G

in which de denotes the increment of the intrinsic energy in the apparatus, dy the increment of entropy, de the quantity of electricity which passes through it, V' and V" the electrical potentials in pieces of the same kind of metal connected with the anode and cathode respectively, d Wo the work done by gravity, and dWp the work done by the pressures which act on the external surface of the apparatus. The term dW, may generally be neglected. The same is true of dWP, when gases are not concerned. If no heat is supplied or withdrawn the term td will vanish. But in the calculation of electromotive forces, which is the most important application of the equation, it is convenient and customary to suppose that the temperature is maintained constant. Now this term t do, which represents the heat absorbed by the cell, is frequently neglected in the consideration of cells of which the temperature is supposed to remain constant. In other words, it is frequently assumed that neither heat or cold is produced by the passage of an electrical current through a perfect electro-chemical apparatus (except that heat which may be indefinitely diminished by increasing the time in which a given quantity of electricity passes), unless it be by processes of a secondary nature, which are not immediately or necessarily connected with the process of electrolysis.

That this assumption is incorrect is shown by the electromotive force of a gas battery charged with hydrogen and nitrogen, by the currents caused by differences in the concentration of the electrolyte, by electrodes of zinc and mercury in a solution of sulphate of zinc, by a priori considerations based on the phenomena exhibited in the direct combination of the elements of water or of hydrochloric acid, by the absorption of heat which M. Favre has in many cases observed in a galvanic or electrolytic cell, and by the fact that the solid or liquid state of an electrode (at its temperature of fusion) does not affect the electromotive force.

ART. LIII.-On an Anatomical Peculiarity by which Crania of the Mound builders may be distinguished from those of the Modern Indians;* by W. J. MCGEE, Farley, Iowa.

THE difficulty of determining whether a skull from a mound belonged to a modern Indian or to an individual of the mys terious race which erected the mounds of the Mississippi Valley is well known; and so complex is the problem that only an anatomist of long experience and tried skill can satisfactorily solve it. Even then it frequently happens that "doctors

* Read before the American Association for the Advancement of Science at St. Louis.

disagree;" as when Col. Foster, at one time president of this Association, declared that the only cranium figured by Squier and Davis in their great work on the "Ancient Monuments of the Mississippi Valley" as representative of the cranial structure of the Mound-builders, did not belong to that race at all. Any observations throwing light on the question of the relations of these crania will therefore be of practical value.

The writer has made a pretty thorough study of the archæology of northeastern Iowa, and has examined several skulls unearthed in that region, as well as some from Wisconsin, Illinois and Kentucky. The total number of Mound-builders' crania examined will not, however, exceed fifty or seventy-five; and a part of these were fragmentary. Hence the observations. cannot be considered to afford a perfectly reliable guide in the determination of crania, and too great weight should not be attached to them until verified by authentic cases of a similar nature from other quarters. At present they have but a provisional significance. The structural peculiarity which has been found to be a more trustworthy distinguishing feature than differences in the capacity or general contour of the skulls, relative length and breadth, thickness of walls, or condition and state of preservation of the bone, is the greater relative size of the posterior molars or "wisdom teeth" in both maxillaries of the Mound-builders' crania than in those of the recent red race. Measurements have not been made to illustrate this difference in relative size, principally because the preparation of this paper was occasioned by the discussion following the reading on yesterday morning of an archæological paper in this section, since which time specimens from which dimensions could be taken have not been accessible.

Aside from the simple difference in relative size of the posterior and anterior molars, it seems that the "wisdom teeth" were earlier developed in the individuals of the Moundbuilding race than in either the Indian or the white man. It is well known that the posterior molars do not usually appear in civilized man until near maturity. Exceptions to this rule are not infrequent but they may be put down as cases of reversion. That this is warrantable will be more obvious further on. Again, these teeth are rarely so fully developed during the lifetime of the individual, in the white races, as to have their grinding surfaces worn down equally with the anterior molars. They therefore partake to some extent of the nature of rudimentary organs. In crania from the mounds, which were from young individuals as attested by the imperfect anchylosis of the sutures permitting fractures to easily occur along these lines, sometimes even the complete decomposition of the symphyses supervened, these

teeth have been found fully developed and the grinding surface nearly or quite as far worn down as in their anterior neighbors. In more mature crania the surface of the posterior molar is usually the largest and apparently the most worn down. Hence in the Mound-builder this tooth was not by any means rudimentary, but was a useful organ throughout nearly the whole of the lifetime of its possessor.

The corresponding tooth of the modern Indian occupies-if the Indian crania examined were typical, as they seemed to be -an intermediate stage in development between that of the Mound-builder on the one hand and that of the Caucassian on the other. As to the period at which the tooth makes its appearance and when it reaches its full development, the writer has been able to learn nothing thus far. This point seems to have escaped the notice of ethnologists heretofore. The difference in relative size and in the comparative maturity of these teeth is sufficient, however, in nearly all the specimens examined, to allow of their ready determination. Nevertheless this rule could not be indiscriminately applied, as due allowance must be made for differences in age, etc., of the individual; but with care and judgment the writer is convinced that it is competent.

The greater development of the posterior molars seems to be common to the lower and earlier races. This peculiarity has been observed in several of the fossil skulls of paleolithic man exhumed in Europe, as in the jaw-bone from the cave of Naulette, Belgium, in which, as reported by the Belgian geologists, the molar teeth increased in size backward. Dr. E. Lambert, of Brussels, has recently made an extensive collection of crania of various races, and has found that the posterior molar is relatively larger, not only in the red but in the black races than in the Caucassian. The dentation of the yellow races, however, corresponds more nearly with that of the white. So far as known to the writer Dr. Lambert has not noted the period of development of these teeth in any of the races.

This morphological variation in the different stocks of mankind is probably a concomitant of the principle of cephalization if not directly coördinated therewith. It has been shown by Prof. Dana that cephalization is "a fundamental principle in the development of the system of animal life," and that there has been an increase in cerebral volume in many if not all mammals since early cenozoic time; and Professor Marsh has shown that this tendency is manifested in a striking degree

*Scientific American, vol. xxxviii, p. 98.

This Journal, III, vol. xii, October, 1876, p. 245. References to Professor Marsh's papers are given in this memoir.

in the Eocene Dinoceras and Coryphodon, in the Miocene Brontotherium, and in the Pliocene Mastodon. But the researches of Marsh, Leidy, Cope, Hayden and others, in the Cretaceous and Tertiary beds of the western territories have shown us that there is a concurrent tendency toward a decrease in size of the posterior and increase in size of the anterior molars observable in perhaps any class of mammals which we may examine. The tendency is just as plainly marked as that toward increase in cranial capacity or toward compactness and abbreviation of the anterior organs,—indeed it is undoubtedly correlated with the shortening and compacting of the jaws. And it is probable that the degree of development of any mammal, as the horse or pig, can be just as readily and reliably measured by the relative size of its molars as by the size of its brain-case or by the presence or absence of certain bones of manus or pes. Casual statements to the effect that the relative size of the posterior molar varies inversely as the volume of the brain have indeed been met with, but no critical discussion of the true significance of such relations; and their practical bearing on the work of the determination of native American crania seems to have been wholly overlooked, as it certainly was in the discussion of yesterday.

Planters' Hotel, St. Louis, Aug. 23, 1878.

ART. LIV.-On the Limits of Hypotheses regarding the Properties of the Matter composing the Interior of the Earth; by HENRY HENNESSY, F.R.S, Professor of Applied Mathematics in the Royal College of Science for Ireland.*

1. FROM direct observation we are able to obtain only a very moderate knowledge of the materials existing below the solid crust of the earth. The depth to which we can penetrate by mining and boring operations into this crust is comparatively insignificant; and these operations give us little knowledge of the earth's interior in comparison with what is afforded by the outporings of volcanoes. Two hundred active volcanoes are said to still exist, while geologists have established that many thousands of such deep apertures in the earth's crust have existed during remote epochs of its physical history. The source or sources of supply for all these volcanoes have poured out a predominating mass of matter in a state of liquidity from fusion. Evidence is thus furnished that matter in a state of fluidity exists very widely distributed through the earth. The

*From the Phil. Mag. for Oct., 1878. Read before the Mathematical and Physical Section of the British Association for the Advancement of Science, Dublin, August, 1878.

supposition that this fluid fills the whole interior, and that the solid crust is a mere exterior envelope, is usually designated as the hypothesis of internal fluidity. From this hypothesis mechanical and physical results of primary importance in terrestrial physics may be deduced.

Newton, Clairaut, Laplace, Airy, and other illustrious mathematicians have used an extension of this hypothesis in discussing the earth's figure. They supposed the particles composing the earth to retain the same positions after solidification as that which they held before it. I ventured, for the first time, to discard the latter portion of the hypothesis as useless and contrary to physical laws. I now venture to say that, in framing any hypotheses as to the physical character of the matter of the earth, we should not affix any property to the supposed matter which is opposed to the properties observed in similar kinds of matter coming under our direct observation. Observation has disclosed that liquids are in general viscid, and that they possess what has been designated internal friction in a high degree.* Observation has recently shown that among the three states of matter (gaseous, liquid and solid) a law of continuity exists. Observation also discloses that gases and vapors are, of all forms of matter, the most compressible, that liquids are much less compressible, and that solids are still less compressible. Thus, for instance, water is about fourteen times more compressible than copper or brass.

2. If these general comparative properties of liquids and solids are admitted, it follows that in the hypotheses regarding the earth's internal structure we should most carefully guard against any assumption directly in contradiction to such properties. By assuming that the earth contained a fluid totally devoid of viscidity and internal friction, the late Mr. Hopkins attempted to prove the earth's entire solidity. He only proved that it did not contain any of this imaginary fluid; but he by no means proved the non-existence of a liquid possessing the properties of viscidity and internal friction common to all liquids. In the Comptes Rendus of the Academy of Sciences of Paris for 1871 is a paper in which I have given a résumé of the arguments against Mr. Hopkins's conclusions as to the earth's complete solidity; and in the subsequent discussions my priority on this matter seems to have been fairly and honorably acknowledged. In a recent admirable work on

* As having a special connection with this subject, see a Report by the Author on Experiments on the influence of the molecular condition of fluids, on their motion when in rotation and in contact with solids (Proceedings of the Royal Irish Academy, 2nd series, vol. iii, p. 55).

"Remarques à propos d'une Communication de M. Delaunay sur les résultats fournis par l'Astronomie concernant l'épaisseur de la croûte solide du Globe," Comptes Rendns de l'Inst. France, Mars 6, 1871, p. 250.