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stration of this principle, which I then satisfied myself was associated with and dominated by that of 'adaptation to purpose,' the step was plain—to me inevitable—to the conception of the operation of a secondary cause of the entire series of species, whether of plants, or vertebrates, or other groups of organisms, such cause being the servant of predetermining intelligent Will.

But, besides derivation' or 'filiation,' another principle influencing organization became recognizable in the course of studies and researches on Invertebrate animals. To this principle, as more especially antagonistic to the theological idea, I gave the name of irrelative repetition ;' sometimes also, as it prevailed most in plants and zoophytes, of 'vegetative repetition.'+ The demonstrated constitution of the vertebrate endoskeleton, as a series of essentially similar segments, out of which, as corollary, came the power of enunciating not only special' but 'general' and 'serial' homologies, appeared to me to illustrate also the law of irrelative repetition. The recurrence of similar segments in the spinal column and of similar elements in a vertebral segment, struck me as analogous to the repetition of similar crystals as the result of polarizing force in the growth of an inorganic body. I

Accordingly, these results of extensive, patient, and unbiassed inductive research-or, if there were a bias, it was toward Cuvier-swayed with me in rejecting the principle of direct or miraculous creation, and in recognizing a'natural law or secondary cause' as operative in the production of species in orderly succession and progression.'S

$ 424. Succession of Species, broken or linked ?-To the hypothesis that existing are modifications of extinct species Cuvier replied, that, in every mooted form of transmutation, the species were made to alter by small degrees, and that, therefore,'traces of such gradual modifications were due from the fossil world :-'You ought,' he said, 'to be able to show, e. g., the intermediate forms between the Palæotherium and existing hoofed quadrupeds.'ll

The progress of Paleontology since 1830 has brought to light many missing links unknown to the founder of the science. My own share in the labor led me, after a few years' research,

CXLI, (1849) p. 86. ť ccxLix, p. 641 (1843;) and vol. i, Preface, p. ix. CXL, p. 171.

& CXLI, loc. cit * Cependant on peut leur répondre, dans leur propre système, que si les esp.. ces ont changé par degrés, on devroit trouver des traces de ces modifications graduelles; qu'entro la palæotherium et les espèces d'aujourd'hui l'on devroit découvrir quelques formes intermédiaires, et que jusqu'à présent cela n'est point arrivé.' – CXXXIX, tom. i, p. lvii.

to discern what I believed, and still hold, to be a tendency to a more generalized or less specialized, organization as species recede in date of existence from the present time.* Even instances which to some have appeared to oppose the rule, really exemplify it. The little marsupial carnivore, e. 9., of the Purbeck beds, Plagiaulax (p. 294, fig. 234,) retained the typical number of premolars (p. 1-4,) all of them being carnassials : the more modified pliocene Thylacoleo had them reduced to the last (p. 4, fig. 233.) So likewise in the latter placental Carnivora, the eocene form Hymnodon, fig. 266, had the typical number of teeth, the three true molars here showing the carnassial form : in the existing Hyæna and Felines the carnassials are reduced to, or concentrated in, a single molar. The oolitic Phascolotherium, with the typical marsupial number of teeth, shows less differentiation in their form than in modern Opossums and Dasyures: the colitic Amphitheria and Spalacotheria manifest an earlier and more generalized type of dentition in the great number and similarity of character of their small molars. Both Anoplotherium and Palæotherium, with the majority of eocene placental Mammals, had the type-dentition of diphyodonts.t

The two notable examples of Cuvier's powers of restoration, viewed as Pachyderms, must have seemed widely different from any of the existing species of the order, and were so deemed. The Anoplotherium more especially, among its singular peculiarities, unexpectedly exemplified one dental character, previously known only in the human subject. These seeming anomalies, however, lost much of their import as evidence of insulated form, or special creation, when they came to be viewed by the light of the law of the more generalized character of extinct species.' Such law in its application to Anoplotherium also exemplifies the analogy between the earlier species of a class and the earlier stages of a fotus. When, for example, the divided metapodials, the persistent upper

incisors, and the hornless cranium of the Anoplothere were recognized as retentions of 'fætal peculiarities' of existing ruminants, that extinct species was seen to favor rather than oppose the idea of organization by secondary law.

* CCXLIX, Ed. 1843, pp. 129, 165; Ed. 1855, pp. 223, 332, 312. XVII', pp. 1, 361, passim. Agassiz had been struck by indications of the same law in fossil fishes, and expressed it by the analogy of fætal and mature structures (CCCXXIX'', (1844) p. xxvi), and this, in some degree, is true. The earlier forms of Mammalia, however, are not toothless, have rather an excess of teeth as compared with later and modern forms; but they exemplify, in the main, a more 'geneTalized' type.

v. p. 524, clxxx, p. 361.
CLXXX. p. 367.

CLXXX, and

The discovery of the remains of the Hipparion" supplied one of the links required by Cuvier, between the Palæotherium and the Horse of the present day, and it is still more significant of the fact of filiation of species that the remains of such three-toed horses are found only in deposits of that tertiary period which intervene between the older palæotherian one and the newer strata in which the modern Horse first appears to have lost its lateral hooflets. These relations I illustrated in my Lectures on Fossil Mammalia at the School of Mines (1857) by the diagram, fig. 614.

Other evidences of gradation, in the case in question, have been brought to light. The molar series of the Horse includes six large complex grinders, individually recognizable by developmental characters as they are symbolized in fig. 280, p. 352. The representative of the first premolar is minute and soon shed. Its homologue in Palæotherium is functionally developed and retained, the type-dentition being adhered to.f In Hipparion, d, is succeeded by a pri smaller than in Palæotherium, but functional, with inflected folds of enamel on the grinding surface,

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Palcothere.
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Horse. Derivation of Equines. * OCCIII'', tom. ii. p. 25 (1832). Another species was discovered in the Miocene at Eppelsheim-the Hippotherium,' of Kaup; a third in deposits of similar age on the Sewalik Hills; a fourth, Hipparion prostylum Gv., at Vaucluse, in the southeast of France, in deposits 'peut-être plus récents que la molasse dans ces localités.'-Occxxx'', p. 432. + v. PL 35, figs. 4, 5, 6.

COCHI'', Pl. 19, figs. 1, la.

and permanent. It exemplifies a condition intermediate to that in Palæotherium and Equus. It is not that the jaws of the Horse are too short to hold the full complement of grinders; on the contrary they are relatively longer than in the Palæothere, being specially produced between the grinders and cutters : the first grinder might seem, indeed, to have been taken away in order to add to the space for the application of the 'bit.' The transitory and singularly small and simple denticle, fig. 614, Pu, compared with the large contiguous massive molar, mi, in the Horse, exemplifies the rudiment of an ancestral structure, in the same degree as do the hoofless splint-bones,' ib., Equus, II, IV : just as the spurious hoofs dangling therefrom in Hipparion, ib. ii, iv, are retained rudiments of the functionally developed lateral hoofs in the broader foot of Palæotherium, ib. II, iv.

Other missing links of this series of species have been supplied; as, e. g., by the Paloplotherium* of the newer eocene of Hordwell, Hants., by the Palæotherium aurelinense from the 'molasse marine of Orleans, † and by the Palæotherium hippoïdes of the lacustrine calcareous beds of Sansan, all which deposits are miocene, or are transitional between eocene and miocene. In the first-cited example, the swollen termination of the lobe of the molar, answering to c, m, fig. 268, remains longer as a detached column, m, fig. 269. In the two other Palæotherioids, the whole foot is longer and more slender, with a longer and thicker middle toe, than in the older eocene typegenus, whence the generic name Anchitherium applied to them by von Meyer. It is interesting, also, to find that the transitional character is further marked by the smaller relative size of the first premolar, whereby Anchitherium intervenes, as in the modification of the feet, between the Palæotherium and Hipparion.

Thus amply and satisfactorily has been fulfilled Cuvier's requisition of 1821 :— Entre le palæotherium et les espèces d'aujourd'hui l'on devrait decouvrir quelques formes intermédiaries.' How, then, is the origin of these intermediate gradations to be interpreted ? One may first remark, that as Palæotherium, Paloplotherium, Anchitherium, Hipparion and Equus, differ from each other in a greater degree than do the Horse, Zebra, and Ass, the difficulty of interbreeding would be greater, and the probability of fertility less, supposing those extinct genera to have co-existed. One cannot doubt, also, that every well-marked species of these genera paired within itself, and that they exemplified respectively the character of a group of individuals descended from common parents, or from such as resembled them as closely as they resembled each other.' They did not, however, exist as species, during the same periods of time, far less so from the beginning of things.' The singlehoofed Horse-family cannot be traced further back than the pliocene tertiary period : the tridactyle equine species have not been found in strata earlier than miocene, and disappear in the upper eocene : the heavier-bodied shorter-legged species with three functional hoofs to each foot belong to upper and middle eocenes. Furthermore, in the oldest eocene (London clay, super-cretaceous Conglomerates and Plastic clay at Meudon, Paris,) we get evidence of Ungulates (Pliolophus, Hyracotherium, Coryphodon,) in which the perisso-and artio-dactyle characters were less differentiated than in Palæotherium and Anoplotherium, affording additional significant evidence of progressive departure from generalized type. Thus, the succession in time accords with the gradational modifications by which Palæotherium is linked on to Equus.

* This modification, as the Palæotherium ovinum Aymard, began to be shown at the upper eocene at Velay, e. g., ere Palæotherium proper had passed away. (Bulletin du Congrès Scientifique de France tenu à Puy, 1855.)

Also in the upper eocene of the Basin of the Garonne, with Acerotherium. $ Anchitherium occurs, also, in the marine-molasse,' or lower miocene, of St. Genies, Languedoc.

With this additional knowledge the question, 'whether actual races may not be modifications of those ancient races which are exemplified by fossil remains ?' presents itself under very different conditions from those under which it passed before the minds of Cuvier* and the Academicians of 1830. If the alternative—species by miracle or by law ?-be applied to Palæotherium, Paloplotherium, Anchitherium, Hipparion, Equus, I accept the latter, without misgiving, and recognize such law as continuously operative throughout tertiary time.

In respect to its mode of operation, we may suppose Lamarck to say, 'as the surface of the earth consolidated, the larger and more produced mid-hoof of the old three-toed Pachyderms took a greater share in sustaining the animal's weight; and, more blood being required to meet the greater demand of the more active middle-toe, it grew; whilst the side-toes, losing their share of nourishment and becoming more and more withdrawn from use, shrank ;' and so on, according to the hardening of the ground, until only the hidden rudiments of metapodials remained and one hoof became maximized for all the work. Mr. Darwin, I conceive, would modify this, like other Lamarckian instances, by saying that some individuals of Palæotherium happening to be born with a larger and longer middle-toe, and with shorter and smaller side-toes, such variety was better

* Pourquoi les races actuelles. me dirait-on, ne seraient-elles pas des modifications de cos races anciennes que l'on trouve parmi les fossiles ?--cxxxix, i, p. lvii.

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