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"HERE are very few great problems in physical science which



that which involves the dynamical causes of the present inequalities of the earth's surface. An attempt to compose the history of this problem will end in the conviction that it contains more of warning to rash philosophers than of help to cautious ones. For the earlier speculations in this field are indebted chiefly to who were unskillful geologists, or unskillful physicists, and sometimes both. The wiser naturalists have usually kept silent or confined themselves to the safest ground, and carefully avoided conjectures, except such as could be sustained by some respectable evidence. Until very recently no comprehensive solution of the great problem has been attempted in such a manner as to entitle it to be called a theory, although a considerable number of subsidiary propositions have been advanced, and some highly important ones have been sustained in an admirable manner by eminent scientific men in Europe. But these latter are iemmas which precede, and form parts of, the required comprehensive theory. Of this character are the arguments of Babbage and Herschel respecting subsidences; the deductions of Poulett Scrope concerning the nature of volcanic action; the theory of metamorphism sustained by Scheerer, Daubree and Sorby. The complete theory must be one which will explain the nature, origin and laws of action of the formative force. Of the effects of this force we already possess considerable knowledge; of its origin we know but little, unless the theory which has recently attracted much attention, and of which Mr. Robert Mallet, F. R. S., is the most conspicuous advocate, be considered as a true solution. This theory-or hypothesis, as it will be called here—is an old one, having been dis. cussed in some of its general features in the last century by Poisson and Lagrange; but it appears to have lain dormant until about three years ago, when it was revived and elaborated by Mr. Mallet and put forth in a very definite form. It is the only hypothesis which has ever been advanced upon this great question to a sufficient degree of explicitness and comprehensiveness to merit criticism ; and its

author is entitled to credit for having brought to bear upon the argument a series of experimental researches and a laborious mathematical analysis, and has been throughout apparently anxious to give due weight to every objection which might be offered. It may be summarized as follows.

The earth is assumed to be a mass which is hot within and cold without, and to be continuously radiating into space its interior heat, which is slowly conducted through the colder crust, and this process has continued during the entire period covered by the evolution of the surface features. In consequence of this loss of heat from the interior, the portions which suffer a loss of temperature contract, while the portions near the surface, remaining at a temperature due to their position in space, suffer no change of volume. The nucleus thus stends to shrink away from the crust, leaving the latter partially unsupported. This, which during a much more rapid rate of cooling from a higher temperature of the whole globe and from a thinner crust, gave rise in former epochs to mountain elevation, in the present state of things, gives rise to volcanic heat. By the application of a theorem of Lagrange the author proves that the earth's solid crust, however great may be its thickness, and even if of materials far more cohesive and rigid than those of which we must suppose it to consist, must, if even to a very small extent left unsupported by the shrinking away of the nucleus, crush up in places by its own gravity and by the attraction of the nucleus.

“ This is actually going on, and in this partial crushing at places or depths dependent on the material and on conditions pointed out, the author discovers the true cause of volcanic heat. As the solid crust sinks together to follow down after the shrinking nucleus, the work expended in mutual crushing and dislocation of its parts, is transformed into heat, by which, at the places where the crushing sufficiently takes place, the material of the rock so crushed and of that adjacent to it is heated to fusion. The access of water to such points determines volcanic eruption. Volcanic heat therefore is one result of the secular cooling of a terraqueous globe subject to gravitation, and needs no strange or gratuitous hypothesis as to its origin.

“In order to test the validity of this view by contact with known facts, the author gives in detail two important series of experiments completed by him : the one on the actual amount of heat capable of being developed by the crushing of sixteen different species of rocks, chosen so as to be representative of the whole series of known rock formations, from Oolites down to the hardest crystalline rocks; the other, on the co-efficients of total contraction between fusion and solidification at existing and mean temperature of the atmosphere, of basic and acid slags, analogous to melted rocks. The latter experiments were conducted on a very large scale, and the author points out the great errors of preceding experimenters, Bischoff and others, as to these co-efficients. By the aid of these experimental data he is enabled to test the theory produced, when compared with such facts as we possess as to the rate of present cooling of our globe, and the total amount of volcanic action taking place upon its surface and within its crust.

“ He shows by estimates which allow an ample margin to the best data we possess as to the total annual vulcanicity of all sorts of our globe at present, that less than one-fourth of the total heat at present annually lost by our globe, is upon his theory sufficient to account for it; so that the secular cooling, small as it is, now going on, is a sufficient primum mobile, leaving the greater portion still to be dissipated by radiation. The author then brings his views into contact with various facts of vulcanology and seismology, showing their accordance.

“ He also shows that to the heat developed by partial tangential thrusts within the solid crust, are due those perturbations of hypogeal increment of temperature, which Hopkins has shown cannot be referred to a cooling nucleus and to differences of conductivity alone. He further shows that this view of the origin of volcanic heat is independent of any particular thickness being assigned to the earth's solid crust, or to whether there be at present a liquid fused nucleus; all that is necessary, being a hotter nucleus than crust, so that the rate of contraction is greater for the former than the latter. The author points out that as the same play of tangential pressures has elevated the mountain chains in past epochs, the nature of the forces employed sets a limit to the height of mountain possible of the materials of our globe.

«« That volcanic action due to the same class of forces was more energetic in past time, and is not a uniform, but a decaying energy now. Lastly, he brings his views into relation with vulcanicity, produced in like manner in other planets or in our satellite, and shows that it supplies an adequate solution of the singular and so far unexplained fact, that the elevations upon our moon's surface and the evidences of former volcanic activity are upon a scale so vast when compared with those upon our globe. Finally, he submits that if his view will account for all the known facts, leaving none inexplicable, and presenting no irreconcilable conditions or necessary deductions, then it should be accepted as a true picture of nature."

Although it appears from the foregoing abstract that Mr. Mallet uses his hypothesis as an explanation of the origin of volcanic forces, yet he brings within the range of the same system of causation the origin of terrestrial features. They are unquestionably associated, and any theory must similarly connect them. The primary assumption, that the earth is cold without and hot within, radiating its interior heat into space, has been a well-settled conviction for at least a century; and with whatever reservation some philosophers may have accepted it, no respectable authority within that period has ever ventured to dispute it. This portion of Mr. Mallet's argument may therefore pass without a challenge. The questions which will be asked and to which answers will be offered are:

First, Admitting that the earth is a cooling body and that it is contracting internally, is the cause appealed to quantitatively sufficient to produce the effects ascribed to it?

Second, Admitting (for the sake of argument only) that the assigned cause is sufficient, does it explain, and is it consistent with, known facts and the observed structure of the earth's surface?

In connection with the first inquiry it may be remarked that Mr. Mallet has not attempted to indicate the stage which the secular cooling of the earth has now reached, but has arbitrarily assumed it to be an advanced one. This is quite necessary to the validity of his hypothesis, for it is obvious that if the secular cooling has been hitherto small, it is insufficient to explain the various known phenomena of structure which, if produced by contraction at all, would have required a very great amount of it—of which more will be said hereafter.

In the year 1822, Baron J. J. Fourier published his celebrated “ Théorie Analitique de la Chaleur." Among other theorems it contains a general solution of what may be termed the law of cooling in solid bodies. It is one of those solutions which form the delight of mathematicians, and illustrates the power of mathematical analysis in the hands of a master. Sir William Thomson calls this theorem a “mathematical poem," and with some amplification has applied it to the cooling earth, upon the supposition that at some initial epoch the earth was a uniformly heated body, radiating its heat into space and receiving no subsequent additions of temperature either from without or from within. The particular problem which he proposed was, What has been the duration of the cooling, and what is the present distribution of subterranean temperature? To solve the problem it was necessary to assume arbitrarily the initial temperature. There are certain other quantities, or “constants," entering into the algebraical expression, which he determined by experiment, viz: the conducting power and specific heat of the most common rock materials. One other quantity is necessary before the solution becomes possible, and this is the rate at which temperature increases with the depth, near the surface of the earth. Since any assumption of the degree of initial temperature must be arbitrary, he took the highest reasonable one in order to avoid any objections which might be made by geologists to the smallness of the deduced quantities, placing it at 7000° F., which may be regarded as extravagantly high. It will be unnecessary to advert to his determinations of conducting power and specific heat, since no values which will probably be placed upon them in the future will materially affect the conclusions which we intend to draw. But the rate at which temperature increases with depth requires some discussion. That such an increase occurs wherever the solid earth is penetrated by boring or mining is popularly known. Among scientific men it has always been supposed to be a direct indication of great interior temperature. The rate of increase, however, is not uniform in all localities, but, is subject to wide variations, being five or six times greater in some places than in others. There is, however, a mean rate of increase around which nearly all the results of observation tend to cluster: this is approximately one degree F. per every sixty feet of descent-an estimate somewhat smaller than that used by Sir William. From these data he proceeds to deduce the period of cooling and the present distribution of temperature within the globe, reaching the following results: The period cannot be less than twenty million, nor greater than four hundred million years. Below a depth of one hundred and forty miles the amount of cooling has been immaterially small—the nucleus being very nearly as hot

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