but if a movement is given, a part of the gravity will be employed to produce it, and it is only with the surplus that the fixed points will be charged; thus, in this case the sum of the vertical resistances of the fixed points will be less at the first instant than the total weight of the system: thus from these two forces combined (the gravity of the system and the vertical charge of the fixed points) there will result from it a single force equal to their difference, and which will push the system from top to bottom as if it were free: thus the centre of gravity will descend necessarily with a velocity equal to this difference divided by the total mass of the system. Again, if the centre of gravity of the system does not descend, there will necessarily be an equilibrium. In general therefore-For ascertaining that several weights applied to any given machine should make a mutual equilibrium, it is sufficient to prove that if we abandon this machine to itself, the centre of gravity of the system will not descend. III. The immediate consequence of this principle, which is true without exception, is, that if the centre of gravity of the system is at the lowest possible point, there will necessarily be an equilibrium; for, according to this proposition, it is sufficient, in order to prove it, to show that the centre of gravity will not descend: Now, how could it descend, when upon this hypothesis it is at the lowest point possible? IV. In order to give another application of this principle, I suppose that it is required to find the general law of equilibrium between two weights, A and B, applied to a given machine: I say then, that in consequence of the preceding principle, there will be an equilibrium between these two weights A and B, if by supposing that one of the two has to bear it, and the machine has to take a small movement, it would happen that one of these bodies would ascend while the other descended; and that at the same time these weights were in the reciprocal rates of their estimated velocities in the vertical direction: in fact, if we suppose that A then descends with the vertical velocity V, while the velocity of B, also estimated in the vertical direction would be 8 u, we AV-Bu = 0. This being done, since the Bu, therefore bodies are supposed to be in motion, the one from top to bottom, and the other vice versâ, it is evident that the first member of this equation is the vertical velocity of the centre of gravity of the system: thus this centre of gravity will not descend, and therefore by the preceding position there must be an equilibrium. [To be continued.] III, Additional Memoir upon living and fossil Elephants. By M. CUVIER, [Concluded from vol. xxix. p. 254.] Article VII. Comparison of the Crania of the Elephant of India and that of Africa-External Characters taken from the EarsParts of the Cranium susceptible of Variation in one and the same Species. I HAD the good fortune to be the first to remark, in 1795, the distinctive characters presented by the crania of the two elephants, and which are so much the more interesting, as they may be applied to living, or entire individuals, without being obliged to examine their jaws *. I was able to recognise them at first only by the comparison of a cranium of each species; I have now verified these observations by inspecting seven real crania, (five of which are Indian, and two African,) and several drawings. When these crania are separated from their lower jaws and placed upon the grinders, and upon the edges of the alveoli of the tusks, the zygomatical arcades are nearly horizontal in both species. If we next view them laterally, what is very striking is, Plate II. was long ago engraved from my own drawings. I gave a proof impression of it several years ago to M. Wiedeman of Brunswick, who copied it into his Archives de Zootomie, tome ii. cah. I. pl. I.-THE AUTHOR. that that the summit of the head is almost round in the African elephant, and that it rises in the Indian elephant into a kind of double pyramid. This summit answers to the occipital arcade of man and other animals, and is so high in the elephant merely for the purpose of giving to the occipital face of the cranium a sufficient extent for a cervical ligament and occipital muscles, proportionate to the weight of the enormous mass they have to support. This difference in the form of the summits proceeds from the difference in the inclination of the frontal line, which retreats much further in the African elephant, where it forms with the occipital line an angle of 115°, than in the Indian elephant, where it makes an angle of 90° only. From this come the principal differences of the profile, such as, 1st, The proportion of the vertical height of the head at the distance from the end of the bones of the nose to the occipital condyles, which are nearly equal in the African elephant, (being as 33 to 32,) and the first of which is nearly one-fourth larger in the Indian elephant (being as 24 to 19). 2d, The proportion of the distance from the edges of the alveoli of the tusks at the summit to a line which is perpendicular to it and goes from the end of the bones of the nose to the anterior edge of the occipital hollow. The first of these lines is almost double that of the other in the Indian elephant (being as 26 to 14). It is little less than one-fourth larger in the African elephant (being as 21 to 16). Besides these in the proportions, there are also differences in the contour: 1st, The front of the Indian elephant is hollowed into a sinking and concave curve; that of the African elephant is on the contrary a little convex. 2d, The sub-orbitary hole is larger in the Indian elephant. In the African, it resembles a channel rather than a simple hole. 3dly, The temporal hollow is rounder in the African elephant; and the apophysis, which distinguishes it from the orbit, is thicker than in that of India, in which this hollow has an oval contour. When When observed by their front view, these crania also present very remarkable differences. 1st, The greatest length of this front, taken from the summit to the edge of the alveolus, is at its greatest breadth, taken between the post-orbitary apophyses of the frontal bone, as 5 to 3 in the Indian elephant, and as 3 to 2 in the African elephant. 2d, The aperture of the nose is nearly in the middle of the face in the Indian elephant; it is one-fifth further removed from the edge of the alveolus than from the summit of the head in the African elephant. When seen from above, these crania differ, particularly by their zygomatical arcades; they are more salient in the African than in the Indian elephant. When we look at them behind, we are struck with new characters: 1st, The height of the wings of the sphenoidal bones, forms in the Indian elephant more than three-fourths of that of the occipital surface, while in the African elephant it scarcely forms one half. 2d, In the African elephant the posterior extremity of the zygomatical arcades is nearly on a level with the occipital condyles; in the Indian elephant it is much lower. 3d, The occiput is terminated in the upper part in the African elephant, by a semi-elliptic curve, and its base is formed by two lines in a very open angle. In the Indian elephant, the sides are in convex arcs, and the upper part of the arc is slightly concave. The grinders are placed in both species upon two lines which converge before; they differ only by their laminæ, as we have said above. Most of the characters we have described, contributing to the general configuration of the head, are sensible externally; there is one still more prominent, and which may distinguish the two species at the first glance. I think I was the first to remark it: it consists in the size of the ears. The Indian elephant has middling-sized ears they are so large as to cover the whole shoulders in the African elephant. Vol. 30. No. 117. Feb. 1808. B I made I made myself certain of the first point: 1st, In three elephants which I saw alive; and I dissected two of them: two were from Ceylon, and the third from Bengal. 2d, In two other individuals which I saw in a state of preservation. 3d, In all the figures well known to belong to the Indian species, particularly those of Buffon, Blair, and Camper. 4th, In the figure of a foetus elephant from Ceylon, described by Zimmermann, in a quarto volume upon the subject *. Upon the second point, I have the following proofs: 1st, The elephant from Congo, dissected by Duverney. We may see its figure in the Mémoire pour servir á l'Hist. des Anim. par. iii.; and I am sure that the ear is not exaggerated, for it is still preserved in the Museum, and I have seen and examined it. 2d, An ear preserved in the king of Denmark's cabinet, and taken from an elephant killed at the Cape of Good Hope by captain Magnus Jacobi, in 1675. It is three feet and a half long, and two feet and a half broad †. 3d, A young African elephant in our Museum; its ears, although shrivelled up by being dried, are still as large as its head. 4th, An embryo elephant from Africa, in our Museum. 5th, All the well-known figures of the African elephants. From these characters we may be assured from what species those figures have been drawn the origin of which is unknown, or such as are to be seen on antient monu ments. Thus that of Gessner ‡, copied by Aldrovandus §, is an African elephant. That of Valentine |, copied by Labat¶, and altered by Kolbe **, is equally so. On the contrary, those of Jonston tt, which are very good, and which have served as a model to those of Hartenfels‡‡, from which Ludolph §§ afterwards borrowed Erlang, 1783, in 4to. † Oliger Jacobæus, Mus. reg. Dan. 1697, fol. p. S. Quad. p. 377. § Quad. lib. i. P. 465. || Amphithéâtr. Zoot. tab. i. f. 3. Afr. Occ. iii. p. 271. **Relation du Cap. trad. Fr. in 12mo, tome iii. p. 11. Elephantograph. curious. passim. tt Quadr. tab. vii. viii. et ix. SS Ethiop. lib. i. cap. 9. |