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CONCLUDING REMARKS.

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sidering the interior heat, if the surrounding space had not a determinate temperature differing but little from that which we should find at the poles, if we could precisely estimate it. It is remarkable that, of the two new thermological causes discovered by Fourier, one may be directly observed at the equator and the other at the poles; whilst, for all the intermediate points, our observation must be guided and interpreted by mathematical analysis.

New as this difficult inquiry is, our progress in it depends only on the perfecting of the observations which Fourier's theory has marked out for us. When the data of the problem thus become better known, this theory will enable us to lay hold of some certain evidences of the ancient thermological state of our globe, as well as of its future modifications. We have already learned one fact of high importance; that the periodical state of the earth's surface has become essentially fixed, and cannot undergo any but imperceptible changes by the continuous cooling of the interior mass through future ages. This rapid

sketch will suffice to show what a sudden scientific consistency has been given, by the labours of one man of genius, to this fundamental portion of natural history, which, before Fourier's time, was made up of vague and arbitrary opinions, mingled with incomplete and incoherent observations, out of which no exact general view could possibly arise.

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Its nature.

THI

CHAPTER IV.

ACOUSTICS.

HIS science had to pass, like all the rest, through the theological and metaphysical stages; but it assumed its positive character about the same time with Barology, and as completely, though our knowledge of it is, as yet, very scanty, in comparison with what we have learned of gravity. The exact information which was obtained in the middle of the seventeenth century about the elementary mechanical properties of the atmosphere, opened up a clear conception of the production and transmission of sonorous vibrations. The analysis of the phenomena of sound shows us that the doctrine of vibrations offers the exact expression of an incontestable reality. Besides its philosophical interest, and the direct importance of the phenomena of Acoustics, this department of Physics appeals to special attention in two principal relations, arising from its use in perfecting our fundamental ideas regarding inorganic bodies, and Man himself.

Relation to the study of inorganic bodies.

By studying sonorous vibrations, we obtain some insight into the interior mechanical constitution of natural bodies, manifested by the modifications undergone by the vibratory motions of their molecules. Acoustics affords the best, if not the only means for this inquiry; and the small present amount of our acquisitions seems to me no reason why we should not obtain abundant results when the study of acoustics is more advanced. It has already revealed to us some delicate properties of natural bodies which could not have been perceived in any other way. For instance, the capacity to contract habits,-a faculty which seemed to belong exclusively to living beings (I mean the power of contracting fixed dispositions, according to a prolonged series

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of uniform impressions),-is clearly shown to exist, in a greater or smaller degree, in inorganic apparatus. By vibratory motions, also, two mechanical structures, placed apart, act remarkably upon each other, as in the case of two clocks placed upon the same pedestal.

Relation to
Physiology.

On the other hand, acoustics forms a basis to physiology for the analysis of the two elementary functions which are most important to the establishment of social relations,--hearing and the utterance of sound. Putting aside, in this place, all the nervous phenomena of the case, it is clear that the inquiry rests on a knowledge of the general laws of acoustics, which regulate the mode of vibration of all auditory apparatus. It is remarkably so with regard to the production of the voice,- -a phenomenon of the same character with that of the action of any other sonorous instrument, except for its extreme complication, through the organic variations which affect the vocal system. Yet, it is not to physicists that the study of these two great phenomena belongs. The anatomists and physiologists ought not to surrender it to them, but to derive from physics all the ideas necessary for conducting the research themselves: for physicists are not prepared with the anatomical data of the problem, nor yet to supply a sound physiological interpretation of the results obtained. Science has indeed suffered from the prejudices which have grown out of the introduction into physics of superficial theories of hearing and phonation, from physical inquirers having intruded upon the province of the physiologists.

Relation to
Mathematics.

After Barology, there is no science which admits of the application of mathematical doctrines and methods so well as Acoustics. In the most general view, the phenomena of sound evidently belong to the theory of very minute oscillations of any system of molecules round a situation of stable equilibrium; for, in order to the sound being produced, there must be an abrupt perturbation in the molecular equilibrium; and this transient derangement must be followed by a quick return to the primitive state. Once produced, in the body directly shaken, the vibrations may be transmitted at considerable intervals, by means of an elastic

medium, by exciting a gradual succession of expansions and contractions which are in evident analogy with the waves formed on the surface of a liquid, and have given occasion to the term sonorous undulations. In the air, in particular, so elastic as it is, the vibration must propagate itself, not only in the direction of the primitive concussion, but in all directions, in the same degree. The transmitted vibrations, we must observe, are always necessarily isochronal with the primitive vibrations, though their amplitude may be widely different.

It is clear from the outset that the science of acoustics becomes, almost from its origin, subject to the laws of rational Mechanics. Since the time of Newton, who was the first to attempt to determine the rate of propagation of sound in the air, acoustics has always been more or less mixed up with the labour of geometers to develope abstract Mechanics. It was from simple considerations of acoustics that Daniel Bernouilli derived the general principle relating to the necessary and separate co-existence, or independency, of small and various oscillations occasioned at the same time in any system, by distinct concussions. The phenomena of sound afford the best realization of that law, without which it would be impossible to explain the commonest phenomenon of acoustics,-the simultaneous existence of numerous and distinct sounds, such as we are every moment hearing.

Though the connection of acoustics with rational Mechanics is almost as direct and complete as that of Barology, this mathematical character is far less manageable in the one case than the other. The most important questions in barology are immediately connected with the clearest and most primitive mechanical theories; whereas the mathematical study of sonorous vibrations depends on that difficult and delicate dynamical theory,-the theory of the perturbations of equilibrium, and the differential equations which it furnishes relative to the highest and most imperfect part of the integral calculus. Vibratory motion of one dimension is the only one, even in regard to solids, whose mathematical theory is complete. Of such motion of three dimensions we are, as yet, wholly ignorant.

To form any idea of the difficulties of the case, we must

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remember that vibratory motions must occasion certain physical modifications of another nature in the molecular constitution of bodies; and that these changes, though affecting the vibratory result, are too minute and transient to be appreciable. The only attempt that has been made to analyse such a complication is in the case of the thermological effects which result from the vibratory motion. Laplace used this case to explain the difference between the velocity of sound in the air as determined by experiment and that prescribed by the dynamic formula, which indicated a variation of about one-sixth. This difference is accounted for by the heat disengaged by the compression of the atmospheric strata, which must make their elasticity vary in a greater proportion than their density, thereby accelerating the propagation of the vibratory motion. It is true, a great gap is left here; since, as it is impossible to measure this disengagement of heat, we must assign to it conjecturally the value which compensates for the difference or the two velocities. But we learn from this procedure of Laplace the necessity of combining thermological considerations with the dynamical theory of vibratory motions. The modification is less marked in the case of liquids; and still less in that of solids; but we are too far behind with our comparative experiments to be able to judge whether the modification is or is not too inconsiderable for notice.

Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion. —This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide upon the neces

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