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ART. II.-1. Théorie Analytique de la Chaleur. Par M. Fourier. 4to. Paris, 1822.

2. Essai sur la Température de l'Intérieur de la Terre. Par M. Cordier. (Mémoires de l'Académie Royale des Sciences, Tom. VII.) Paris, 1827.

FEW questions possess a greater speculative interest than those which relate to the past condition or future fortunes of our globe. Physical Astronomy teaches us that it occupies an invariable place in the planetary system; that it has always revolved, and must ever continue to revolve about the sun, at the same mean distance, and in the same period of time. In its astronomical elements science can discover no trace of a beginning, no symptom of decay, no evidence even of its having ever been different from what it actually is. But when we consider its condition in respect of temperature, the order of the climates, the relative distribution of sea and land, and, in general, of all those circumstances which adapt it to the support of organic life, and the preservation of the existing animal and vegetable species, we are far from being able to recognise the same characters of unchangeableness and stability. On the contrary, the crust of the earth every where abounds with the monuments of great convul sions and physical revolutions. If these revolutions were operated abruptly and by violence, are we secure against their recurrence? If they have been the necessary consequences of the continued operation of physical laws, has that equilibrium yet been attained which admits of no farther disturbance? Such questions as these, if they have no immediate bearing on the present generation, affect at least the future destinies of mankind, and have accordingly formed, in every age of philosophy, a subject of curious and interesting inquiry.

The evidences of convulsion and disturbance, which abound among the superficial materials of the globe, have given rise to numberless theories respecting the cause and the order of that series of revolutions which the earth has successively undergone. Fire, water, the collision of comets, a change in the position of the terrestrial axis, have been in turn assumed as the immediate agents of nature in the production of the imagined catastrophes. One theorist attends only to the disposition of the strata, another to the animal remains which they contain; and each, on stumbling on a plausible explanation of the phenomena with which he happens to be peculiarly conversant, imagines he has solved the problem of the formation of the earth. But the great revolutions of the globe have been produced not by single, but by compli cated causes; and cannot be explained merely by the superposi

tion of rocks, and the species of shells and other organic remains found imbedded in them. They involve considerations of a more abstract nature, and the solution of questions of mechanics and general physics; sciences with which the geologists of bygone times appear to have had very little acquaintance. Hence their systems have so frequently abounded with assumptions and conclusions at variance with the established laws of nature, and their science itself been exposed, not without reason, to be stigmatized as a "series of illusory conjectures." In the course of the last half century, however, geology has been rescued from the hands of the mere mineralogist, and now begins to partake of the certainty of an experimental science. Observations of all kinds have been accumulated; the thermometer has been carried to great depths, and the state of the globe in respect of temperature been examined at many different places; the laws of the propagation and communication of heat, which plays so important a part in every geological system, have been determined by accurate experiments; and the geologist, instead of going back to the primitive chaos, and travelling out of nature" in search of knowledge, now confines himself to the consideration of observed facts, and traces out their consequences by the rules of inductive reasoning.

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On giving an attentive consideration to the actual condition of the earth, the first thing that strikes us as remarkable, is an appearance of a primitive and universal fluidity among the solid materials of the superficial strata. Nor is this fluidity merely indicated by geological appearances; it is in a manner demonstrated by astronomical considerations. The very form of the terrestrial spheroid; the regular disposition of the materials about the centre in elliptical layers, which is proved by experiments on the pendulum; the density of the layers increasing regularly with the depth; all attest that the materials of the globe have been once, and simultaneously, in a state of fusion:-or, at least, in such a state that the constituent molecules have been at liberty to obey the gravitating and centrifugal forces by which they are acted on, and arrange themselves according to the laws of hydrostatics. Now we are acquainted with no other agent in nature than heat, capable of producing the liquefaction of the greater part of the substances of which the earth is composed; for as to the hypothesis of an aqueous solution, it has entirely vanished before the mathematical and physical difficulties, or rather impossibilities, with which it is surrounded.

Admitting the existence of an intense heat in the interior of the globe, two theories have been proposed for its explanation. One of these is founded on the supposition of chemical affinities

among the materials of the nucleus, as the action of water on inflammable bases assumed to abound at great depths under the surface. This hypothesis originated with the celebrated Boyle, who ascribed the internal heat of the earth to the decomposition of pyrites, or rather to a species of fermentation going forward in the interior, and it has lately been employed by Dr. Daubeny, of Oxford, as the basis of an ingenious theory of volcanos. The other theory supposes that the original heat which the earth had at its formation, and which caused the fusion of all its elements, is still preserved in the central parts, and that the consolidation of the exterior crust is only due to its slow and gradual dissipation. This hypothesis, as we shall see, affords an adequate mechanical reason for those great convulsions of which the vestiges are so apparent among the superficial strata; and, besides leaving unexplained none of those effects which have been ascribed to the action of chemical heat, it has the advantage of accounting for that universal and simultaneous fluidity which is demanded by the conformity of the figure of the earth with that of hydrostatical equilibrium. In the present state of science it may not be possible to demonstrate the existence of a general high temperature in the interior of the earth, but the data on which the proofs of it must be founded are not beyond the reach of experimental inquiry. If the primitive temperature of the globe was such as to cause the reduction of the whole of its constituent materials to a fluid, perhaps an aëriform state, we are warranted by the recent discoveries that have been made respecting the propagation of heat, to conclude that this temperature may not only be still served at the centre, but that indications of its existence may even be manifest at accessible depths under the surface. The utmost depths to which we can penetrate are, indeed, inconsiderable when compared with the dimensions of the earth, scarcely extending to a ten-thousandth part of the radius; yet they far exceed the limits at which the annual variations of solar heat cease to be felt, and therefore afford the means of determining the thermometrical state of the earth beyond the influence of any external source of heat. The materials of the earth also receive and part with heat according to fixed and known laws, which enable the mathematician to compute the ultimate condition at which every part of the mass arrives after having been heated in any arbitrary manner whatever. For these reasons the hypothesis admits of a direct appeal to experience; and the question of a central heat, which was started in the remotest ages, and has frequently been revived, is not now, as formerly, merely a question of speculation and conjecture; it has been brought within the domain of analysis, and can be attacked and discussed with precise data.

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For the mathematical theory of the propagation of heat through solid bodies, science is mainly indebted to the ingenious labours of the late Baron Fourier, perpetual secretary of the Academy of Sciences of Paris. This illustrious philosopher and mathematician appears to have made the theory of heat the chief object of his scientific researches during the last twenty years of his life. His great work, entitled Théorie de la Chaleur, which was published in 1822, was preceded and followed by a series of important memoirs, which appeared from time to time among those of the Academy, all distinguished by comprehensive and philosophic views of the operations of nature, acute reasoning, and great skill and ingenuity in the use of the calculus. They furnish us, indeed, with specimens of some of the finest applications that have yet been made of the mathematical analysis to physical subjects of great difficulty; and it is in them alone that the important question of terrestrial temperature has been analytically discussed with all the requisite details. The problem of the secular cooling of the globe has also been treated by La Place, in the Connoissance des Temps for 1823, and the general question of the propagation of heat, by Poisson, in two elaborate memoirs published in the Journal of the Polytechnic School. The principal observations relative to the temperature of the interior of the earth have been collected and discussed by Cordier in the Memoir whose title stands at the head of this Article. From these sources we will endeavour to present our readers with an outline of the principal results of the mathematical theory of heat, the observations tending to prove. the existence of a high temperature in the interior of the earth, and some of the most remarkable deductions following from that hypothesis.

In all applications of mathematics to questions appertaining to physics, certain principles, or postulates, must be assumed as the basis of the calculus. These may be either laws of nature deduced from anterior observation and experience, or they may be mere hypotheses which we wish to verify by a comparison of their consequences with known facts. The calculus confers no certainty on the consequences of our assumptions; it is merely the instrument by means of which we are enabled to trace out and examine those consequences in detail. In the present question the principles assumed are three, and relate to the specific capacity, the interior conductibility, and the radiation from the surface of bodies. 1st. That in all solid bodies the increments of temperature are proportional to the increments of heat; 2d. That the velocity of the communication of heat through a solid body, the different parts of which have been unequally heated, depends on the relative temperatures of the molecules; and 3d. That

quantity of heat which traverses every element of the surface, and escapes by radiation, is proportional to the excess of the temperature of the cooling body above that of the medium in which it is placed. These three principles, or laws, are expressed by coefficients, which can only be determined by experience for every particular substance, and which are also found not to continue constant, but to vary with the temperature and other circumstances. By means of them all the questions that can be proposed relative to the transmission of heat through a solid body, of a given form and substance, and its successive thermometrical conditions when placed in a medium of a constant temperature, or exposed to the action of any uniform source of exterior heat, admit of being expressed by differential equations.

It seldom happens in the hands of a skilful analyst, that the investigation of a new subject is not attended by some collateral advantages to science, altogether independent of the particular solution sought after. When Fourier undertook to investigate the laws of the motion of heat, the equations comprehending the solutions even of the most elementary questions of the theory were found to be of so intricate a nature that they could not, by any known method, be reduced to such a form as would allow of any certain results being deduced from them. Various methods of treating equations of this class have since been discovered, both by Fourier and the other geometers who have pursued the same track of inquiry. Numerous theorems have been found for the transformation of functions into exponential series and definite integrals, and the calculus of partial differences has been enriched with new and extensive methods of integration, applying to various questions of natural philosophy which had resisted all previous attempts at solution. We cannot in this place pretend to explain the peculiar methods of analysis to which the theory of heat has given rise: they belong to the very highest departments of mathematical science, and deserve to be considered as an important extension of the discoveries of D'Alembert, and the great analysts of the last century.

The most important and interesting application of the mathematical theory of heat is to the temperature of the terrestrial spheroid; but before any inference can be deduced from the hypothesis of a central heat, it is necessary to consider the effect of the solar rays, which, on penetrating the surface, are converted into obscure heat, and therefore have a constant tendency to elevate the temperature of the envelope. The heat, however, which is produced in this manner, does not indefinitely accumulate in the interior. It makes its way only to a certain depth through the materials of the earth, and escapes from the surface by radiation; and so nicely

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