back to the famous disputes of the later schoolmen on the question of realism and nominalism—that question on which each new-fledged masculine intellect likes to try its powers of disputation. But the motive of the schoolmen who started this question or gave it prominence, was not in any sense egotistical, however pugilistic it may have been, but was profoundly religious—more religious, in fact, than anything modern, and, perhaps, more fitly to be compared to the devotion that produced the Gothic architecture than to anything else. The most remarkable thing in the essay is Mr. Peirce’s interpretation of the actual question so earnestly agitated. This, it should seem, is not at all what has become the universally accepted account of this voluminous dispute—an account derived, it appears, from Bayle’s Dictionary. The realistic schoolmen were not such dolts as to contend for an incognizable reality beyond any powers we have for apprehending it, nor for the existence of universals as the objects of general conceptions existing outside of the mind. They only contended (against the sceptical or nominalistic tendency) that reality, or the truth of things, depends on something besides the actual courses of experience in individual minds, or is independent of differences and accidents in these; and that truth is not determined by the conventions of language, or by what men choose to mean by their words. So far from being the reality commonly supposed—that is to say, the vivid, actual, present contact with things—the reality of the realists was the final upshot of experience, the general agreement in all experience, as far removed as possible from any particular body’s sight, or hearing, or touch, or from the accidents which are inseparable from these. Yet it is essentially intelligible, and, in fact, is the very most intelligible, and is quite independent of conventions in language. The faith of the realists (for theirs was a philosophy of faith) was that this result of all men’s experience would contain agreements not dependent on the laws and usages of language, but on truths which determine these laws and usages. Modern science affords ample evidence of the justness of this position.

—That this truly was the position of the realistic schoolmen, Mr. Peirce contends; and he bases his opinion and belief on an original examination of their works, such as has not, we venture to say, been undertaken, outside of Germany, for a very long time. In spite of the confirmation of this position which modern science gives, the course of the development of modern science has, nevertheless, as Mr. Peirce points out, been closely associated with the opposite doctrine—nominalism, the representative of the sceptical spirit. This appears in Berkeley’s philosophy, who is a nominalist, notwithstanding his penchant for Platonic ideas or spiritual archetypes. Hume, a complete representative of the nominalistic and sceptical spirit, is an historical product of Berkeley’s nominalism; and, though commonly

regarded as the author of modern philosophical movements, was not, historically considered, so different from Berkeley but that Mr. Peirce regards the latter as entitled to “a far more important place in the history of philosophy than has usually been assigned to him.” So far as Berkeley was a link in the chain, this is undoubtedly true. So far as Hume (in common with all independent thinkers of the sceptical type) was not such a link, he was, we think, a starting-point in the movement of thought which has resulted in English empiricism, or the so-called “Positivism” of modern science, which Mr. Peirce seems inclined to attribute to a regular development of philosophical thought. Scepticism, though perhaps never original, as we are taught by orthodoxy, and only a revival of old and the oft-exploded errors, is, nevertheless, by its criticism, the source of most of the impulses which the spirit of enquiry has received in the history of philosophy. The results of modern science, the establishment of a great body of undisputed truths, the questions settled beyond debate, may be testimony in favor of the realistic schoolmen; but this settlement was the work, so far as it depended on the impulse of philosophy, of the nominalistic or sceptical tendencies of modern thought, which has put itself in opposition, not to the faith of the realists, as Mr. Peirce understands them, but to their conservatism and dogmatism, to their desire to agree with authority—that admirable devotion of theirs. It is curious that these things, the most certain of all on which the actual arts of life are now dependent, should be the results equally of the faith of the realists and the sceptical enquiries of the nominalists. But this is enough to account for the gratitude and the indifference which we owe to both of them, especially as the confirmation which science has afforded is not of the sort which the realists anticipated. It is the empirical conjectures of the visionary, not the inspired teachings of the wise, that have established realities for themselves and for truth in general. There are many other curious points of history and criticism in this article which will engage the scrutiny of the student of metaphysics, and doubtless afford him great delight. We are afraid to recommend it to other readers, as Mr. Peirce’s style reflects the difficulties of the subject, and is better adapted for persons who have mastered these than for such as would rather avoid them.

John Stuart Mill. [From The Nation 16.412 (22 May 1873): 351.] ⁴⁰

MR. MILL was, in many respects, one of the most singular men ever produced by English society. His father was a prominent, member of the small sect or coterie of Benthamites, whose attempts to reform the world, during the whole of the earlier part of the present century, furnished abundant matter for ridicule to the common run of politicians and social philosophers; and this ridicule was heightened, as the years rolled on, by the. extraordinary jargon which their master adopted for the communication of his discoveries to the world. The author of the ‘Defence of Usury,’ of the ‘Fragment on Government’ and of the ‘Book of Fallacies’ had, however, secured a reputation very early in his career which his subsequent eccentricities could not shake, but the first attempts of his disciples to catch the public ear were not fortunate. Macaulay’s smart review of James Mill’s hook on ‘ Government’ gives a very fair expression to the common feeling about them in English literary and political circles during John Stuart’s boyhood. About the value of the father’s labors as a mental philosopher there are of course a variety of opinions, but he gave two proofs of capacity for the practical work of life which there was no gainsaying. Became to London an obscure man of humble origin, but managed, without ever having been in India, and at a period when authors were held in much less esteem by politicians than they were at a later period, to produce such an impression of his knowledge of Indian affairs, by his elaborate history of that country, on the minds of the Directors of the Company, that they gave him an important office in the India House, and this, too, in spite of the fact that he lived in a circle generally considered visionary—answering, in fact, in some degree to what we call the “long-haired people.” Besides this, he himself personally gave his son an education which made him, perhaps, all things considered, the most accomplished man of his age, and without help from the universities or any other institution of learning. The son grew up with a profound reverence for his father as a scholar and thinker, and rarely lost an opportunity of expressing it, though, curiously enough, he began very early to look on Bentham, the head of the school, with a critical eye. The young man’s course was, however, still more remarkable than the father’s. Although brought up in a narrow coterie holding peculiar and somewhat unpopular opinions, and displaying, from his first entrance in life, as intense hostility as it was in his nature to feel against anything, against the English universities as then organized and conducted, though they were the centre of English culture and indeed one might say of intellectual activity, he saw himself, before he reached middle life, the most potent influence known to educated Englishmen, and perhaps that which has most contributed to the late grave changes in English public opinion on several of the leading social and political problems. Indeed, it is not too much to say that his writings produced a veritable debacle in the English mind. The younger generation were a good deal stirred by Carlyle; but Carlyle, after all, only woke people up, and made them look out of the window to see what was the matter, after which most of them went to bed again and slept comfortably. His cries were rather too inarticulate to furnish anything like a new gospel, and he never took hold of the intellectual class. But Mill did. The ‘ Logic ’ and ‘ Political Economy/ as reinforced and expounded by his earlier essays, were generally accepted by the younger men as the teachings of a real master, and even those who fully accepted neither his mental philosophy nor his social economy, acknowledged that the day of old things was passing away under his preaching. His method, however, as applied to politics, was not original—in fact, it was Bentham’s.

Bentham, who was perhaps, in the field of jurisprudence, the most destructive critic that ever appeared, had the merit which in his day was somewhat novel among reformers, and marked him out as something very different from Continental radicals, of being also highly constructive. Indeed, his labors in providing substitutes for what he sought to overthrow are amongst the most curious and, we might add, valuable monuments of human industry and ingenuity. His proposed reforms were based, too, on a theory of human nature which differed from that in use among a large number of radicals in our day in being perfectly sound, that is, in perfect accordance with observed facts, as far as it went. But it did not go nearly far enough. It did not embrace the whole of human nature, or even the greater part of it, and for the simple reason, which Mr. Mill himself has pointed out in his analysis of Bentham’s character, that its author was almost entirely wanting in sympathy and imagination. A very large proportion of the springs of human action were unknown or incomprehensible to him. The result was that, although he exerted a powerful influence on English law reform by his exposure of specific abuses, he made little impression on English sociology, properly so called. This was in part duo to his narrowness of view, and in part to the absence of an interpreter, none of his followers having attempted to put his wisdom into readable shape, except

Dumont, and he only partially and in French. The application of his method to the work of general reform was indeed left to Mr. Mill, who brought to the task an amount of culture to which Bentham could make no claim, and a large share of the sympathy of which there was also so little in Bentham’s composition, and a style which, for expository and didactic purposes, has perhaps never been surpassed. Moreover, Mr. Mill lost no time, as most men do, in maturing. He was a full-blown philosopher at twenty-five, and discourses in his earliest essays with almost the same measure, circumspection, and gravity exhibited in the latest of his works, and with all the Benthamite precision and attention to limitations. He was however wanting, as his master was, in imagination, and wanting too in what we may call, though not in any bad sense, the animal side of man's nature. He suffered in his treatment of all the questions of the day from excess of culture and deficiency of blood. He understood and allowed for men's errors of judgment and for their ignorance, and for their sloth and indifference; but of appreciation of the force of their passions, his speculations contain little sign. For instance, he was the first to point out the fact that the principle of competition, the eager desire to sell, which furnishes the motive power of the English and American social organization, is almost unknown and unfelt among the greater part of mankind, but his remedy for redundancy of population, and his lamentations over “the subjection of women,” are those of a recluse or valetudinarian.

His influence as a political philosopher may be said to have stood highest after the appearance of the ‘Political Economy.’ Ho had then perhaps the most remarkable following of hard-headed men which any English philosopher was ever able to show. But the reverence of his disciples waned somewhat rapidly after ho began to take a more active part in the treatment of the questions of the day. His ‘ Representative Government,’ valuable as it was as a philosophical discussion, offered no solution of the problem then pressing on the public mind in England which bitter Radicals or Conservatives could consider comforting. The plan of having the number of a man’s votes regulated by his calling and intelligence was thoroughly Benthamite. It was as complete and logical as a proposition in Euclid, and in 1825 would have looked attractive; but in 1855 the power of doing this nice work had completely passed out of everybody’s hands—indeed, the desire of political perfection had greatly abated. His lofty and eloquent plaints on the decline of social freedom helped to strengthen the charge of want of practicalness which in our day is so injurious to a man’s political influence, and when he entered Parliament, although he disappointed none of those who best understood him, the outside multitude, who had begun to look on him as a prophet, were somewhat chagrined that he was not readier in parrying the thrusts of the trained gladiators of the House of Commons. It was the book on the ‘Subjection of Women,’ however, which most shook the allegiance of his more educated followers, because it was marked by the widest departures from his own rules of thinking. It would be impossible to find any justification in his other works for the doctrine that women are inferior to men for the same reason that male serfs are inferior to their masters. His refusal to consider difference of sex as even one probable cause of women’s inferiority to men in mental and moral characteristics, was something for which few of his disciples were prepared, or which they ever got over; and indeed his whole treatment of the question of sex showed, in the opinion of many, a constitutional incapacity to deal with the gravest problems of social economy.

The standing of Mr. Mill as a mental philosopher appears to be very differently estimated by late critics and opponents and by himself, whether we consider the extent of his influence, or the relations of his doctrines to his nation and times; and there is a most singular inversion in these estimates of what we should naturally expect from friend and foe—an estimate of Mill’s position and influence by his opponents which, compared to his own, seems greatly exaggerated. For example, Dr. McCosh, a thoroughgoing opponent, regards Mill’s influence as the most active and effective philosophical force now alive in Great Britain, the strongest current of philosophic thought even at Oxford; and M. Taine, who some years ago discovered at Oxford that the British nation was not wanting in “general ideas” or principles in its modes of thought above the requirements of the accountant and assayer, found these principles in a really living English philosophy of which the head and founder was Stuart Mill—a philosophy which has brought forth one of M. Taine’s most elaborate critical studies in his work on ‘ Intelligence.’ In contrast with these estimates we have from Mr. Mill himself the opinion, in a letter to M. Taine, that his views are not especially English, and that they have not been so since the philosophical reaction in Scotland, Germany, and later in England, against Hume; that when his ‘System of Logic’ was written he “stood almost alone in his opinions; and though they have met with a degree of sympathy which he by no means expected, we may still count in England twenty à priori and spiritualist philosophers for every partisan of the doctrine of Experience.”

This estimate of his own influence and of the importance to metaphysical discussion at the present time of the philosophy he “adopted,” is entitled to much more consideration than ought in general to be allowed for an opinion inspired by the ambition, the enthusiasm, the disappointments, or even the modesty of a philosophical thinker. Nevertheless, the far different opinion of his standing as a metaphysician which his critics entertain is undoubtedly more correct, though in a sense which was not so clearly apparent to him. They see clearly that a philosophy of which he was not the founder, and never pretended to be, has gained through his writings a hold not only on English speculation, but on that of the civilized world, which it did not acquire even in England when it was an especially English philosophy, as it was “in the first half of the eighteenth century, from the time of Locke to that of the reaction against Hume.”

What, then, is it in Mill’s philosophical writings that has given him this eminence as a thinker? Two qualities, we think, very rarely combined: a philosophical style which for clearness and cogency has, perhaps, never been surpassed, and a conscientious painstaking, with a seriousness of conviction and an earnestness of purpose which did not in general characterize the thinkers whose views he adopted. It was by bringing to the support of doctrines previously regarded as irreligious a truly religious spirit, that Mill acquired in part the influence and respect which have given him his eminence as a thinker. He thus redeemed the word “utility” and the utilitarian doctrine of morals from the ill repute they had, for “the greatest happiness principle” was with him a religious principle. An equally important part of his influence is doubtless due to the thoroughness of his early training—the education received from his father’s instruction—which, as we have said, has made him truly regarded as the most accomplished of modern dialecticians.

To these grounds of influence may be added, so far as his influence on English thought is concerned, the fact that he was not a metaphysician in a positive fashion, though he dealt largely with metaphysical topics. He represented the almost instinctive aversion to metaphysics, as such, which has characterized the English since the time of Newton and Locke, we might almost say since the time of Bacon. Metaphysics, to pass current in England, has now to be baptized and become part of authoritative religious instruction, else it is foreign and barbarous to the English matter-of-fact ways of thinking. Mill’s ‘ System of Logic ’ was not intended as a system of philosophy in the German, French, or even Scotch sense of the term. It is not through the à priori establishment or refutation of highest principles that experiential, inductive, fact-proven principles of science are regarded or tested by the unmetaphysical English mind. Metaphysical doctrines prevail, it is true, in England to the extent probably that Mr. Mill estimates —twenty to one of its thinkers holding to some such views. Yet it would be a misconception to suppose those to be products of modern English thought. They are rather preserves, tabooed, interdicted to discussion, not the representatives of its living thought.

Mr. Mill estimated the worth of contemporary thinkers in accordance with this almost instinctive distrust of rational “illumination”; setting Archbishop Whately, for example, as a thinker above Sir W. Hamilton, for his services to philosophy, on account of “the number of true and valuable thoughts” which he originated and put into circulation, not as parts of a system, but as independent truths of sagacious or painstaking observation and reflection. It is by such a standard that Mr. Mill would doubtless wish to be judged, and by it he would be justly placed above all or nearly all of his contemporaries. Nevertheless, as a conscientious student of metaphysics, he held in far higher esteem than is shown in general by English thinkers the powers peculiar to the metaphysician—the ability and disposition to follow out into their consequences, and to concatenate in a system, the assumptions of à priori principles. Descartes, Leibnitz, Comte, and, as an exceptional English thinker, even Mr. Spencer, receive commendation from him on this account. It is clear, however, that his respect for this talent was of the sort which docs not aspire to imitate what is admired.

Sir Charles Lyell. [From The Nation 20.505 (4 March 1875): 146-147.] ⁴¹

The telegraph announces the death of Sir Charles Lyell on Monday, February 22. His name is not less inseparably connected with the progress and, we might almost say, the completion of a great revolution in geological science (though less conspicuously connected with it) than the greater names in astronomy are with similar periods of transition in that science. The establishment of geology as a strictly inductive or positive science was in a great measure due to the early, clear, and steady conception of true method in its pursuit, which Sir Charles Lyell’s works have done more to expound and promulgate than all other geological publications in this century. It would be difficult to estimate how much of the patient, soberly-directed labor of the modern army of geological explorers has been inspired by his researches and the influence of his teachings; but it is clear that the position early won by him through his writings and observations was a most important one for the guidance of a movement in which, from its magnitude and need of many leaders, no master-mind could by wisdom or energy have attained to such relative rank as has been won by genius in lesser movements of scientific progress. Lyell was bom in 1797, at a time when the principles of sound method in geology were just beginning to be adequately appreciated. In that year Playfair published his illustrations of Hutton’s geological theories, which as completed and amended may be said to have determined the chief line of progress in this century. Ten years later, in 1807, the Geological Society of London was founded. Of this body Lyell was made president at an early age in 1836-7, and again in 1850-1. He had published the first edition of his ‘ Principles of Geology ’ in 1832. The eleven editions of this work, of which the last appeared in 1872, and the seven editions of his ‘ Elements of Geology,’ the last in 1871, may be regarded as chronicles of a progress of which he was the principal historian and a chief actor. Narratives of two visits to the United States, one for geological observation and the second for social as well as geological studies, were published in 1841 and 1845.

The publication in 1863 of his work on the ‘ Antiquity of Man ’ marks an interesting déenoûment of the great movement with which his lifetime was almost coincident, and with which his name and work are inseparably joined. At the end of the last century, the transmutation or development theory was independently and almost simultaneously proposed by three great thinkers, Goethe, Geoffroy St. Hilaire, and Erasmus Darwin. Its final triumph in our day was almost a direct consequence of the principles adopted by Lyell from Hutton and the Huttonians, and urged so clearly and effectively by him in his ‘ Principles.’ Yet Lyell—and this was an interesting exhibition of a worthy trait of his mind—resisted the theory of development for a long time; until after the publication of that most remarkable book of the century, Darwin’s ‘Origin of Species.’ He showed in the early editions of his ‘ Principles ’ a decided, though just and appreciative, opposition to Lamarck’s theories; and it thus happened that Lyell was one of the few veterans in science who were converted from their older view's by Mr. Darwin’s arguments. Though nearly seventy years of age, he showed the genuineness of his conversion by rewriting in the tenth edition of his ‘Principles ’ the chapter on the development theory, and other matters relating to it. This change gives his masterpiece a greater logical completeness and coherency than it had ever had before, and redounded to his credit in this way quite as much as in the exhibition it gave of his openness of mind to scientific arguments, or of the moderation of the conservatism which characterized him as a true English Liberal.

Hutton, the knowledge and practice of whose principles Lyell did so much to extend, was the first to declare that geology was in no wise concerned “with questions as to the origin of things.” By “origin” was then meant the origin of the natures which things have and their first introduction in the theatre of the world. That cosmology should have been so far banished in half a century from zoological conceptions that Mr. Darwin could use, without incurring serious misunderstanding, the title ‘ Origin of Species ’ for his great work, is evidence of the progress made. “Origin” has now come to mean the coming to pass of anything in the course of events, and is concerned only with how things go on from one determinate appearance to another. “In the economy of the world,” said Hutton, “I can find no traces of a beginning, no prospect of an end”; “a declaration,” Lyell remarks, “the more startling when coupled with the doctrine that all past changes in the globe had been brought about by the slow agency of existing causes.” But Lyell was not free at the outset, nor for a long time, from another misleading scholastic conception which scientific progress has also nearly banished, namely, the scholastic meaning of the word “species.” From his deference to the authority of leading minds in systematic natural history he attributed to the authority of their observations what was only involved in a received meaning of a word, namely, that a species was only properly so called because it exhibited invariable characters, and yet that the word was applicable to actual existences. These naturalists, with this meaning in their minds, applied the name to existing and past organic races, implicitly asserting thereby more than their authority as observers could warrant. The word now means not an absolute, but only a comparative fixity of character, so that in Darwin’s treatise both words of the title, ‘ Origin of Species,’ appear with modern unscholastic meanings. But this was in great measure due to the influence of the doctrines and methods which Lyell has done so much to promulgate. In perfect sympathy with the scientific aspirations of earlier Italian geologists to explain the phenomena of the earth’s formations “without violence, without fictions, without hypotheses, without miracles,” he early perceived the value of scientific societies devoted to the patient collection of data for science, and principled against the premature speculation of theories. The Geological Society of London was such an institution, in which no “theories of the earth,” as they were called, were tolerated. Such institutions, like the monastic refuges for culture of old, were securities to scientific observation against the vanity and ferocity of scholastic disputation.

Among the many graphic and instructive illustrations of geological changes from slowly-working natural causes, Lyell gives an account of a great flood at Tivoli, in 1836, in which the “headlong stream,” as Horace had called it, the Anio, produced the most destructive effects; the flood coming “within two hundred yards of the precipice on which the beautiful temple of Vesta stands. But fortunately, this precious relic of antiquity was spared, while the wreck of modern structures was hurled down the abyss.” Vesta, the goddess of the hearth, was the mythological representative of the stability of the earth; and when Aristarchus, the Samian astronomer, first taught the Pythagorean doctrine of the earth’s motion on its axis and around the sun, he was publicly accused of impiety, for “moving the everlasting Vesta from her place.” Lyell is reminded by this coincidence of Playfair’s remark, that when “Hutton ascribed instability to the earth’s surface, and represented the continents which we inhabit as the theatre of incessant change and movement, his antagonists, who regarded them as unalterable, assailed him in a similar manner with accusations founded on religious prejudices.” There appears to be a strong natural association of religious feeling with the idea of stability; and three wrongly consecrated stabilities—that of the earth, that of its continents, and that of its forms of life—have one after another given way to the progress of knowledge, and, though with obstinate resistance from religious sentiment, the changes have taken place without permanent injury to religion.

It is in Lyell’s character as a scholar and writer, however, quite as much as in that of thinker and observer, that his influence has been and will bo felt. His style reveals the man in its calm, clear, scholarly spirit of accuracy. His sentences win confidence and disarm prejudice by their entire freedom from overstatement and advocacy. The man revealed by the style is a model of the qualities in mind and character which distinguish the highest modern social and scientific culture. A tender regard, akin to reverence—to reverence without servility—toward established standards of custom and opinion, kept him, while a Liberal in politics, religion, and science, very far from radicalism in any direction. He was a warm friend of America, and, during his two visits to this country, endeared to him many personal friends. He was married to a lady whose father was also distinguished in geology, Mr. Leonard Homer, formerly a president of the Geological Society, and especially distinguished in the annals of science for the researches for a chronological standard in geology in his examination of the age of the deposits of the Nile mud. Lady Lyell, whom death removed

from her illustrious husband two years ago, had been to him a most devoted and efficient helpmate, through powers and interests trained in the same direction, and by an amiability akin to his own. Sir Charles Lyell was born in Scotland, educated at Exeter College, Oxford, and called to the bar. He was knighted in 1848, and was created a baronet in 1864.

Note on Bastian. [From The Nation 20.508 (24 March 1875): 208.] ⁴²

—The Saturday Review has recently noticed Dr. Bastion’s last experiments favorably; but the incompleteness of his induction of the death-point of bacterial germs will appear from the following considerations. Professor Wyman, having many years ago repeated the original experiments of Pasteur, arrived at the conclusion, as the result of his investigations, that one of two generalizations in biology must be given up: namely, the doctrine that all living beings are derived from germs, or the doctrine that all germs are destroyed by a wet heat of about 150 degrees Fahrenheit, and that direct inductive evidence was not sufficient for deciding which of these two propositions must be considered limited in its generality. There can be little question, however, that on general deductive or philosophical grounds, such as have doubtless determined the scepticism of Dr. Bastian’s critics, the eminent experimenter would not have hesitated as to which of the two doctrines he would limit as to its universality. The temperature at which life is destroyed is one of a class of empirical facts which would not be likely to have the precise generality which belongs to the other principle—omne vivum ex ovo— which Professor Huxley has claimed to be positively settled in biological science. And there are deductive physical reasons for believing that the action of heat on minute organic bodies, like those of infusoria, is not so disorganizing as upon larger organic bodies; so that it is possible that the germs, although paralyzed and injured by a heat necessarily less of course than that which would alter the chemical properties of the infusion itself, might yet so far retain life that their vigor might be more or less recovered under favorable circumstances. Dr. Bastian’s attempt, therefore, to submit the question of the death-point to a test experiment might have been objected to before the experiment was tried, as not ensuring these favorable circumstances, since the mineral salts in which the uninjured germs of bacteria will flourish may be unfavorable to the development of the paralyzed or partially disorganized ones; as is indeed indicated by the fact that the “test-fluids” were chosen because in them life does not arise without inoculation or the introduction of vigorous germs. In fact, it seems obvious that there is a perfectly legitimate hypothesis in this matter of which no experimental tests can be made. All that is undoubtedly proved is that bacteria, when subjected to a temperature of 140 to 100 degrees Fahrenheit, are so far injured as to be unable to recover upon such poor hospital-fare as Dr. Bastian’s test-fluids; ergo, id est non demonstrandum, and the position taken by Professor Wyman is still valid.

Who are our Ancestors? [From The Nation 20.520 (17 June 1875): 405-407.] ⁴³

THE principles of heredity established by modern inductions in biology tell against the barbaric traditions of law and heraldry and for the rights of women, so far, at least, as the influences of strictly inherited qualities, both mental and physical, go towards determining our natures—namely, for the equal right of women to be counted among our ancestors. The likelihood in the average of a grandson’s resembling his maternal grandfather in any quality is as great as that of resembling the paternal one; and a granddaughter is as likely to resemble in any quality her paternal grandmother as the maternal one. This law, which appears rather by the failure of the various fanciful hypotheses held on the subject of heredity than by positive

evidence sought for it, is on this very account the better founded in accordance with the canons of induction—namely, by the method of difference, or the absence of exceptions, taken together with the positive evidence for heredity generally. But this law does not imply that there is any tendency of one sex to transmit to the other any proper qualities of its own, except in that latent state which the law essentially implies, and which, as a mode of transmission, is one of the most important inductions in biological science, having various illustrations and applications.

Nearly all laws of heredity are properly laws of averages, against which, of course, evidences may be massed by a partial or one-sided induction. They can in general be held to be true only as governing averages; or at best as being laws of such real tendencies as mask and modify and even countervail one another. Such real tendencies have been made out by the more philosophical observers, like Dr. Lucas, through the judicious choice of subjects for investigation least likely to be affected by chance or training— e.g., rarely-occurring physiological peculiarities. Some special laws have thus been made out, such as the tendency of transmission to the same sex of individual characters or peculiarities first appearing in one, though otherwise they have no special relation to sex; and on the other hand, the more general secular, slowly-acting, and weaker tendency of transmission to both sexes of qualities, or degrees of qualities, which originally belong to one. This tendency is shown only in connection with the tendency to inherit acquired qualities at earlier and earlier ages, or periods of life, and therefore in a manner independent of adult sex development. The causes which keep the sexes different are, however, much more powerful than this tendency, which is apparently operative only where qualities so transmitted have ceased to be of special sexual importance, or have lost, as they readily might in this case, their original association with sex.

Individual prepotency, again, or the preponderance of influence upon offspring of one parent over the other; the absence of perfect equality of influence in all respects, or the accidental inequality of influence, which may be said to be the most invariable fact of heredity, masks and confuses all other laws, whether of averages or of real tendencies. But this prepotency does not appear to belong to one sex more than to the other; so that the rule holds that in the long run the two sexes are of equal influence in transmitting individual or family characteristics, so far as these are independent of the influences of education and family traditions; and it should be especially noted that characteristics associated with sex are transmitted latently, though none the less really, through the sex in which they do not appear. The very large part, however, which education has to play in human development—in the election and fostering of hereditary tendencies—is another masking and confusing cause, which may account in great measure for traditional and popular notions about descent, but does not really interfere with certain general conclusions in answer to the question, Who and how many are our real ancestors, or those who have determined our really inborn natures? We are quite ready to agree with those who cry, “Great is education!” This power is, indeed, the scientific foundation of law and moral responsibility; but heredity is also great, and even adds to, we believe, instead of diminishing, the true grounds of social institutions, the rights of law and punishment.

The importance of heredity leads to the rather startling consequence from the equality of the sexes in determining descent (exhibiting the role which sexual generation takes in the phenomena of organic life generally), that all living beings, both animals and plants, of races in which sexual generation is the prevailing mode of reproduction, derive their natures on the average from every productive individual of only a few generations back whose descendants have survived within their race or biological province. The true genealogical tree of science branches backwards—a cause of great difficulty and annoyance to the genealogist. When we take account of strictly inherited natures and variations of natures, setting aside the conventions of names and the traditions of external inheritance, we are led by the rule of the equal transmission of inborn qualities by both sexes to search for our origin through two parents and four grandparents, to eight great-grandparents (or six if one’s parents are first-cousins), and sixteen potential great-great-grandparents. And our “gret-gran’thers multiplied by three” would, with their equal spouses, make thirty-two. We call these “potential” ancestors of the fifth degree, since, on account of the intermarriages of relatives within permitted grades of consanguinity, even the sixteen possible ancestors of the fourth degree may be condensed, so to speak, to the lesser number even of eight. Such reticulation or interlacing of branches in the back-reaching lines of ancestry through which one may arrive by several paths to the same individual ancestor (who, therefore, fills the place of several potential ancestors), becomes more and more frequent, and ultimately, or in the long run, a predominant feature of the natural genealogical tree; for it takes but twenty generations or about live hundred years to reach a generation with more than a million potential ancestors in it, or one which can bo reached through more than a million various lines of ancestry. We call two lines different, even though they may coincide in all but small portions of their courses.

It is in a high degree probable in the average case that a few thousand individuals have filled the larger number of these million places, since true races, even of men, are usually confined to narrow provinces. An insular position like that of Iceland is not the only kind of isolation in a race which would make any one of the present generation a descendant by so many thousands of lines (on the average) from every productive individual of twenty generations ago, as almost certainly to make every such individual, who has any living descendants at all, an ancestor of all now living in the province of his race. The agricultural peoples of the counties of England appear to be thus isolated in great measure, so that of a few thousands, five hundred years ago, each would be an ancestor of almost all living at the present time in his county. But neither such provincial limitations of a race, nor any but the most rigid caste interdictions of marriage, would prevent an English lord’s being the descendant of a very large number of peasants of five hundred years ago, since the interdicted marriages are not between absolutely separated castes, and alliances descend by small grades in the social scale, without scandal, through collateral lines, in the course of a few generations, from the noble to the serf; and ascend by the same grades.

The case of Iceland affords an instructive illustration of the remarkable effect of the biological principle of bi-sexual generation, namely, that in a comparatively short, almost insignificant, period in the duration of a race, even the most advanced has the solidarity of a zoophyte. Iceland has been occupied for about thirty-eight generations by a nearly fixed population of fifty thousand—an isolated race of Scandinavians. The number of potential ancestors which any one has of the thirty-eighth degree is about two hundred and seventy-five thousand millions. All these were represented in the case of the present Icelanders by fifty thousand emigrants; so that on the average each emigrant filled the places of five and a half millions potential ancestors, or could be reached on the average by this number of partially differing reticulate lines of descent. If we reckon the average duration of human life at a third of a century, the condensation on the whole has been from five hundred and fifty thousand million possible ancestors of all degrees, to the thirty-eighth inclusive, down to the one million four hundred thousand who have actually lived in the island, or to one in three hundred and ninety-three thousand of potential ancestors. It is thus made almost certain that every original emigrant to this island who has any present descendants at all is an ancestor of all now living. A doubt of this conclusion arises, however, from the circumstance that the inhabitants have been more or less divided into isolated provinces; but if occasional intermarriages between members of different provinces have amounted to one in ten thousand marriages, a connection through these of every present inhabitant with all the original settlers would be in a very high degree probable.

Common qualities in the Icelander distinguishing him from others of the Scandinavian races, such as travellers have noticed, and especially physiological ones like that early noted by Sir Henry Holland (of a superior stature in the Icelandic men, due mainly to the greater lengths of their spinal column) would not necessarily require the supposition of a close intermixture of the race to account for it, unless it be an instance of that morphological variation to which limited races are more subject than extensive ones. But such a physiological character is more likely to be the direct common consequence of similar conditions, exercises, and modes of life, and of their inherited effects, than of the mere drifting of morphological variation on one hand, or the survival of characters from the advantages of them in the struggle for existence. The human struggle usually depends, or has come to depend, on other than merely bodily or athletic grounds of advantage. Intelligence and strength in union or brotherhood have long been the vantage-grounds of the human contest in the competition of race with race, or tribe with tribe, and in opposition to unfavorable external conditions. And biology affords a proof, in the natural genealogical tree, of the merely natural brotherhood of men quite as impressive as the theological derivation of the race from a single pair; but does not make so complete and emphatic a reference back to one concentrated responsibility for human weaknesses and sins. How great this becomes on the theological theory can also be estimated by the above mathematical reasoning. Thus, if the degree of relationship of any ancestor to a descendant be represented by the number of places of potential ancestors of his degree occupied by him, compared to the whole number of that degree, then the relationship of each parent to their offspring would

be one-half; that of each grandparent one-quarter; of each great-grandparent one-eighth; except from the marriage of first-cousins, which would make a pair of the eight fill two-eighths each, or one-quarter, or be of the same degree as grandparents: and if in any remote generation a single pair could have filled all the places of the potential ancestors of that generation, their relationship to all their descendants would be of the same degree as that of immediate parents; so that though the number of potential ancestors of the generation of the estimated time of Adam would be a number requiring more than seventy numeral figures to express it, yet with all these concentrated, as was possible, in a single pair, this pair comes to have the proximity of relationship to us of immediate parents. Such ancestors as Adam and Eve would therefore be nearer relatives to us than our grandparents.

A recent newspaper correspondence has discussed the statement that the Roman Princess Torlonia, though of a family which became prominent only eight centuries ago, was yet the descendant of a thousand Colonnas. The thirty-two generations which may be assumed for this period would give the princess about eighty-six hundred millions of potential ancestors in all. This number, which would of course in any case be greatly reduced by the intermarriage of remote relatives, might easily include among its representatives many thousands of persons bearing this family name, but would doubtless also be represented by many more thousands of persons as humble in name and origin as the Colonnas were eight centuries ago.

Joseph Winlock. [From The Nation 20.520 (17 June 1875): 409-410.] ⁴⁴

—Professor Joseph Winlock, Director of the Observatory of Harvard College, died suddenly after a brief illness last Friday morning, June 11, at the age of forty-nine. One of the foremost of American astronomers, whose honorable career in science began thirty years ago, who has filled with great credit several important positions of scientific labor and trust, is thus cut off in the midst of a life whose usefulness cannot be estimated by ordinary standards. Well-known and highly estimated by all active collaborators in astronomy, both at home and abroad, he was never so well-known to others or to the public as his important services deserved. This was chiefly on account of a modest shrinking from any candidacy for honors, amounting almost to an aversion from them, and an indifference to an uncritical or merely popular reputation. Immediately upon graduating from Shelby College, Kentucky, in 1845, he was appointed Professor of Mathematics and Astronomy in that College, where he remained until 1853, when he removed to Cambridge, Mass., and took part in the computations of the ‘American Ephemeris and Nautical Almanac,’ then under the superintendence of Admiral C. H. Davis. In 1857, he was appointed Professor of Mathematics of the United States Navy; and in that capacity served in succession as Assistant at the Naval Observatory at Washington, as Superintendent of the Nautical Almanac and as Director of the Mathematical Department of the Naval Academy at Annapolis, Md. On the breaking out of the war, in 1801, he was a second time made Superintendent of the Nautical Almanac. His next service to astronomy was in the position of Director of the Observatory of Harvard College, and Phillips Professor of Astronomy, to which he was appointed in 1865—a position already made highly honorable by the labors of his predecessors, the distinguished astronomers, Professors W. C. Bond and G. P. Bond. Ho has also served at the same time as Professor of Geodesy in the Mining School of Harvard College. Only a few months ago, Mr. Bristow appointed him the Chairman of the Congressional Commission for Investigating the Causes of Steam-Boiler Explosions. These many appointments to places of responsibility are evidences of the rare sagacity, skill, sound judgment, and integrity of character which were qualities conspicuous to all who knew him well or dealt with him in his various duties. Upon taking charge of the Cambridge Observatory, he proceeded with energy to complete its equipment, adding to its already famous resources a meridian circle, constructed in accordance with his designs by Throughton &Simms of London—an instrument whose performance has been pronounced by competent judges the best of its kind in the world. The distinguished astronomer, Adams, of Cambridge, England, subsequently ordered an instrument from the same makers to be constructed on the same model. Professor Winlock also secured for this Observatory a very perfect astronomical clock, made by Frodsham of London, from which, through contrivances of his own, true time is telegraphed to neighboring cities. He also set the famous equatorial instrument of the Observatory upon a new career of usefulness and glory in astronomical spectroscopy. In 1870, he put into regular working efficiency a mode of observing the sun—namely, by a single lens, a heliostat, and photograph—which he independently conceived, and was the first to utilize as a form of systematic observatory work. French astronomers have lately been contending with one another about priority in the conception of this method of observation, which was so important a part of the equipment for observing the transit of Venus last December furnished to American expeditions; but in all that really constitutes effective originality the honor of this invention undoubtedly belongs to Professor Winlock. He was, however, almost entirely indifferent, in the singleness of his devotion to his favorite science, to popular fame, or even to contemporary recognition. Besides his observatory work, he was engaged on two occasions in the direction of expeditions to observe solar eclipses—namely, that to Kentucky in August, 1869, and that to Spain in December, 1870. Though ingenious as an inventor, his judiciousness was so much more prominent a quality that his originality is shown rather in a thoroughness and detailed efficiency of contrivance than in the more brilliant qualities that distinguish the more famous inventors. Very numerous little but very effective improvements in astronomical methods distinguish the astronomical art of the present day: and in these Professor Winlock's originality was very considerable.

Among his published works, besides the ‘Annals of the Observatory’ under his directorship, are a set of tables of the planet Mercury (arranged with characteristic neatness and ingenuity); brief papers in astronomical journals and in the ‘Proceedings of the American Academy of Arts and Sciences.’ He was a native of Kentucky, and the grandson of General Joseph Winlock, who entered the American army at the beginning of the Revolutionary War and also served in the war of 1812, and was a member of the convention which drew up the constitution of the State of Kentucky.

Sir Henry Maine. [From The Nation 21.522 (1 July 1875): 9.] ⁴⁵

—In his recent Rede Lecture, of which we spoke lately, Sir Henry Maine refers to what he calls “the famous ‘ greatest happiness ’ principle of Bentham” as one of the “maxims of public policy and private conduct” likely to be revised and corrected by what he terms a new method of enquiry. Before discussing this point, it maybe well to note that Bentham himself says: “Priestley was the first (unless it was Beccaria) who taught my lips to pronounce this sacred truth: that the greatest happiness of the greatest number is the foundation of morals and legislation” (‘Works,’ vol. x., p. 142). The credit of being the first to formulate this doctrine seems to belong to Beccaria. In the introduction to his ‘ Treatise on Crimes and Punishments ’ (Dei Delitti e delle Pene), first published in 1704, he says: “If we turn to history we shall see that laws, which are or ought to be the covenants of free men, have been for the most part only the instrument of the passions of some few individuals, or have arisen from a fortuitous and transient necessity, and that they have by no means been dictated by a cool investigator of human nature who had concentrated in a single point the actions of a multitude of men, and considered them from this point of view, namely, the greatest happiness divided among the greatest number (lamassima felicità divisa net maggior numero).” This “greatest happiness” principle, says Sir Henry Maine, “has great imperfections, unless some supplementary qualifying principles be discovered, and for these qualifications I look to some new application of comparative methods to customs, ideas, and motives.” No doubt the wording of this motto of a great and influential school of practical legislation and morality needs to be explicated and explained in a manner quite different from that in which the critics of the school have done it. For these have drawn for the most part their understanding of the principle from the mere wording of it, without consulting the writings of which this motto is more properly to be regarded as the title or summary name. Yet it is far from clear, when we consult these writings, how the principle, as unfolded by them, could be supplemented by any qualifying principle of the sort which Sir Henry Maine suggests. It is true indeed that in what is the real difficulty of the principle in application—namely, in making a true determination of the objective happiness or true well-being of any people for whom a legislator has to make and improve laws—there is involved the consideration of many historical facts, historical products, in the form of existing “customs, ideas, and motives.” That Sir Henry Maine should have supposed the consideration of these to be anything supplementary to the principle, and not rather already and essentially demanded by it, is surprising; for he cannot be supposed to have derived his whole knowledge of the principle, like most sentimental critics of it, from the words of its name. He must have known that in Bentham’s writings, and in those of his immediate followers, a most detailed and laborious discussion of existing laws and usages is made an essential part of criticism on them, and of devices for reforming them. A more thorough knowledge of human nature, and of the force of customs, ideas, and motives, than Bentham possessed, are no doubt requisites for the wisest legislation; yet this can hardly be of the nature of supplementary principles.

—It should not be supposed that the greatest-happiness principle is anything more than the highest practical guide or test, wherever it is applicable, or that it has anything to do with the explanation of the historical development of law. It is not a theoretical principle. No one really acquainted with its meaning and use can suppose it intended for an explanation of the historical phases of laws and morals; for in fact it has had altogether too little to do with the growth of laws. It is, as Beccaria says, the principle which legislators ought to have observed, and is in great measure opposed to what they have really done. Nor again is this principle regarded by its advocates as an exclusive motive principle or sanction, except with the legislator as such, or with the influential citizen who has the power to mould opinions and customs or the secondary morals of society, and to bring to bear in true directions the various more immediate sanctions of laws and morals. To such as these, the guides and benefactors of society, the principle should be an all-inclusive motive principle, or the highest sanction, and cannot in this relation be the selfish principle it is commonly charged with being. Its real place in ethical and legal writings is as the practical principle of all true legislation, including under this the reformation of current moralities through the sanctions of opinion. The advocates of the principle also hold, however, that it is the true foundation of primary morals, as well as of the laws which legislation and opinion can and ought to make; but in this relation the principle can only be a theoretical one, or a summary statement of the rules themselves of human morality, since the primary morals, whether wholly instinctive or a mixed inheritance half-instinctive and half-traditional in a race, like language, are obviously not the devices of legislators and moralists, though such leaders have always had to do with applying various requisite sanctions to the fundamental laws of conscience. Yet the principle of “the greatest happiness for the greater number” is in this form of its enunciation essentially a practical principle or rule of duty for the legal and moral reformers and guides of mankind. As the fundamental theoretical principle of all human morality, or as the principle which has guided nature in the production of moral instincts and universal traditions of law, its statement should be modified; for in this relation it is the principle whereby the greatest numbers of the most prosperous individuals have been produced in races having the social nature of man. In this, its Darwinian form, it is, however, just as obnoxious as in the Benthamite or Beecarian form to believers in an absolute morality, who, on their principles, are bound to regard the conduct of the worker-bees of a hive as morally reprehensible, even from a reflective philosophical bee’s point of view, when they kill their brothers, the drones, at the end of the season; although this apiarian custom conduces to produce the greater number of prosperous communities of the hive.

Review of Blackwell's Sexes in Nature. [From The Nation 21.524 (15 July 1875): 43-44.] ⁴⁶

BLACKWELL’S ‘SEXES IN NATURE.’ ‘The Sexes throughout Nature. By Antoinette Brown Blackwell.’ New York: G. P. Putnam’s Sons. 1875. ⁴⁷

A SINCERE desire for the amelioration of women—for a greater advancement in the same direction in which the progress of civilization has already carried them—ought to have inspired a very different line of argument from what Mrs. Blackwell has seen lit to follow in the principal essay of her book, that “On Sex and Evolution.” The practical good sense and skill in accomplishing desirable ends by appropriate means, which is naturally a true feminine superiority, would have dictated a different course. Like too many of the more prominent feminine leaders of the movement, our author seems to aspire to rival, not men in general, but that small faction among them who are called philosophers, and, by showing how a woman may even cope with these, to demonstrate superiority to all the rest. But men of the Anglo-Saxon race are not in the habit of acknowledging the superiority of philosophers. Even Mr. Herbert Spencer, with whom Mrs. Blackwell ventures to dispute on some points, though apparently in her view the type of this kind of superiority, and though the first genuine universologist and omniscientist which the race has at all honored for more than two centuries, has not hit upon lines of argument likely very soon to subdue the masculine prejudices of this race.

Proofs of superiority or inferiority or equality, as general theses, from profound principles and the nature of things, make small impression on the unsubtle Anglo-Saxon mind. Such minds are apt to challenge a question of this sort, to apply the Socratic elenchus, and demand first of all what the question really means; as by asking, in respect to the assertion of the abstract attributes of superiority, equality, or inferiority, about what these attributes are maintained? Superior in what is the male or the female? Or equal in what are they? To attempt after a French or German philosopher’s fashion to establish the main unqualified thesis, and then freely deduce from it any desirable consequence, has not yet become the philosophical habit of the unimaginative, slow-minded Anglo-Saxon in respect to any question of science or politics. If Mrs. Blackwell had contented herself with simply challenging the meaningless thesis of masculine superiority as an absolute one, trying to find out what kind was claimed, and why or in what respects superiority is maintained, she would have shown the quality which most of all distinguishes the sound feminine mind of her race. But, unfortunately, she has allowed that the general thesis of masculine superiority has a meaning, and she has attempted to oppose it by what appears to us the equally meaningless thesis of the natural equality of the sexes.

Mr. Darwin, as a naturalist, has enquired in his treatise on ‘ Selection in Relation to Sex ’ (without the least conscious approach to any political or sociological sentiment on the subject) into the origin of the most conspicuous differences between closely allied species or races, on the theory of a common descent; namely, those through which it appears, as a very general rule, that the males of closely allied races differ more than the females (differences which are, therefore, to the naturalist the more noticeable and important characters for classification). In doing this, he has, it seems, though it must have been unwittingly, given testimony against the essential equality of the sexes, by “fixing attention, as he does, upon masculine characters only” (p. 59). In thus noticing secondary sexual differences, he seems to Mrs. Blackwell to maintain that there is “no equilibrium of sex.” And she adds that “the two leading philosophers of evolution [Darwin and Spencer], each after his own method of investigation, being intent upon explaining the wider equilibrium between organic nature and its external conditions, it becomes fairly credible that they may have failed to give satisfactory attention to the lesser equilibria, of sex, of each individual organism, and of every organic cell.” It appears to us very unjust, not only to Mr. Spencer’s originality but to his independence, to credit Darwin with any share in the explanations of “equilibria,” since the latter has only undertaken with the inferior intelligence of a naturalist to account for diversities in organic nature, without undertaking at all to weigh them in the scales of absolute science. To do this approximately— for she claims no more—with reference to sex, has been left to the deep insight of our author.

We have studied with care Mrs. Blackwell’s “Tabular View of Equations in Organic Nature” (p. 55), and we confess ourselves completely baffled by its mathematics. Under insects, fishes, cetacea, birds, herbivora, carnivora, and man, she has set down certain characters for comparison, putting pluses and minuses against them for both sexes, according as in each character the one sex exceeds or falls short of the other. Thus, for insects, wo have comparison of the sexes in “structure” (a rather vague character), “size, color, activity, products, sexual love, and parental love.” To these, in the class of fishes, “nurture” is added. And further, “strength” is substituted for color in the order of the cetacea. And still further, in the class of birds, “color” is restored in the place of “strength,” and “ornaments” and “pugnacity” are added. Similar lists are given for higher divisions of animals, including man, who has a long list of nineteen characters by which fairly to compare the sexes. The author thinks that by thus “holding the feininine character up beside the others in a balanced view the equilibrium is restored” which Mr. Darwin’s partial view of the matter has disturbed!

In drawing up this “table of comparative equations, the mean of characters in each class is taken as zero.” We are much puzzled to understand what is meant by a “mean of characters,” when these are not to be compared in quantity. How much size does Mrs Blackwell suppose to be equal to a given amount of color? Or is it the importance of these to an animal’s existence that is thus measured; and does she mean that the characters are so chosen that they are of equal importance to the welfare of the race? Perhaps, however, the solution is (and this may account for the inequality of the number of plus and minus signs, notwithstanding her final estimate of “sex = sex” throughout nature) that the signs affixed to characters, together with the author’s estimate of the comparative importance of them, will foot-up zero. This, however, does not appear from the tables themselves, and must be an estimate by one or the other of the two mental powers which the author sets down in her list for man and counts among feminine superiorities, namely, “direct insight of facts” or “direct insight of relations”; for it is certainly beyond the power of ordinary masculine mathematics.

Such a mode of approaching the practical questions of the coeducation of the sexes and the political and professional qualifications and legal rights of women, is, we venture to believe, rather aside from the usual feminine methods of thought. The soundest intellects, whether feminine or masculine, are not apt to be caught by such meaningless propositions as that of equality between things not at all comparable in quantity, either by themselves or in common influences and effects. That “the male is superior” among the higher animals has, however, a real meaning, independently of the importance of characters in the classifications of natural history, in the common understanding of this elliptical phrase—a meaning which does not refer to any such grounds of comparison as those presented in this book, except where the author has incidentally referred to the quality of “pugnacity” in her lists of characters for birds and mammals. This quality also belongs to certain male fishes and to reptilian males. That the author should have omitted it also from the list of characters for man is remarkable, considering how combative the masculine man is, not only for a cause, but from the love of battle; in how many directions an active competitive disposition urges him; and how his very superiority in reasoning power, which our author allows, is of the nature of belligerency, since arguments are the weapons of the mind. Superiority in the sense of imperiousness, consciousness of the power of victory—a superiority incessantly sought, if not attained, in that active rivalry which is a better name than “pugnacity” for this generic masculine quality—is what we believe to be generally referred to in speaking of the male as the superior. It is not a superiority in the number nor in the importance to life of the qualities that distinguish him, nor a superiority in unconscious endowments of nature— which only science could estimate—but only in those issues of conscious activities which kindle masculine ambitions and active rivalries most readily, and urge the male to battle and to the ultimate arbitrament of the

“Laws of Battle,” on the basis of which all his more refined and civilized rights and superiorities (like the suffrage) really rest. This, which is the greatest mental difference between the human sexes, is probably not so great, however, between the averages of the two in civilized races as is the range of mental difference in either sex. It nevertheless gives a marked tone in connection with the differences of education and occupation, so that men generally gain with greater readiness through this urgent internal impulse what are commonly but wrongly regarded as natural endowments, the power of abstract reasoning, and that sentiment of justice (through a keener observation of the conditions of effective competition) which are allowed by our author to be among possible masculine superiorities (p. 140). Masculine justice is, however, in itself only the sentiment of fair competitive dealing, and distinguishes the active rivalry of the male from that quarrelsomeness which has by some thinkers been mistaken for it, and which the name “pugnacity” does not exclude. The superiority of conscious victory, for which the male is at least the most ardent candidate, determines to so great a degree the competitive exercises and studies of youths that it would be a great loss to them, however beneficial coeducation may be to the other sex, if its use as an incentive to study were abandoned. The boy declines by a true masculine instinct to compete with the girl, half conscious that he labors under a disadvantage for present display, as he instinctively converts his exercises and acquisitions into a firmer command of powers which are to serve for subsequent trials and more important struggles.

No doubt a sympathetic, mutually-aiding aspiration for excellence is a more refined motive, and, though much less effective, is gradually becoming in the progress of civilization a substitute for the motives of active rivalry which are more distinctive of sex. Many most important interests and pursuits have lost in this progress their association with the overshadowing category of sex, the former extent of which even to inanimate objects is indicated by the grammatical genders of the languages which barbarians have transmitted to us. To further this progress, the best thinkers have contended for the irrelevancy of sex to much that is still traditionally associated with it, and for the rights and duties of adult human individuals independently of sex. The absurd metaphysical, unqualified thesis of the equality of the sexes, for which this book contends, is, even with the Spencerian calculus of evolution, a barren argument, quite beyond the comprehension of the masculine arithmetic of justice. Our author adds to the passage we have quoted above on “equilibria” of sex, organism, and cell, that “if these are not each moving points of simpler adjustments within wider and wider systems of more complex adjustments, then I fail utterly to comprehend the first principle of organization.” We fail to comprehend it oven if these “equilibria” are what is thus defined. Such a discussion of a practical question has to us the appearance of a wretched affectation of profundity, rather than of a real interest in the advancement of women.

A Popular Explanation (For those who Understand Botany) of the Mathematical Nature of Phyllotaxis [From American Naturalist 10 (June 1876): 326-329. Published by Harvard Botany professor George Goodale.] ⁴⁸

BY THE LATE CHAUNCY WRIGHT. This article was prepared by Mr. Wright several years ago, at Professor Gray's suggestion. In its manuscript form it has been found of much interest and value to the botanical students in Harvard College. It is here reprinted without change from Mr. Wright's notes. ⁴⁹

Take, by the finger and thumb of your right hand, hold of a spike of Plantago major, Lepidium Virginicum, or other flower-cluster with symmetrically crowded flowers, and with the finger and thumb of the left hand grasp it a little higher up, so as to include between the two hands a dozen or twenty buds on a piece of stem about equally tough from end to end. Twist the stem, and if it twists equally in all parts you will bring your buds into a small number of ranks, let us say 8. By twisting a little in the opposite direction you will get them into 5 ranks. Twist harder, and if your stem is tough enough to stand the twist you will bring them into two ranks. Turn back to 8 rows, and twist harder in that direction; you will fetch your buds into 3 rows. Then twist still harder in that direction, and if you have an old, tough, plaintain spike, you may get the seed-vessels all into one row before your stalk is twisted off.

Thus by mechanical twisting, if the twist is equal in all parts of the stem, we get on one side of the natural position the number of rows 5 and 2, and on the other side 8, 3, and 1. Hence if we begin with the most twisted position and come toward the natural position, we get the numbers

Now these series of numbers indicate the approach towards the untwisted position. What would be the number of ranks in that theoretically perfect untwisted state? As both these series of numbers are increasing, that is, the number of ranks decreases as you twist either way, you may infer that in the untwisted state the number of ranks is prodigious or innumerable. Carrying on the series by adding zigzag as the lines are dotted, we should get

Hence we say that the slightest conceivable twist in one direction makes the number of ranks 377, a little more in that direction gives 144, 55, 21, 8, 3, 1, while the slightest twist in the opposite direction gives us 233, a little more 89, 34, 13, 5, 2, 1.

There is, however, a mystery in the space between 233 and 377, between twisting one way and twisting the other. Let us not seek to solve it by running the number of ranks up higher, to 610, 987, 1597, etc., but approach it in another way.

In the stem twisted one way, the angle between the leaves is 1/2 the whole circumference, or or 2/5, or 5/13, etc.; with the stem twisted the other way the angle is or 1/3, or 3/8, or 8/21, or 21/55 etc., the circumference. Let us set these in double rows: —

Or putting them in decimals we shall see how they converge towards the same value: —

Take the high fraction 1597/4181 in the upper series and turn it into decimals, we get .38196603. If the leaves were at this angle they would form 4181 rows or ranks, and the least twist would produce the lower numbers. Let us now attempt to find some

simpler mode of representing these fractions .38196608 or 1597/4181, which are the same.

Dividing both numerator and denominator of 1597/4181 by 1597 will give 1/2 + 987/1597; dividing each term of the last fraction by 987 gives us

and continuing the process gives us

equal to

Now calling the fraction

continued indefinitely by the name of x, it is plain that the phyllotactic fractions beginning with 1/2, 1/3, 2/5, 3/8, 5/13 continually approach nearer and nearer to the value 1/2+x or

whence

This expression, 1/2 is equal to .38196+, and expresses the exact ratio of the leaves in a theoretically untwisted stem when the number of rows is infinite. Other arrangements

are simply approximations to this (as though they aimed at this but got the stem twisted in growing), such as