Chapter XXXVI: Epilogue (1)

In the beginning of this book I said that its scope and treatment were of so prefatory a kind that of other preface it had no need; and now, for the same reason, with no formal and elaborate conclusion do I bring it to a close. The fact that I set little store by certain postulates (often deemed to be fundamental) of our present-day biology the reader will have discovered and I have not endeavoured to conceal. But it is not for the sake of polemical argument that I have written, and the doctrines which I do not subscribe to I have only spoken of by the way. My task is finished if I have been able to shew that a certain mathematical aspect of morphology, to which as yet the morphologist gives little heed, is interwoven with his problems, complementary to his descriptive task, and helpful, nay essential, to his proper study and comprehension of Form. _Hic artem remumque repono._

And while I have sought to shew the naturalist how a few mathematical concepts and dynamical principles may help and guide him, I have tried to shew the mathematician a field for his labour,—a field which few have entered and no man has explored. Here may be found homely problems, such as often tax the highest skill of the mathematician, and reward his ingenuity all the more for their trivial associations and outward semblance of simplicity.

That I am no skilled mathematician I have had little need to confess, but something of the use and beauty of mathematics I think I am able to understand. I know that in the study of material things, number, order and position are the threefold clue to exact knowledge; that these three, in the mathematician’s hands, furnish the “first outlines for a sketch of the Universe”; that by square and circle we are helped, like Emile Verhaeren’s carpenter, to conceive “Les lois indubitables et fécondes Qui sont la règle et la clarté du monde.”

For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural {779} Philosophy are embodied in the concept of mathematical beauty. A greater than Verhaeren had this in mind when he told of “the golden compasses, prepared In God’s eternal store.” A greater than Milton had magnified the theme and glorified Him “who sitteth upon the circle of the earth,” saying: He measureth the waters in the hollow of his hand, he meteth out the heavens with his span, he comprehendeth the dust of the earth in a measure.

Moreover the perfection of mathematical beauty is such (as Maclaurin learned of the bee), that whatsoever is most beautiful and regular is also found to be most useful and excellent.

The living and the dead, things animate and inanimate, we dwellers in the world and this world wherein we dwell,—πάντα γα μὰν τὰ γιγνωσκόμενα,—are bound alike by physical and mathematical law. “Conterminous with space and coeval with time is the kingdom of Mathematics; within this range her dominion is supreme; otherwise than according to her order nothing can exist, and nothing takes place in contradiction to her laws.” So said, some forty years ago, a certain mathematician; and Philolaus the Pythagorean had said much the same.

But with no less love and insight has the science of Form and Number been appraised in our own day and generation by a very great Naturalist indeed:—by that old man eloquent, that wise student and pupil of the ant and the bee, who died but yesterday, and who in his all but saecular life tasted of the firstfruits of immortality; who curiously conjoined the wisdom of antiquity with the learning of to-day; whose Provençal verse seems set to Dorian music; in whose plainest words is a sound as of bees’ industrious murmur; and who, being of the same blood and marrow with Plato and Pythagoras, saw in Number “la clef de la voûte,” and found in it “le comment et le pourquoi des choses.”

NOTES:

[1] These sayings of Kant and of Du Bois, and others like to them, have been the text of many discourses: see, for instance, Stallo’s _Concepts_, p. 21, 1882; Höber, _Biol. Centralbl._ XIX, p. 284, 1890, etc. Cf. also Jellett, _Rep. Brit. Ass._ 1874, p. 1.

[2] “Quum enim mundi universi fabrica sit perfectissima, atque a Creatore sapientissimo absoluta, nihil omnino in mundo contingit in quo non maximi minimive ratio quaepiam eluceat; quamobrem dubium prorsus est nullum quin omnes mundi effectus ex causis finalibus, ope methodi maximorum et minimorum, aeque feliciter determinari queant atque ex ipsis causis efficientibus.” _Methodus inveniendi_, etc. 1744 (_cit._ Mach, _Science of Mechanics_, 1902, p. 455).

[3] Cf. Opp. (ed. Erdmann), p. 106, “Bien loin d’exclure les causes finales..., c’est de là qu’il faut tout déduire en Physique.”

[4] Cf. p. 162. “La force vitale dirige des phénomènes qu’elle ne produit pas: les agents physiques produisent des phénomènes qu’ils ne dirigent pas.”

[5] It is now and then conceded with reluctance. Thus Enriques, a learned and philosophic naturalist, writing “della economia di sostanza nelle osse cave” (_Arch. f. Entw. Mech._ XX, 1906), says “una certa impronta di teleologismo quà e là è rimasta, mio malgrado, in questo scritto.”

[6] Cf. Cleland, On Terminal Forms of Life, _J. Anat. and Phys._ XVIII, 1884.

[7] Conklin, Embryology of Crepidula, _Journ. of Morphol._ XIII, p. 203, 1897; Lillie, F. R., Adaptation in Cleavage, _Woods Holl Biol. Lectures_, pp. 43–67, 1899.

[8] I am inclined to trace back Driesch’s teaching of Entelechy to no less a person than Melanchthon. When Bacon (_de Augm._ IV, 3) states with disapproval that the soul “has been regarded rather as a function than as a substance,” R. L. Ellis points out that he is referring to Melanchthon’s exposition of the Aristotelian doctrine. For Melanchthon, whose view of the peripatetic philosophy had long great influence in the Protestant Universities, affirmed that, according to the true view of Aristotle’s opinion, the soul is not a substance, but an ἑντελέχεια, or _function_. He defined it as δύναμις _quaedam ciens actiones_—a description all but identical with that of Claude Bernard’s “_force vitale_.”

[9] Ray Lankester, _Encycl. Brit._ (9th ed.), art. “Zoology,” p. 806, 1888.

[10] Alfred Russel Wallace, especially in his later years, relied upon a direct but somewhat crude teleology. Cf. his _World of Life, a Manifestation of Creative Power, Directive Mind and Ultimate Purpose_, 1910.

[11] Janet, _Les Causes Finales_, 1876, p. 350.

[12] The phrase is Leibniz’s, in his _Théodicée_.

[13] Cf. (_int. al._) Bosanquet, The Meaning of Teleology, _Proc. Brit. Acad._ 1905–6, pp. 235–245. Cf. also Leibniz (_Discours de Métaphysique; Lettres inédites, ed._ de Careil, 1857, p. 354; _cit._ Janet, p. 643), “L’un et l’autre est bon, l’un et l’autre peut être utile ... et les auteurs qui suivent ces routes différentes ne devraient point se maltraiter: _et seq._”

[14] The reader will understand that I speak, not of the “severe and diligent inquiry” of variation or of “fortuity,” but merely of the easy assumption that these phenomena are a sufficient basis on which to rest, with the all-powerful help of natural selection, a theory of definite and progressive evolution.

[15] _Revue Philosophique._ XXXIII, 1892.

[16] This general principle was clearly grasped by Dr George Rainey (a learned physician of St Bartholomew’s) many years ago, and expressed in such words as the following: “......it is illogical to suppose that in the case of vital organisms a distinct force exists to produce results perfectly within the reach of physical agencies, especially as in many instances no end could be attained were that the case, but that of opposing one force by another capable of effecting exactly the same purpose.” (On Artificial Calculi, _Q.J.M.S._ (_Trans. Microsc. Soc._), VI, p. 49, 1858.) Cf. also Helmholtz, _infra cit._, p. 9.

[17] Whereby he incurred the reproach of Socrates, in the _Phaedo_.

[18] In a famous lecture (Conservation of Forces applied to Organic Nature, _Proc. Roy. Instit._, April 12, 1861), Helmholtz laid it down, as “the fundamental principle of physiology,” that “There may be other agents acting in the living body than those agents which act in the inorganic world; but those forces, as far as they cause chemical and mechanical influence in the body, must be _quite of the same character_ as inorganic forces: in this at least, that their effects must be ruled by necessity, and must always be the same when acting in the same conditions; and so there cannot exist any arbitrary choice in the direction of their actions.” It would follow from this, that, like the other “physical” forces, they must be subject to mathematical analysis and deduction. Cf. also Dr T. Young’s Croonian Lecture On the Heart and Arteries, _Phil. Trans._ 1809, p. 1; _Coll. Works_, I, 511.

[19] _Ektropismus, oder die physikalische Theorie des Lebens_, Leipzig, 1910.

[20] Wilde Lecture, _Nature_, March 12, 1908; _ibid._ Sept. 6, 1900, p. 485; _Aether and Matter_, p. 288. Cf. also Lord Kelvin, _Fortnightly Review_, 1892, p. 313.

[21] Joly, The Abundance of Life, _Proc. Roy. Dublin Soc._ VII, 1890; and in _Scientific Essays_, etc. 1915, p. 60 _et seq._

[22] Papillon, _Histoire de la philosophie moderne_, I, p. 300.

[23] With the special and important properties of _colloidal_ matter we are, for the time being, not concerned.

[24] Cf. Hans Przibram, _Anwendung elementarer Mathematik auf Biologische Probleme_ (in Roux’s _Vorträge_, Heft III), Leipzig, 1908, p. 10.

[25] The subject is treated from an engineering point of view by Prof. James Thomson, Comparisons of Similar Structures as to Elasticity, Strength, and Stability, _Trans. Inst. Engineers, Scotland_, 1876 (_Collected Papers_, 1912, pp. 361–372), and by Prof. A. Barr, _ibid._ 1899; see also Rayleigh, _Nature_, April 22, 1915.

[26] Cf. Spencer, The Form of the Earth, etc., _Phil. Mag._ XXX, pp. 194–6, 1847; also _Principles of Biology_, pt. II, ch. I, 1864 (p. 123, etc.).

[27] George Louis Lesage (1724–1803), well known as the author of one of the few attempts to explain gravitation. (Cf. Leray, _Constitution de la Matière_, 1869; Kelvin, _Proc. R. S. E._ VII, p. 577, 1872, etc.; Clerk Maxwell, _Phil. Trans._ vol. 157, p. 50, 1867; art. “Atom,” _Encycl. Brit._ 1875, p. 46.)

[28] Cf. Pierre Prévost, _Notices de la vie et des écrits de Lesage_, 1805; quoted by Janet, _Causes Finales_, app. III.

[29] Discorsi e Dimostrazioni matematiche, intorno à due nuove scienze, attenenti alla Mecanica, ed ai Movimenti Locali: appresso gli Elzevirii, MDCXXXVIII. _Opere_, ed. Favaro, VIII, p. 169 seq. Transl. by Henry Crew and A. de Salvio, 1914, p. 130, etc. See _Nature_, June 17, 1915.

[30] So Werner remarked that Michael Angelo and Bramanti could not have built of gypsum at Paris on the scale they built of travertin in Rome.

[31] Sir G. Greenhill, Determination of the greatest height to which a Tree of given proportions can grow, _Cambr. Phil. Soc. Pr._ IV, p. 65, 1881, and Chree, _ibid._ VII, 1892. Cf. Poynting and Thomson’s _Properties of Matter_, 1907, p 99.

[32] In like manner the wheat-straw bends over under the weight of the loaded ear, and the tip of the cat’s tail bends over when held upright,—not because they “possess flexibility,” but because they outstrip the dimensions within which stable equilibrium is possible in a vertical position. The kitten’s tail, on the other hand, stands up spiky and straight.

[33] _Modern Painters._

[34] The stem of the giant bamboo may attain a height of 60 metres, while not more than about 40 cm. in diameter near its base, which dimensions are not very far short of the theoretical limits (A. J. Ewart, _Phil. Trans._ vol. 198, p. 71, 1906).

[35] _Trans. Zool. Soc._ IV, 1850, p. 27.

[36] It would seem to be a common if not a general rule that marine organisms, zoophytes, molluscs, etc., tend to be larger than the corresponding and closely related forms living in fresh water. While the phenomenon may have various causes, it has been attributed (among others) to the simple fact that the forces of growth are less antagonised by gravity in the denser medium (cf. Houssay, _La Forme et la Vie_, 1900, p. 815). The effect of gravity on outward _form_ is illustrated, for instance, by the contrast between the uniformly upward branching of a sea-weed and the drooping curves of a shrub or tree.

[37] The analogy is not a very strict one. We are not taking account, for instance, of a proportionate increase in thickness of the boiler-plates.

[38] Let _L_ be the length, _S_ the (wetted) surface, _T_ the tonnage, _D_ the displacement (or volume) of a ship; and let it cross the Atlantic at a speed _V_. Then, in comparing two ships, similarly constructed but of different magnitudes, we know that _L_ = _V_^2, _S_ = _L_^2 = _V_^4, _D_ = _T_ = _L_^3 = _V_^6; also _R_ (resistance) = _S_ ⋅ _V_^2 = _V_^6; _H_ (horse-power) = _R_ ⋅ _V_ = _V_^7; and the coal (_C_) necessary for the voyage = _H_/_V_ = _V_^6. That is to say, in ordinary engineering language, to increase the speed across the Atlantic by 1 per cent. the ship’s length must be increased 2 per cent., her tonnage or displacement 6 per cent., her coal-consumpt also 6 per cent., her horse-power, and therefore her boiler-capacity, 7 per cent. Her bunkers, accordingly, keep pace with the enlargement of the ship, but her boilers tend to increase out of proportion to the space available.

[39] This is the result arrived at by Helmholtz, Ueber ein Theorem geometrisch ähnliche Bewegungen flüssiger Körper betreffend, nebst Anwendung auf das Problem Luftballons zu lenken, _Monatsber. Akad. Berlin_, 1873, pp. 501–14. It was criticised and challenged (somewhat rashly) by K. Müllenhof, Die Grösse der Flugflächen, etc., _Pflüger’s Archiv_, XXXV, p. 407, XXXVI, p. 548, 1885.

[40] Cf. also Chabrier, Vol des Insectes, _Mém. Mus. Hist. Nat. Paris_, VI–VIII, 1820–22.

[41] _Aerial Flight_, vol. II (_Aerodonetics_), 1908, p. 150.

[42] By Lanchester, _op. cit._ p. 131.

[43] Cf. _L’empire de l’air; ornithologie appliquée à l’aviation_. 1881.

[44] _De Motu Animalium_, I, prop. cciv, ed. 1685, p. 243.

[45] Harlé, On Atmospheric Pressure in past Geological Ages, _Bull. Geol. Soc. Fr._ XI, pp. 118–121; or _Cosmos_, p. 30, July 8, 1911.

[46] _Introduction to Entomology_, 1826, II, p. 190. K. and S., like many less learned authors, are fond of popular illustrations of the “wonders of Nature,” to the neglect of dynamical principles. They suggest, for instance, that if the white ant were as big as a man, its tunnels would be “magnificent cylinders of more than three hundred feet in diameter”; and that if a certain noisy Brazilian insect were as big as a man, its voice would be heard all the world over: “so that Stentor becomes a mute when compared with these insects!” It is an easy consequence of anthropomorphism, and hence a common characteristic of fairy-tales, to neglect the principle of dynamical, while dwelling on the aspect of geometrical, similarity.

[47] I.e. the available energy of muscle, in ft.-lbs. per lb. of muscle, is the same for all animals: a postulate which requires considerable qualification when we are comparing very different _kinds_ of muscle, such as the insect’s and the mammal’s.

[48] Prop. clxxvii. Animalia minora et minus ponderosa majores saltus efficiunt respectu sui corporis, si caetera fuerint paria.

[49] See also (_int. al._), John Bernoulli, _de Motu Musculorum_, Basil., 1694; Chabry, Mécanisme du Saut, _J. de l’Anat. et de la Physiol._ XIX, 1883; Sur la longueur des membres des animaux sauteurs, _ibid._ XXI, p. 356, 1885; Le Hello, De l’action des organes locomoteurs, etc., _ibid._ XXIX, p. 65–93, 1893, etc.

[50] Recherches sur la force absolue des muscles des Invertébrés, _Bull. Acad. E. de Belgique_ (3), VI, VII, 1883–84; see also _ibid._ (2), XX, 1865, XXII, 1866; _Ann. Mag. N. H._ XVII, p. 139, 1866, XIX, p. 95, 1867. The subject was also well treated by Straus-Dürckheim, in his _Considérations générales sur l’anatomie comparée des animaux articulés_, 1828.

[51] The fact that the limb tends to swing in pendulum-time was first observed by the brothers Weber (_Mechanik der menschl. Gehwerkzeuge_, Göttingen, 1836). Some later writers have criticised the statement (e.g. Fischer, Die Kinematik des Beinschwingens etc., _Abh. math. phys. Kl. k. Sächs. Ges._ XXV–XXVIII, 1899–1903), but for all that, with proper qualifications, it remains substantially true.

[52] Quoted in Mr John Bishop’s interesting article in Todd’s _Cyclopaedia_, III, p. 443.

[53] There is probably also another factor involved here: for in bending, and therefore shortening, the leg we bring its centre of gravity nearer to the pivot, that is to say, to the joint, and so the muscle tends to move it the more quickly.

[54] _Proc. Psychical Soc._ XII, pp. 338–355, 1897.

[55] For various calculations of the increase of surface due to histological and anatomical subdivision, see E. Babak, Ueber die Oberflächenentwickelung bei Organismen, _Biol. Centralbl._ XXX, pp. 225–239, 257–267, 1910. In connection with the physical theory of surface-energy, Wolfgang Ostwald has introduced the conception of _specific surface_, that is to say the ratio of surface to volume, or _S_/_V_. In a cube, _V_ = _l_^3, and _S_ = 6_l_^2; therefore _S_/_V_ = 6/_l_. Therefore if the side _l_ measure 6 cm., the ratio _S_/_V_ = 1, and such a cube may be taken as our standard, or unit of specific surface. A human blood-corpuscle has, accordingly, a specific surface of somewhere about 14,000 or 15,000. It is found in physical chemistry that surface energy becomes an important factor when the specific surface reaches a value of 10,000 or thereby.

[56] Though the entire egg is not increasing in mass, this is not to say that its living protoplasm is not increasing all the while at the expense of the reserve material.

[57] Cf. Tait, _Proc. R.S.E._ V, 1866, and VI, 1868.

[58] _Physiolog. Notizen_ (9), p. 425, 1895. Cf. Strasbürger, Ueber die Wirkungssphäre der Kerne und die Zellgrösse, _Histolog. Beitr._ (5), pp. 95–129, 1893; J. J. Gerassimow, Ueber die Grösse des Zellkernes, _Beih. Bot. Centralbl._ XVIII, 1905; also G. Levi and T. Terni, Le variazioni dell’ indice plasmatico-nucleare durante l’intercinesi, _Arch. Ital. di Anat._ X, p. 545, 1911.

[59] _Arch. f. Entw. Mech._ IV, 1898, pp. 75, 247.

[60] Conklin, E. G., Cell-size and nuclear-size, _J. Exp. Zool._ XII. pp. 1–98, 1912.

[61] Thus the fibres of the crystalline lens are of the same size in large and small dogs; Rabl, _Z. f. w. Z._ LXVII, 1899. Cf. (_int. al._) Pearson, On the Size of the Blood-corpuscles in Rana, _Biometrika_, VI, p. 403, 1909. Dr Thomas Young caught sight of the phenomenon, early in last century: “The solid particles of the blood do not by any means vary in magnitude in the same ratio with the bulk of the animal,” _Natural Philosophy_, ed. 1845, p. 466; and Leeuwenhoek and Stephen Hales were aware of it a hundred years before. But in this case, though the blood-corpuscles show no relation of magnitude to the size of the animal, they do seem to have some relation to its activity. At least the corpuscles in the sluggish Amphibia are much the largest known to us, while the smallest are found among the deer and other agile and speedy mammals. (Cf. Gulliver, _P.Z.S._ 1875, p. 474, etc.) This apparent correlation may have its bearing on modern views of the surface-condensation or adsorption of oxygen in the blood-corpuscles, a process which would be greatly facilitated and intensified by the increase of surface due to their minuteness.

[62] Cf. P. Enriques, La forma come funzione della grandezza: Ricerche sui gangli nervosi degli Invertebrati, _Arch. f. Entw. Mech._ XXV, p. 655, 1907–8.

[63] While the difference in cell-volume is vastly less than that between the volumes, and very much less also than that between the surfaces, of the respective animals, yet there _is_ a certain difference; and this it has been attempted to correlate with the need for each cell in the many-celled ganglion of the larger animal to possess a more complex “exchange-system” of branches, for intercommunication with its more numerous neighbours. Another explanation is based on the fact that, while such cells as continue to divide throughout life tend to uniformity of size in all mammals, those which do not do so, and in particular the ganglion cells, continue to grow, and their size becomes, therefore, a function of the duration of life. Cf. G. Levi, Studii sulla grandezza delle cellule, _Arch. Ital. di Anat. e di Embryolog._ V, p. 291, 1906.

[64] Boveri. _Zellen-studien, V. Ueber die Abhängigkeit der Kerngrösse und Zellenzahl der Seeigellarven von der Chromosomenzahl der Ausgangszellen._ Jena, 1905.

[65] Recent important researches suggest that such ultra-minute “filter-passers” are the true cause of certain acute maladies commonly ascribed to the presence of much larger organisms; cf. Hort, Lakin and Benians, The true infective Agent in Cerebrospinal Fever, etc., _J. Roy. Army Med. Corps_, Feb. 1910.

[66] _Zur Erkenntniss der Kolloide_, 1905, p. 122; where there will be found an interesting discussion of various molecular and other minute magnitudes.

[67] _Encyclopaedia Britannica_, 9th edit., vol. III, p. 42, 1875.

[68] Sur la limite de petitesse des organismes, _Bull. Soc. R. des Sc. méd. et nat. de Bruxelles_, Jan. 1903; _Rec. d’œuvres_ (_Physiol. générale_), p. 325.

[69] Cf. A. Fischer, _Vorlesungen über Bakterien_, 1897, p. 50.

[70] F. Hofmeister, quoted in Cohnheim’s _Chemie der Eiweisskörper_, 1900, p. 18.

[71] McKendrick arrived at a still lower estimate, of about 1250 proteid molecules in the minutest organisms. _Brit. Ass. Rep._ 1901, p. 808.

[72] Cf. Perrin, _Les Atomes_, 1914, p. 74.

[73] Cf. Tait, On Compression of Air in small Bubbles, _Proc. R. S. E._ V, 1865.

[74] _Phil. Mag._ XLVIII, 1899; _Collected Papers_, IV, p. 430.

[75] Carpenter, _The Microscope_, edit. 1862, p. 185.

[76] The modern literature on the Brownian Movement is very large, owing to the value which the phenomenon is shewn to have in determining the size of the atom. For a fuller, but still elementary account, see J. Cox, _Beyond the Atom_, 1913, pp. 118–128; and see, further, Perrin, _Les Atomes_, pp. 119–189.

[77] Cf. R. Gans, Wie fallen Stäbe und Scheiben in einer reibenden Flüssigkeit? _Münchener Bericht_, 1911, p. 191; K. Przibram, Ueber die Brown’sche Bewegung nicht kugelförmiger Teilchen, _Wiener Ber._ 1912, p. 2339.

[78] Ueber die ungeordnete Bewegung niederer Thiere, _Pflüger’s Archiv_, CLIII, p. 401, 1913.

[79] Sometimes we find one and the same diagram suffice, whether the intervals of time be great or small; and we then invoke “Wolff’s Law,” and assert that the life-history of the individual repeats, or recapitulates, the history of the race.

[80] Our subject is one of Bacon’s “Instances of the Course,” or studies wherein we “measure Nature by periods of Time.” In Bacon’s _Catalogue of Particular Histories_, one of the odd hundred histories or investigations which he foreshadowed is precisely that which we are engaged on, viz. a “History of the Growth and Increase of the Body, in the whole and in its parts.”

[81] Cf. Aristotle, _Phys._ vi, 5, 235 _a_ 11, ὲπεὶ γὰρ ἅπασα κίνησις ἐν χρόνῳ, κτλ. Bacon emphasised, in like manner, the fact that “all motion or natural action is performed in time: some more quickly, some more slowly, but all in periods determined and fixed in the nature of things. Even those actions which seem to be performed suddenly, and (as we say) in the twinkling of an eye, are found to admit of degree in respect of duration.” _Nov. Org._ XLVI.

[82] Cf. (e.g.) _Elem. Physiol._ ed. 1766, VIII, p. 114, “Ducimur autem ad evolutionem potissimum, quando a perfecto animale retrorsum progredimur, et incrementorum atque mutationum seriem relegimus. Ita inveniemus perfectum illud animal fuisse imperfectius, alterius figurae et fabricae, et denique rude et informe: et tamen idem semper animal sub iis diversis phasibus fuisse, quae absque ullo saltu perpetuos parvosque per gradus cohaereant.”

[83] _Beiträge zur Entwickelungsgeschichte des Hühnchens im Ei_, p. 40, 1817. Roux ascribes the same views also to Von Baer and to R. H. Lotze (_Allg. Physiologie_, p. 353, 1851).

[84] Roux, _Die Entwickelungsmechanik_, p. 99, 1905.

[85] _Op. cit._ p. 302, “Magnum hoc naturae instrumentum, etiam in corpore animato evolvendo potenter operatur; etc.”

[86] _Ibid._ p. 306. “Subtiliora ista, et aliquantum hypothesi mista, tamen magnum mihi videntur speciem veri habere.”

[87] Cf. His, On the Principles of Animal Morphology, _Proc. R. S. E._ XV, 1888, p. 294: “My own attempts to introduce some elementary mechanical or physiological conceptions into embryology have not generally been agreed to by morphologists. To one it seemed ridiculous to speak of the elasticity of the germinal layers; another thought that, by such considerations, we ‘put the cart before the horse’: and one more recent author states, that we have better things to do in embryology than to discuss tensions of germinal layers and similar questions, since all explanations must of necessity be of a phylogenetic nature. This opposition to the application of the fundamental principles of science to embryological questions would scarcely be intelligible had it not a dogmatic background. No other explanation of living forms is allowed than heredity, and any which is founded on another basis must be rejected ....... To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism.”

[88] Hertwig, O., _Zeit und Streitfragen der Biologie_, II. 1897.

[89] Cf. Roux, _Gesammelte Abhandlungen_, II, p. 31, 1895.

[90] _Treatise on Comparative Embryology_, I, p. 4, 1881.

[91] Cf. Fick, _Anal. Anzeiger_, XXV, p. 190, 1904.

[92] 1st ed. p. 444; 6th ed. p. 390. The student should not fail to consult the passage in question; for there is always a risk of misunderstanding or misinterpretation when one attempts to epitomise Darwin’s carefully condensed arguments.

[93] “In omni rerum naturalium historia utile est _mensuras definiri et numeros_,” Haller, _Elem. Physiol._ II, p. 258, 1760. Cf. Hales, _Vegetable Staticks_, Introduction.

[94] Brussels, 1871. Cf. the same author’s _Physique sociale_, 1835, and _Lettres sur la théorie des probabilités_, 1846. See also, for the general subject, Boyd, R., Tables of weights of the Human Body, etc. _Phil. Trans._ vol. CLI, 1861; Roberts, C., _Manual of Anthropometry_, 1878; Daffner, F., _Das Wachsthum des Menschen_ (2nd ed.), 1902, etc.

[95] Dr Johnson was not far wrong in saying that “life declines from thirty-five”; though the Autocrat of the Breakfast-table, like Cicero, declares that “the furnace is in full blast for ten years longer.”

[96] Joly, _The Abundance of Life_, 1915 (1890), p. 86.

[97] “_Lou pes, mèstre de tout_ [Le poids, maître de tout], _mèstre sènso vergougno, Que te tirasso en bas de sa brutalo pougno_,” J. H. Fabre, _Oubreto prouvençalo_, p. 61.

[98] The continuity of the phenomenon of growth, and the natural passage from the phase of increase to that of decrease or decay, are admirably discussed by Enriques, in “La morte,” _Riv. di Scienza_, 1907, and in “Wachsthum und seine analytische Darstellung,” _Biol. Centralbl._ June, 1909. Haller (_Elem_. VII, p. 68) recognised _decrementum_ as a phase of growth, not less important (theoretically) than _incrementum_: “_tristis, sed copiosa, haec est materies_.”

[99] Cf. (_int. al._), Friedenthal, H., Das Wachstum des Körpergewichtes ... in verschiedenen Lebensältern, _Zeit. f. allg. Physiol._ IX, pp. 487–514, 1909.

[100] As Haller observed it to do in the chick (_Elem._ VIII, p. 294): “Hoc iterum incrementum miro ordine ita distribuitur, ut in principio incubationis maximum est: inde perpetuo minuatur.”

[101] There is a famous passage in Lucretius (v. 883) where he compares the course of life, or rate of growth, in the horse and his boyish master: _Principio circum tribus actis impiger annis Floret equus, puer hautquaquam_, etc.

[102] Minot, C. S., Senescence and Rejuvenation, _Journ. of Physiol._ XII, pp. 97–153, 1891; The Problem of Age, Growth and Death, _Pop. Science Monthly_ (June–Dec.), 1907.

[103] Quoted in Vierordt’s _Anatomische ... Daten und Tabellen_, 1906. p. 13.

[104] _Unsere Körperform_, Leipzig, 1874.

[105] No such point of inflection appears in the curve of weight according to C. M. Jackson’s data (On the Prenatal Growth of the Human Body, etc., _Amer. Journ. of Anat._ IX, 1009, pp. 126, 156), nor in those quoted by him from Ahlfeld, Fehling and others. But it is plain that the very rapid increase of the monthly weights, approximately in the ratio of the cubes of the corresponding lengths, would tend to conceal any such breach of continuity, unless it happened to be very marked indeed. Moreover in the case of Jackson’s data (and probably also in the others) the actual age of the embryos was not determined, but was estimated from their lengths. The following is Jackson’s estimate of average weights at intervals of a lunar month:

Months 0 1 2 3 4 5 6 7 8 9 10 Wt in gms. ·0 ·04 3 36 120 330 600 1000 1500 2200 3200

[106] G. Kraus (after Wallich-Martius), _Ann. du Jardin bot. de Buitenzorg_, XII, 1, 1894, p. 210. Cf. W. Ostwald, _Zeitliche Eigenschaften_, etc. p. 56.

[107] Cf. Chodat, R., et Monnier, A., Sur la courbe de croissance des végétaux, _Bull. Herb. Boissier_ (2), V, pp. 615, 616, 1905.

[108] Cf. Fr. Boas, Growth of Toronto Children, _Rep. of U.S. Comm. of Education_, 1896–7, pp. 1541–1599, 1898; Boas and Clark Wissler, Statistics of Growth, _Education Rep._ 1904, pp. 25–132, 1906; H. P. Bowditch, _Rep. Mass. State Board of Health_, 1877; K. Pearson, On the Magnitude of certain coefficients of Correlation in Man, _Pr. R. S._ LXVI, 1900.

[109] _l.c._ p. 42, and other papers there quoted.

[110] See, for an admirable résumé of facts, Wolfgang Ostwald, _Ueber die Zeitliche Eigenschaften der Entwickelungsvorgänge_ (71 pp.), Leipzig, 1908 (Roux’s _Vorträge_, Heft V): to which work I am much indebted. A long list of observations on the growth-rate of various animals is also given by H. Przibram, _Exp. Zoologie_, 1913, pt. IV (_Vitalität_), pp. 85–87.

[111] Cf. St Loup, Vitesse de croissance chez les Souris, _Bull. Soc. Zool. Fr._ XVIII, 242, 1893; Robertson, _Arch. f. Entwickelungsmech._ XXV, p. 587, 1908; Donaldson. _Boas Memorial Volume_, New York, 1906.

[112] Luciani e Lo Monaco, _Arch. Ital. de Biologie_, XXVII, p. 340, 1897.

[113] Schaper, _Arch. f. Entwickelungsmech._ XIV, p. 356, 1902. Cf. Barfurth, Versuche über die Verwandlung der Froschlarven, _Arch. f. mikr. Anat._ XXIX, 1887.

[114] Joh. Schmidt, Contributions to the Life-history of the Eel, _Rapports du Conseil Intern. pour l’exploration de la Mer_, vol. V, pp. 137–274, Copenhague, 1906.

[115] That the metamorphoses of an insect are but phases in a process of growth, was firstly clearly recognised by Swammerdam, _Biblia Naturae_, 1737, pp. 6, 579 etc.

[116] From Bose, J. C., _Plant Response_, London, 1906, p. 417.

[117] This phenomenon, of _incrementum inequale_, as opposed to _incrementum in universum_, was most carefully studied by Haller: “Incrementum inequale multis modis fit, ut aliae partes corporis aliis celerius increscant. Diximus hepar minus fieri, majorem pulmonem, minimum thymum, etc.” (_Elem._ VIII (2), p. 34).

[118] See (_inter alia_) Fischel, A., Variabilität und Wachsthum des embryonalen Körpers, _Morphol. Jahrb._ XXIV, pp. 369–404, 1896. Oppel, _Vergleichung des Entwickelungsgrades der Organe zu verschiedenen Entwickelungszeiten bei Wirbelthieren_, Jena, 1891. Faucon, A., _Pesées et Mensurations fœtales à différents âges de la grossesse_. (Thèse.) Paris, 1897. Loisel, G., Croissance comparée en poids et en longueur des fœtus mâle et femelle dans l’espèce humaine, _C. R. Soc. de Biologie_, Paris, 1903. Jackson, C. M., Pre-natal growth of the human body and the relative growth of the various organs and parts, _Am. J. of Anat._ IX, 1909; Post-natal growth and variability of the body and of the various organs in the albino rat, _ibid._ XV, 1913.

[119] _l.c._ p. 1542.

[120] Variation and Correlation in Brain-weight, _Biometrika_, IV, pp. 13–104, 1905.

[121] _Die Säugethiere_, p. 117.

[122] _Amer. J. of Anatomy_, VIII, pp. 319–353, 1908. Donaldson (_Journ. Comp. Neur. and Psychol._ XVIII, pp. 345–392, 1908) also gives a logarithmic formula for brain-weight (_y_) as compared with body-weight (_x_), which in the case of the white rat is _y_ = ·554 − ·569 log(_x_ − 8·7), and the agreement is very close. But the formula is admittedly empirical and as Raymond Pearl says (_Amer. Nat._ 1909, p. 303), “no ulterior biological significance is to be attached to it.”

[123] _Biometrika_, IV, pp. 13–104, 1904.

[124] Donaldson, H. H., A Comparison of the White Rat with Man in respect to the Growth of the entire Body, _Boas Memorial Vol._, New York, 1906, pp. 5–26.

[125] Besides many papers quoted by Dubois on the growth and weight of the brain, and numerous papers in _Biometrika_, see also the following: Ziehen, Th., _Das Gehirn: Massverhältnisse_, in Bardeleben’s _Handb. der Anat. des Menschen_, IV, pp. 353–386, 1899. Spitzka, E. A., Brain-weight of Animals with special reference to the Weight of the Brain in the Macaque Monkey, _J. Comp. Neurol._ XIII, pp. 9–17, 1903. Warneke, P., Mitteilung neuer Gehirn und Körpergewichtsbestimmungen bei Säugern, nebst Zusammenstellung der gesammten bisher beobachteten absoluten und relativen Gehirngewichte bei den verschiedenen Species, _J. f. Psychol. u. Neurol._ XIII, pp. 355–403, 1909. Donaldson, H. H., On the regular seasonal Changes in the relative Weight of the Central Nervous System of the Leopard Frog, _Journ. of Morph._ XXII, pp. 663–694, 1911.

[126] Cf. Jenkinson, Growth, Variability and Correlation in Young Trout, _Biometrika_, VIII, pp. 444–455, 1912.

[127] Cf. chap. xvii, p. 739.

[128] “ ...I marked in the same manner as the Vine, young Honeysuckle shoots, etc....; and I found in them all a gradual scale of unequal extensions, those parts extending most which were tenderest,” _Vegetable Staticks_, Exp. cxxiii.

[129] From Sachs, _Textbook of Botany_, 1882, p. 820.

[130] Variation and Differentiation in Ceratophyllum, _Carnegie Inst. Publications_, No. 58, Washington, 1907.

[131] Cf. Lämmel, Ueber periodische Variationen in Organismen, _Biol. Centralbl._ XXII, pp. 368–376, 1903.

[132] Herein lies the easy answer to a contention frequently raised by Bergson, and to which he ascribes great importance, that “a mere variation of size is one thing, and a change of form is another.” Thus he considers “a change in the form of leaves” to constitute “a profound morphological difference.” _Creative Evolution_, p. 71.

[133] I do not say that the assumption that these two groups of earwigs were of different ages is altogether an easy one; for of course, even in an insect whose metamorphosis is so simple as the earwig’s, consisting only in the acquisition of wings or wing-cases, we usually take it for granted that growth proceeds no more after the final stage, or “adult form” is attained, and further that this adult form is attained at an approximately constant age, and constant magnitude. But even if we are not permitted to think that the earwig may have grown, or moulted, after once the elytra were produced, it seems to me far from impossible, and far from unlikely, that prior to the appearance of the elytra one more stage of growth, or one more moult took place in some cases than in others: for the number of moults is known to be variable in many species of Orthoptera. Unfortunately Bateson tells us nothing about the sizes or total lengths of his earwigs; but his figures suggest that it was bigger earwigs that had the longer tails; and that the rate of growth of the tails had had a certain definite ratio to that of the bodies, but not necessarily a simple ratio of equality.

[134] Jackson, C. M., _J. of Exp. Zool._ XIX, 1915, p. 99; cf. also Hans Aron, Unters. über die Beeinflüssung der Wachstum durch die Ernährung, _Berl. klin. Wochenbl._ LI, pp. 972–977, 1913, etc.

[135] The temperature limitations of life, and to some extent of growth, are summarised for a large number of species by Davenport, _Exper. Morphology_, cc. viii, xviii, and by Hans Przibram, _Exp. Zoologie_, IV, c. v.

[136] Réaumur: _L’art de faire éclore et élever en toute saison des oiseaux domestiques, foit par le moyen de la chaleur du fumier_, Paris, 1749.

[137] Cf. (_int. al._) de Vries, H., Matériaux pour la connaissance de l’influence de la température sur les plantes, _Arch. Néerl._ V, 385–401, 1870. Köppen, Wärme und Pflanzenwachstum, _Bull. Soc. Imp. Nat. Moscou._ XLIII, pp. 41–110, 1870.

[138] Blackman, F. F., _Ann. of Botany_, XIX, p. 281, 1905.

[139] For various instances of a “temperature coefficient” in physiological processes, see Kanitz, _Zeitschr. f. Elektrochemie_, 1907, p. 707; _Biol. Centralbl._ XXVII, p. 11, 1907; Hertzog, R. O., Temperatureinfluss auf die Entwicklungsgeschwindigkeit der Organismen, _Zeitschr. f. Elektrochemie_, XI, p 820, 1905; Krogh, Quantitative Relation between Temperature and Standard Metabolism, _Int. Zeitschr. f. physik.-chem. Biologie_, I, p. 491, 1914; Pütter, A., Ueber Temperaturkoefficienten, _Zeitschr. f. allgem. Physiol._ XVI, p. 574, 1914. Also Cohen, _Physical Chemistry for Physicians and Biologists_ (English edition), 1903; Pike, F. H., and Scott. E. L., The Regulation of the Physico-chemical Condition of the Organism, _American Naturalist_, Jan. 1915, and various papers quoted therein.

[140] Cf. Errera, L., _L’Optimum_, 1896 (_Rec. d’Oeuvres, Physiol. générale_, pp. 338–368, 1910); Sachs, _Physiologie d. Pflanzen_, 1882, p. 233; Pfeffer, _Pflanzenphysiologie_, ii, p. 78, 1904; and cf. Jost, Ueber die Reactionsgeschwindigkeit im Organismus, _Biol. Centralbl._ XXVI, pp. 225–244, 1906.

[141] After Köppen, _Bull. Soc. Nat. Moscou_, XLIII, pp. 41–110, 1871.

[142] _Botany_, p. 387.

[143] Leitch, I., Some Experiments on the Influence of Temperature on the Rate of Growth in _Pisum sativum, Ann. of Botany_, XXX, pp. 25–46, 1916. (Cf. especially Table III, p. 45.)

[144] Blackman, F. F., Presidential Address in Botany, _Brit. Ass._ Dublin, 1908.

[145] _Rec. de l’Inst. Bot. de Bruxelles_, VI, 1906.

[146] Hertwig, O., Einfluss der Temperatur auf die Entwicklung von _Rana fusca_ und _R. esculenta_, _Arch. f. mikrosk. Anat._ LI, p. 319, 1898. Cf. also Bialaszewicz, K., Beiträge z. Kenntniss d. Wachsthumsvorgänge bei Amphibienembryonen, _Bull. Acad. Sci. de Cracovie_, p. 783, 1908; Abstr. in _Arch. f. Entwicklungsmech._ XXVIII, p. 160, 1909.

[147] Der Grad der Beschleunigung tierischer Entwickelung durch erhöhte Temperatur, _A. f. Entw._ Mech. XX. p. 130, 1905. More recently, Bialaszewicz has determined the coefficient for the rate of segmentation in Rana as being 2·4 per 10° C.

[148] _Das Wachstum des Menschen_, p. 329, 1902.

[149] The _diurnal_ periodicity is beautifully shewn in the case of the Hop by Joh. Schmidt (_C. R. du Laboratoire de Carlsberg_, X, pp. 235–248, Copenhague, 1913).

[150] _Trans. Botan. Soc. Edinburgh_, XVIII, 1891, p. 456.

[151] I had not received, when this was written, Mr Douglass’s paper, On a method of estimating Rainfall by the Growth of Trees, _Bull. Amer. Geograph. Soc._ XLVI, pp. 321–335, 1914. Mr Douglass does not fail to notice the long period here described; but he lays more stress on the occurrence of shorter cycles (of 11, 21 and 33 years), well known to meteorologists. Mr Douglass is inclined (and I think rightly) to correlate the variations in growth directly with fluctuations in rainfall, that is to say with alternate periods of moisture and aridity; but he points out that the temperature curves (and also the sunspot curves) are markedly similar.

[152] It may well be that the effect is not due to light after all; but to increased absorption of heat by the soil, as a result of the long hours of exposure to the sun.

[153] On growth in relation to light, see Davenport, _Exp. Morphology_, II, ch. xvii. In some cases (as in the roots of Peas), exposure to light seems to have no effect on growth; in other cases, as in diatoms (according to Whipple’s experiments, quoted by Davenport, II, p. 423), the effect of light on growth or multiplication is well-marked, measurable, and apparently capable of expression by a logarithmic formula. The discrepancy would seem to arise from the fact that, while light-energy always tends to be absorbed by the chlorophyll of the plant, converted into chemical energy, and stored in the shape of starch or other reserve materials, the actual rate of growth depends on the rate at which these reserves are drawn on: and this is another matter, in which light-energy is no longer directly concerned.

[154] Cf. for instance, Nägeli’s classical account of the effect of change of habitat on Alpine and other plants: _Sitzungsber. Baier. Akad. Wiss._ 1865, pp. 228–284.

[155] Cf. Blackman, F. F., Presidential Address in Botany, _Brit. Ass._ Dublin, 1908. The fact was first enunciated by Baudrimont and St Ange, Recherches sur le développement du fœtus, _Mém. Acad. Sci._ XI, p. 469, 1851.

[156] Cf. Loeb, _Untersuchungen zur physiol. Morphologie der Thiere_, 1892; also Experiments on Cleavage, _J. of Morph._ VII, p. 253, 1892; Zusammenstellung der Ergebnisse einiger Arbeiten über die Dynamik des thierischen Wachsthum, _Arch. f. Entw. Mech._ XV, 1902–3, p. 669; Davenport, On the Rôle of Water in Growth, _Boston Soc. N. H._ 1897; Ida H. Hyde, _Am. J. of Physiol._ XII, 1905, p. 241, etc.

[157] _Pflüger’s Archiv_, LV, 1893.

[158] Beiträge zur Kenntniss der Wachstumsvorgänge bei Amphibienembryonen, _Bull. Acad. Sci. de Cracovie_, 1908, p. 783; cf. _Arch. f. Entw. Mech._ XXVIII, p. 160, 1909; XXXIV, p. 489, 1912.

[159] Fehling, H., _Arch. für Gynaekologie_, XI, 1877; cf. Morgan, _Experimental Zoology_, p. 240, 1907.

[160] Höber, R., Bedeutung der Theorie der Lösungen für Physiologie und Medizin, _Biol. Centralbl._ XIX, 1899; cf. pp. 272–274.

[161] Schmankewitsch has made other interesting observations on change of size and form, after some generations, in relation to change of density; e.g. in the flagellate infusorian _Anisonema acinus_, Bütschli (_Z. f. w. Z._ XXIX, p. 429, 1877).

[162] These “Fezzan-worms,” when first described, were supposed to be “insects’ eggs”; cf. Humboldt, _Personal Narrative_, VI, i, 8, note; Kirby and Spence, Letter X.

[163] Cf. _Introd. à l’étude de la médecine expérimentale_, 1885, p. 110.

[164] Cf. Abonyi, _Z. f. w. Z._ CXIV, p. 134, 1915. But Frédéricq has shewn that the amount of NaCl in the blood of Crustacea (_Carcinus moenas_) varies, and all but corresponds, with the density of the water in which the creature has been kept (_Arch. de Zool. Exp. et Gén._ (2), III, p. xxxv, 1885); and other results of Frédéricq’s, and various data given or quoted by Bottazzi (Osmotischer Druck und elektrische Leitungsfähigkeit der Flüssigkeiten der Organismen, in Asher-Spiro’s _Ergebn. d. Physiologie_, VII, pp. 160–402, 1908) suggest that the case of the brine-shrimps must be looked upon as an extreme or exceptional one.

[165] Cf. Schmankewitsch, _Z. f. w. Zool._ XXV, 1875, XXIX, 1877, etc.; transl. in appendix to Packard’s _Monogr. of N. American Phyllopoda_, 1883, pp. 466–514; Daday de Deés, _Ann. Sci. Nat._ (_Zool._), (9), XI, 1910; Samter und Heymons, _Abh. d. K. pr. Akad. Wiss._ 1902; Bateson, _Mat. for the Study of Variation_, 1894, pp. 96–101; Anikin, _Mitth. Kais. Univ. Tomsk_, XIV: _Zool. Centralbl._ VI, pp. 756–760, 1908; Abonyi, _Z. f. w. Z._ CXIV, pp. 96–168, 1915 (with copious bibliography), etc.

[166] According to the empirical canon of physiology, that (as Frédéricq expresses it) “L’être vivant est agencé de telle manière que chaque influence perturbatrice provoque d’elle-même la mise en activité de l’appareil compensateur qui doit neutraliser et réparer le dommage.”

[167] Such phenomena come precisely under the head of what Bacon called _Instances of Magic_: “By which I mean those wherein the material or efficient cause is scanty and small as compared with the work or effect produced; so that even when they are common, they seem like miracles, some at first sight, others even after attentive consideration. These magical effects are brought about in three ways ... [of which one is] by excitation or invitation in another body, as in the magnet which excites numberless needles without losing any of its virtue, _or in yeast and such-like_.” _Nov. Org._, cap. li.

[168] Monnier, A., Les matières minérales, et la loi d’accroissement des Végétaux, _Publ. de l’Inst. de Bot. de l’Univ. de Genève_ (7), III, 1905. Cf. Robertson, On the Normal Rate of Growth of an Individual, and its Biochemical Significance, _Arch. f. Entw. Mech._ XXV, pp. 581–614, XXVI, pp. 108–118, 1908; Wolfgang Ostwald, _Die zeitlichen Eigenschaften der Entwickelungsvorgänge_, 1908; Hatai, S., Interpretation of Growth-curves from a Dynamical Standpoint, _Anat. Record_, V, p. 373, 1911.

[169] _Biochem. Zeitschr._ II, 1906, p. 34.

[170] Even a crystal may be said, in a sense, to display “autocatalysis”: for the bigger its surface becomes, the more rapidly does the mass go on increasing.

[171] Cf. Loeb, The Stimulation of Growth, _Science_, May 14, 1915.

[172] _B. coli-communis_, according to Buchner, tends to double in 22 minutes; in 24 hours, therefore, a single individual would be multiplied by something like 10^{28}; _Sitzungsber. München. Ges. Morphol. u. Physiol._ III, pp. 65–71, 1888. Cf. Marshall Ward, Biology of _Bacillus ramosus_, etc. _Pr. R. S._ LVIII, 265–468, 1895. The comparatively large infusorian Stylonichia, according to Maupas, would multiply in a month by 10^{43}.

[173] Cf. Enriques, Wachsthum und seine analytisehe Darstellung, _Biol. Centralbl._ 1909, p. 337.

[174] Cf. (_int. al._) Mellor, _Chemical Statics and Dynamics_, 1904, p. 291.

[175] Cf. Robertson, _l.c._

[176] See, for a brief resumé of this subject, Morgan’s _Experimental Zoology_, chap. xvi.

[177] _Amer. J. of Physiol._, X, 1904.

[178] _C.R._ CXXI, CXXII, 1895–96.

[179] Cf. Loeb, _Science_, May 14, 1915.

[180] Cf. Baumann u. Roos, Vorkommen von Iod im Thierkörper, _Zeitschr. für Physiol. Chem._ XXI, XXII, 1895, 6.

[181] Le Néo-Vitalisme, _Rev. Scientifique_, Mars 1911, p. 22 (of reprint).

[182] _La vie et la mort_, p. 43, 1902.

[183] Cf. Dendy, _Evolutionary Biology_, 1912, p. 408; _Brit. Ass. Report_ (Portsmouth), 1911, p. 278.

[184] Lucret. v, 877. “Lucretius nowhere seems to recognise the possibility of improvement or change of species by ‘natural selection’; the animals remain as they were at the first, except that the weaker and more useless kinds have been crushed out. Hence he stands in marked contrast with modern evolutionists.” Kelsey’s note, _ad loc._

[185] Even after we have so narrowed the scope and sphere of natural selection, it is still hard to understand; for the causes of _extinction_ are often wellnigh as hard to comprehend as are those of the _origin_ of species. If we assert (as has been lightly done) that Smilodon perished owing to its gigantic tusks, that Teleosaurus was handicapped by its exaggerated snout, or Stegosaurus weighed down by its intolerable load of armour, we may be reminded of other kindred forms to show that similar conditions did not necessarily lead to extermination, or that rapid extinction ensued apart from any such visible or apparent disadvantages. Cf. Lucas, F. A., On Momentum in Variation, _Amer. Nat._ xli, p. 46, 1907.

[186] See Professor T. H. Morgan’s _Regeneration_ (316 pp.), 1901 for a full account and copious bibliography. The early experiments on regeneration, by Vallisneri, Réaumur, Bonnet, Trembley, Baster, and others, are epitomised by Haller, _Elem. Physiologiae_, VIII, p. 156 _seq._

[187] _Journ. Experim. Zool._ VII, p. 397, 1909.

[188] _Op. cit._ p. 406, Exp. IV.

[189] The experiments of Loeb on the growth of Tubularia in various saline solutions, referred to on p. 125, might as well or better have been referred to under the heading of regeneration, as they were performed on cut pieces of the zoophyte. (Cf. Morgan, _op. cit._ p. 35.)

[190] _Powers of the Creator_, I, p. 7, 1851. See also _Rare and Remarkable Animals_, II, pp. 17–19, 90, 1847.

[191] Lillie, F. R., The smallest Parts of Stentor capable of Regeneration, _Journ. of Morphology_, XII, p. 239, 1897.

[192] Boveri, Entwicklungsfähigkeit kernloser Seeigeleier, etc., _Arch. f. Entw. Mech._ II, 1895. See also Morgan, Studies of the partial larvae of Sphaerechinus, _ibid._ 1895; J. Loeb, On the Limits of Divisibility of Living Matter, _Biol. Lectures_, 1894, etc.

[193] Cf. Przibram, H., Scheerenumkehr bei dekapoden Crustaceen, _Arch. f. Entw. Mech._ XIX, 181–247, 1905; XXV, 266–344, 1907. Emmel, _ibid._ XXII, 542, 1906; Regeneration of lost parts in Lobster, _Rep. Comm. Inland Fisheries, Rhode Island_, XXXV, XXXVI, 1905–6; _Science_ (n.s.), XXVI, 83–87, 1907. Zeleny, Compensatory Regulation, _J. Exp. Zool._ II, 1–102, 347–369, 1905; etc.

[194] Lobsters are occasionally found with two symmetrical claws: which are then usually serrated, sometimes (but very rarely) both blunt-toothed. Cf. Calman, _P.Z.S._ 1906, pp. 633, 634, and _reff._

[195] Wilson, E. B., Reversal of Symmetry in _Alpheus heterochelis_, _Biol. Bull._ IV, p. 197, 1903.

[196] _J. Exp. Zool._ VII, p. 457, 1909.

[197] _Biologica_, III, p. 161, June. 1913.

[198] _Anatomical and Pathological Observations_, p. 3, 1845; _Anatomical Memoirs_, II, p. 392, 1868.

[199] Giard, A., L’œuf et les débuts de l’évolution, _Bull. Sci. du Nord de la Fr._ VIII, pp. 252–258, 1876.

[200] _Entwickelungsvorgänge der Eizelle_, 1876; _Investigations on Microscopic Foams and Protoplasm_, p. 1, 1894.

[201] _Journ. of Morphology_, I, p. 229, 1887.

[202] While it has been very common to look upon the phenomena of mitosis as sufficiently explained by the results _towards which_ they seem to lead, we may find here and there a strong protest against this mode of interpretation. The following is a case in point: “On a tenté d’établir dans la mitose dite primitive plusieurs catégories, plusieurs types de mitose. On a choisi le plus souvent comme base de ces systèmes des concepts abstraits et téléologiques: répartition plus ou moins exacte de la chromatine entre les deux noyaux-fils suivant qu’il y a ou non des chromosomes (_Dangeard_), distribution particulière et signification dualiste des substances nucléaires (substance kinétique et substance générative ou héréditaire, _Hartmann et ses élèves_), etc. Pour moi tous ces essais sont à rejeter catégoriquement à cause de leur caractère finaliste; de plus, ils sont construits sur des concepts non démontrés, et qui parfois représentent des généralisations absolument erronées.” A. Alexeieff, _Archiv für Protistenkunde_, XIX, p. 344, 1913.

[203] This is the old philosophic axiom writ large: _Ignorato motu, ignoratur natura_; which again is but an adaptation of Aristotle’s phrase, ἡ ἀρχὴ τῆς κινήσεως, as equivalent to the “Efficient Cause.” FitzGerald holds that “all explanation consists in a description of underlying motions”; _Scientific Writings_, 1902, p. 385.

[204] As when Nägeli concluded that the organism is, in a certain sense, “vorgebildet”; _Beitr. zur wiss. Botanik_, II, 1860. Cf. E. B. Wilson, _The Cell, etc._, p. 302.

[205] “La matière arrangée par une sagesse divine doit être essentiellement organisée partout ... il y a machine dans les parties de la machine Naturelle à l’infini.” _Sur le principe de la Vie_, p. 431 (Erdmann). This is the very converse of the doctrine of the Atomists, who could not conceive a condition “_ubi dimidiae partis pars semper habebit Dimidiam partem, nec res praefiniet ulla_.”

[206] Cf. an interesting passage from the _Elements_ (I, p. 445, Molesworth’s edit.), quoted by Owen, _Hunterian Lectures on the Invertebrates_, 2nd ed. pp. 40, 41, 1855.

[207] “Wir müssen deshalb den lebenden Zellen, abgesehen von der Molekularstructur der organischen Verbindungen welche sie enthält, noch eine andere und in anderer Weise complicirte Structur zuschreiben, und diese es ist welche wir mit dem Namen _Organisation_ bezeichnen,” Brücke, Die Elementarorganismen, _Wiener Sitzungsber._ XLIV, 1861, p. 386; quoted by Wilson, _The Cell_, etc. p. 289. Cf. also Hardy, _Journ. of Physiol._ XXIV, 1899, p. 159.

[208] Precisely as in the Lucretian _concursus_, _motus_, _ordo_, _positura_, _figurae_, whereby bodies _mutato ordine mutant naturam_.

[209] Otto Warburg, Beiträge zur Physiologie der Zelle, insbesondere über die Oxidationsgeschwindigkeit in Zellen; in Asher-Spiro’s _Ergebnisse der Physiologie_, XIV, pp. 253–337, 1914 (see p. 315). (Cf. Bayliss, _General Physiology_, 1915, p. 590).

[210] Hardy, W. B., On some Problems of Living Matter (Guthrie Lecture), _Tr. Physical Soc. London_, xxviii, p. 99–118, 1916.

[211] As a matter of fact both phrases occur, side by side, in Graham’s classical paper on “Liquid Diffusion applied to Analysis,” _Phil. Trans._ CLI, p. 184, 1861; _Chem. and Phys. Researches_ (ed. Angus Smith), 1876, p. 554.

[212] L. Rhumbler, Mechanische Erklärung der Aehnlichkeit zwischen Magnetischen Kraftliniensystemen und Zelltheilungsfiguren, _Arch. f. Entw. Mech._ XV, p. 482, 1903.

[213] Gallardo, A., Essai d’interpretation des figures caryocinétiques, _Anales del Museo de Buenos-Aires_ (2), II, 1896; La division de la cellule, phenomène bipolaire de caractère electro-colloidal, _Arch. f. Entw. Mech._ XXVIII, 1909, etc.

[214] _Arch. f. Entw. Mech._ III, IV, 1896–97.

[215] On various theories of the mechanism of mitosis, see (e.g.) Wilson, _The Cell in Development_, etc., pp. 100–114; Meves, _Zelltheilung_, in Merkel u. Bonnet’s _Ergebnisse der Anatomie_, etc., VII, VIII, 1897–8; Ida H. Hyde, _Amer. Journ. of Physiol._ XII, pp. 241–275, 1905; and especially Prenant, A., Theories et interprétations physiques de la mitose, _J. de l’Anat. et Physiol._ XLVI, pp. 511–578, 1910.

[216] Hartog, M., Une force nouvelle: le mitokinétisme, _C.R._ 11 Juli, 1910; Mitokinetism in the Mitotic Spindle and in the Polyasters, _Arch. f. Entw. Mech._ XXVII, pp. 141–145, 1909; cf. _ibid._ XL, pp. 33–64, 1914. Cf. also Hartog’s papers in _Proc. R. S._ (B), LXXVI, 1905; _Science Progress_ (n. s.), I, 1907; _Riv. di Scienza_, II, 1908; _C. R. Assoc. fr. pour l’Avancem. des Sc._ 1914, etc.

[217] The configurations, as obtained by the usual experimental methods, were of course known long before Faraday’s day, and constituted the “convergent and divergent magnetic curves” of eighteenth century mathematicians. As Leslie said, in 1821, they were “regarded with wonder by a certain class of dreaming philosophers, who did not hesitate to consider them as the actual traces of an invisible fluid, perpetually circulating between the poles of the magnet.” Faraday’s great advance was to interpret them as indications of _stress in a medium_,—of tension or attraction along the lines, and of repulsion transverse to the lines, of the diagram.

[218] Cf. also the curious phenomenon in a dividing egg described as “spinning” by Mrs G. F. Andrews, _J. of Morph._ XII, pp. 367–389, 1897.

[219] Whitman, _J. of Morph._ II, p. 40, 1889.

[220] “Souvent il n’y a qu’une séparation _physique_ entre le cytoplasme et le suc nucléaire, comme entre deux liquides immiscibles, etc.;” Alexeieff, Sur la mitose dite “primitive,” _Arch. f. Protistenk._ XXIX, p. 357, 1913.