Under the old term conductibility, two,,, ^.,.,.^ properties were confounded, which J^ouner separated, giving them the names of penetrability and jpermeability; the first signifying that by which heat is admitted at the surface, or dispersed from it, and the other that by which the changes at the surface are propagated thi-ough the interior. Permeability p,...^ depends altogether on the nature of the body and its state of aggregation. The differences of bodies in this respect have always been open to observation; for instance, the rapid propagation of heat in metallic bodies in comparison with coal, which may be burning at one point and scarcely warm a few inches off, while the heat rapidly i:)ervades the whole body of metal. It varies with the physical constitution of bodies, so diminishing in fluids that even Rumford went so far as to deny jjermeability in them altogether, ascribing the propagation of heat in them to interior agitation. This was a mistake; but permeability is very weak in liquids, and weaker,,,.,...still in gases. As to penetrability, while ^' partly depending on the state of aggregation of bodies, it depends much more on the state of their surfaces, — on colour, polish, and the regularity in which radiation in various directions can take place, and divers other modifi- 264- POSITIVE PIIILOSOPHV.
cations: and it changes in the same surface as it is exposed to the action of different media.
Strictly speaking, the different degrees of these two kinds of conductibility cannot affect the final thermological state of the two bodies, but only the time at which it is reached. Yet, as real questions often become mere questions of time, it is clear that if the inequalities are very mai'ked, they must affect the intensity of the phenomena under study; for instance, where the permeability is so feeble that the requisite interior heat cannot be obtained in time, but by applying such heat to the surface as will break or burn it; in which case, the phenomenon cannot take place; or, not within any practicable time. In general, the more perfect both kinds of conductibility, the better the bodies will obey the laws of thermological action, at a distance or in contact. It would therefore be very important to measure the value of these two coefficients for all bodies under stvidy: but unhappily such estimates are at present extremely imperfect. The business was vague enough, of course, when the two kinds of conductibility were confounded; but Fourier has taught us how to estimate permeability directly, and, of course, penetrability indirectly, by subtracting the permeability from the total of conductibility. But the application of his methods is as yet hardly initiated.
o -ii,. One consideration, that of specific heat, remains to be noticed, as concurring to regulate the results of thermological action. Whether luider conditions of equal weight, or of equal volume, the different substances consume distinct quantities of heat to raise their temperature equally. This property, of which little was known till the latter half of the last century, depends, like permeability, only in a less degree, on the physical constitution of bodies, while it is independent of the state of their surfaces. It must considerably affect the equalized temperatui'e common to two bodies, which cannot be equally different from the primitive temperature of each, if they differ from each other in the point of their specific heat. Physicists have achieved a good deal in the estimate of specific heat. The best method is that of experiment with the calorimeter, invented by Lavoisier and Laplace, for its CONSTITUENT CHANGES BY HEAT. 265 measui-ement. The quantity of lieat consumed bv any body at a deteiininate elevation of temperature, is estimated by the quantity of ice melted by the heat it gives out in its passage from the highest to the lowest temperature. The apparatus is so contrived as to isolate the experiment from all thermological action of the vessel and of the medium; and thus the results obtained are as precise as can be desired.
These are the three coefficients which serve to fix the final temperatures which result from the thermological equilibrium of bodies. Till we know more of the laws of their variations, it is natural to suppose them essentially uniform and constant: but it would not be rational to conceive of conductil:)ility as identical in all directions, in all bodies, however their structure may vary in different directions; and specific heat probablv undergoes changes at extreme temperatures, and especially in the neighbourhood of those which determine a new state of aggregation, as some experiments already seem to indicate. However, these modifications are still so uncertain and obscure, that physicists cannot be blamed for not keeping them, at this day, perpetually in view.
CONSTITUENT CHANGES BY HEAT.
The second part of thermology is that Second part. which relates to the alterations caused by Constituent heat in the physical constitution of bodies. changes by These alterations are of two kinds; changes "eat. of volume, and the production of a new state of aggregation; and this is the part of thermology of which we ai'e least ignorant.
These phenomena are independent of those of warming and cooling, though they are found together. When we heat any substance, the elevation of temperature is determined solely by the portion of heat consumed, the rest of which (often the greater part), insensible to the thermometer, is absorbed to modify the physical constitution.
J,,,, This is what we mean when we say that a portion of heat has become latent; a term which we may retain, though it was originally used in connection with a theory about the nature of heat. This is the fundamental law discovered by Black, by observation of the indisputable cases in which a physical modification takes place without any change of temperature in the modified body. When the two effects co-exist, it is much more difficult to analyse and apportion them. ^,, ^^. Considering first the laws of change of vol'uine. volume, it is a general truth that every homogeneous body dilates with heat and contracts with cold; and the fact holds good with heterogeneous bodies, such as organized tissues especially, in regard to their constituent parts. There are very few exceptions to this rule, and those few extend over a very small portion of the thermometrical scale. The principal anomaly however being the case of water, it has great importance in natural history, though not much in abstract physics, except from the use that philosophers have made of it to j^rocure an invariable unity of density, always at command. These anomalies, too rare and restricted to invalidate any general law, are sufficient to discredit all a priori explanations of expansions and contractions, according to which every increase of temperature should cause an expansion, and every diminution a contraction, contrai-y to the facts.
Solids dilate less than liquids, under the same elevation of temperature, and liquids than gases; and not only when the same substance passes through the three states, but also when different substances are employed. The expansion of solids proceeds, as far as we know, with perfect uniformity. We know more of the case of liquids, which is rendered extremely important from its connection with the true theory of the thermometer, without which all thermological inquiries would be left in a very dubious state. Experiments, devised by Dulong and Petit, have shown that for above three hundred centigrade degrees the expansion of the mercury follows an exactly uniform course, — equal increase of volume being prodi;ced by heat able to melt equal weights of ice at zero. This is the only CHANGE IN STATE OF AGGREGATION. 267 case fully established; but we have reason to believe that the rule extends to that of all liquids. The most marked case of such regularity is that of gases. Not only does the expansion take place by equal gradations, as usually in liquids and solids, but it affects all gases alike. Gases differ from each other, like liquids and solids, in their density, their specific heat, and their permeability; yet they all dilate uniformly and equally, their volume increasing three-eighths, from the temperature of meltingice to tliat of boiling water. Vapours are like gases in this particular, as in so many others. These are the simple general laws of the expansion of elastic fluids, discovered at once by Gay-Lussac at Paris, and Dalton at Manchester.
Next, we have to notice the changes pro- Change in duced by heat in the state of aggregation of state of bodies. ' aggregation.
Solidity and fluidity used to be regarded as absolute qualities of bodies; whereas, we now know them to be relative, and are even certain that all solid bodies might be rendered fluid if we could apply heat enough, avoiding chemical alteration. In the converse way, we used to suppose that gases must preserve their elasticity, through all degrees of cooling and of compression; whereas Bussy and Faraday have shown us that most of them easily become liquid, when they are seized in their nascent state; and there is every reason to believe that by a due combination of cold and pressure, they may be always liquefied, even in their developed state. Under this view therefore, different substances are distinguished only by the different parts of the indefinite thermometrical scale to which their successive states, solid, liquid, aud gaseous, correspond. But this simple inequality is an all-important characteristic, which is not yet thoroughly connected with any other fundamental quality of each substance. Density is the relation which is the least obscure and variable, — gases being in general less dense than liquids, and liquids than solids. But there are striking exceptions in the second case, and might be in the first, if we knew more of gases in regard to compression, and in varied circumstances of other kinds. As for the three states of the same substance, there is always, except in some cases of scarce anomaly, rarefaction in tlie fusion of solids and in the evaporatio\^ of liquids. All these changes have been brought by the^ illustrious Black under one fundamental law, which is, both from its importance and its universality, one of the Law of en- finest discoveries in natviral jihilosophy. It o-agement and is this: that in the passage from the solid disengage- to the liquid state, and from that to the nient or heat, jraseous, every substance always absorbs a more or less distinguishable C[uantity of heat, without raising its temperature; while the inverse process occasions a disengagement of heat, precisely correspondent to the absorption. These disengagements and absorptions of heat are evidently, after chemical phenomena, the principal sources of heat and cold. In an experiment of Leslie's, an evaporation, rendered extremely rapid by artificial means, has produced the lowest temperatures known. Eminent natural philosophers have even believed that the heat which is so abundantly disengaged in most great chemical combinations could proceed only from the different changes of state which commonly result from them. But this opinion, though true in regard to a great number of cases, has too many exceptions to deal with to become a general jDrinciple.
y We have now done with physical thermology. But the laws of the formation and tension of vapours now form an appendix to it; and also of course hygrometry. The theory is, in fact, the necessary complement of the doctrine of changes of state; and this is its proper place.
Before Saussure's time, evaporation was regarded as a chemical fact, occasioned by the dissolving action of air upon liquids. He showed that the action of the air was adverse to evaporation, excei:)t in the case of the renovation of the atmosphere. The test was found in the formation of vapour in a restricted space. Saussure found that, in such a case, with a given time, temperature, and space, the quantity and elasticity of the vapour wei'e always the same, whether the space was a vacuum or filled with gas. The mass and tension of the vapour increased steadily with the temperature; Avhereas it appears that no degree of cold suffices to stop the process entirely, since ice itself produces VAPOURS. 269 a vapour aj^preciable by very delicate means of observation. We do not know by what law the increase of temperature accelerates the evaporation, at least while the liquid remains below boiling point; but the variations in elasticity of the vapour produced have been successfully studied.
One term common to all liquids is the boiling point. At that point, the rising tension of the vapour formed has become ecj^ual to the atmospheric pressure; a fact which can be ascertained by direct experiment. Proceeding from this point, Dr. Dalton dis- o/eWlition. covered the important law that the vapours of different liquids have tensions always equal between themselves to temperatures equi-distant from the corresponding boiling points, whatever may be otherwise the direction of the difference. Thus, the boiling of water taking place at one hundred degrees, and that of alcohol at eighty degrees, the two vaj^ours, having at that point the same tension, equal to the atmospheric pressure, will then have equal elasticities, superior or inferior to the preceding, when their two temperatures are made to vary in the same number of degrees. The many new liquids discovered by chemists since this law was found have all tended to confirm it. It is very desirable that some harmony should be discovered between the boiling temj^eratures of different liquids and their other properties; but this remains to be done, and these temj^eratures appear to us entirely incoherent, though there is every reason to believe that they are not so.
It is evident that this law of Dalton' s simplifies prodigiously the inquiry into the variation of the tension of vapours, according to their temperatures; since the analysis of these variations in one instance will serve for all the rest. The experiments undertaken for this purpose by Dr. Dalton and his successors have not fully established the rule of proportion between the tension and the temperature: but an empirical law proposed by Dulong has thus far answered to the observed phenomena. All a priori determinations of the law have utterly failed.
The study of hvgrometrical equilibrium.. ^ ■ i between moist bodies seems a natural acl- e(,\{iiiiji-inni.
j unct to the theory of evaporation. Saussure and Deluc have wiven us a valuable insti'ument for this inquirv; but we know scarcely anythins^ of the laws which res^ulate the equilibrium of moisture. Prevision, which is the exact measure of science of every kind, is almost nonexistent in the case of hygrometry. Tlie small part that it plays in the inorganic departments of nature is, no doubt, the reason of the little attention that physicists have devoted to it: but we shall hereafter find how important is its share in vital phenomena. According to M. de Blainville, hygrometrical action constitutes the first degree and elementary mode of the nv^trition of living bodies, as capillarity is the germ of the most simple organic motions. In this view, the neglect is much to be regretted. It is one instance among a multitude of the mischiefs arising from the restricted training of natural philosophers. In this case, two important studies, which can be accomplished only by physical inquirers, are neglected, merely because their chief destination concerns another department of science.
After this survey, we can form some idea of the characteristics of this fine section of Physics. We see the rational connection of the different questions comprised in it; the degree of perfection which each of them has attained; and the gaps which remain to be filled up. A vast advance was made when, by the genius of Fourier, the most simple and fundamental phenomena of heat were attached to an admirable mathematical theorv.
CONNECTION WITH ANALYSIS.
Thermolofjy This theory relates to the first class of connected cases, — those in which an equalization of with Analysi-s. heat takes place between bodies at a distance or in contact; and not at all to those in which the physical constitution is altered by heat. It is only by an indirect investigation that we can learn how heat, once introduced into a body from the surface, extends through its mass, assigning to each point, at any fixed moment, a THERMOLOGY CONNECTED WITH ANALYSIS. 271 determinate temperature; or the converse — how this interior heat is dissipated, by a gradual dispersion through the surface. As direct observation could not help us here, we must remain in ignorance, if Fourier had not brought mathematical analysis to the aid of observation, so as to discover the laws by which these processes take place. The perfection with which this has been done opens so wide a field of exploration and application, unites so strictly the abstract and the concrete, and is so pure an example of the positive aim and method, that future generations will probably assign to this achievement of Fourier's the next place, as a mathematical creation, to the theory of gravitation. Many contemporaries have hastened into the new field thus opened; but most of them have used it only for analytical exercises which add nothing to our permanent knowledge; and perhaps the labours of M. Duhamel are hitherto the only ones which afford really any extension of Fourier's theory, by perfecting the analytical representation of thermological phenomena.
According to the plan of this work, we ought not to quit the limits of natural philosophy to notice any concrete considerations of natural history, — the secondary sciences being only derivatives from the primary. It is departing from our rule, therefore, to bring forward the important theory of terrestrial temperatures: yet this most important and difficult application of mathematical thermology forms so interesting a part of Fourier's doctrine, that I cannot refrain from offering some notice of it.
SECTION IV.
TERRESTRIAL TEMPERATURES.
Terrestrial The temperature of each point of our globe is owing (putting aside local or acci- temperatures, dental influences) to the action of three general and permanent causes variously combined: first, the solar heat, affecting different parts unequally, and subjected to periodical variations: next, the interior heat proper to the earth since its formation as a planet: and thirdly, the general thermometrical state of the space occupied by the solar system. The second is the only one of the three which acts upon all the points of the globe. The influence of the two others is confined to the surface. The order in which they have become known to us is that in which I have placed them. Before Fourier's time, the whole subject had been so vaguely and carelessly regarded, that all the phenomena were ascribed to solar heat alone. It is true, the notion of a central heat was very ancient; but this hypothesis, believed in and rejected without sufficient reason, had no scientific consistency, — the question having never been raised of the effect of this original heat on the thermological variations at the surface. The theory of Fourier afforded him mathematical evidence that at the surface the temperatures would be widely different from what they are, both in degree and mutual proportion, if T,. 1, the globe were not pervaded by a heat of its Interior heat. °., t ^,.. i,■,. i own, independent of the action of the sun; a heat which tends to disjjersion from the surface, by radiation towards the planets, though the atmosphere must considerably retard this disj^ersion. This original heat contributes very little, in a direct way, to the temperatures at the surface; but without it, the solar influence would be almost wholly lost, in the total mass of the globe; and it therefore prevents the periodical variations of temperature from following other laws than those which result from the solar influence. Immediately below the surface, the central heat becomes preponderant, and soonest in the parts nearest the equator; and it becomes the sole regulator of temperatures, and in a rigorously uniform manner. Temperature in proportion to the depth. — As to the third of the plane- cause, Fourier was the first to conceive of taiy intervals, j^^ ^le was wont to give, in a simple and striking form, the results of his inquiries in the saying that if tlie earth left a thermometer behind it in any part of its orbit, the instrument (supposing it protected from solar influence) could not fall indefinitely: the column would stop at some point or other, which would indicate the temperature of the space in which we revolve. This is one way of saying that the state of the temperatures on the surface of the globe would be inexplicable, even con- CONCLUDING REMARKS. 273 sidering the interior heat, if the siirrounding 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. Wlieu 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.
CHAPTEE IV.
ACOUSTICS.
' I ""HIS science liad to pass, like all the rest, J- 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 scaiity, 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 j^henomena of Acoustics, this department of Physics aj^peals to special attention in two principal relations, arising from its use in perfecting our fundamental ideas regarding inorganic bodies, and Man himself.
Relation to -^J studying sonorous vibrations, we obtain tlie study of some insight into the interior mechanical coninorganic stitution of natural bodies, manifested by the bodies. 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 SCIENTIFIC RELATIONS OF ACOUSTICS. 275 of uniform impressions), — is clearly shown to exist, in a greater or smaller degree, iu 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.
On the other hand, acoustics forms a basis to physiology for the analysis of the two Ph\'siolo"v 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 apjmratus. 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 prepai'ed 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.
After Barology, there is no science which admits of the application of mathematical Matlieruatics 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 T)y a quick return to the jDrimitive 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 wliicli are in evident analogy with the waves formed ou the surface of a liquid, and have giveu occasion to the term sonorous vndulations. 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 attemj^t to determine the rate of propagation of sound in the air, acoustics has always been more or less mixed up with the labovir 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 sej^arate 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 acoiistics 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 SCIENTIFIC RELATIONS OF ACOUSTICS. 277 rein ember 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 comj^ression of the atmospheric strata, which must make their elasticity vary in a greater j^roportion 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 expei'iments to be able to judge whether the modification is or is not too inconsiderable for notice.
Notwithstanding the eminent difiiculties 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 jjlienomena is, independent of their integration, a very important accp;isition, 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- 278 posrrrvK piiilosophv.
sity of the ii1,in()sj)liei'ic- iiKMlimn for the traiisinissioii of soiioroua vibrations; and wc may conceive of the j)ossil)ility of deterniinin*!- by experiment tlie duration of the propa<fation, in tlie air, and then t]irou<>h other media; but the genera,! laws of the vibrations of sonorous bodies escape inuntHliate obs(n-vation. Wo should know almost nothing of ilic wholes case it" ilic malhcmatical theory did not come in to connect the diJTcrcnt ]>h('nomcna of sound, enabling us to sul)stitute for direct observation an equivalent examination of more favourable cases subjected to the same law. For instance, when the analysis of the problem of vibraiiug chords has shown us that, other things being e(pial, the number of oscillations is in inverse })roportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law t'nal)les us to direct our attention to very slow vibrations. The sa.mo substitution is at our command in many cases in which it is less direi-t. Still, it is to be regretted that the ])rocess ol' ('xp<'riHientaii()n has not been further improved.
Acoustics consists of Ihree parts. We Divisions. might perhaps say four, including the timbre (ring or tone) arising from the j)articular mode of vibration of each restnumt body. This (piality is so real thati w(> constantly spi>ak- of it, both in daily life and in natiu'al history: but it would 1k' wandering out of the de])a.rtment of general physics to inquire what constitutes tlu^ ring i)r tone peculiar to different bodies, such as stones, wood, metals, organized tissues, etc., whose properties lie within the scope of concrete -[^hysics. But, if Ave regard this (piality as capable of moditicalion. by changes of eirciiius(anc(>s, then we bring it into the domain of acoustics, and r(>cogni/e its ]U"oper position, tluuigh we know nothing elsi^ a,bout it. 'I'lial part of the science juvsents a mere void.
'J^he thre«' parts referrinl to are, first, the mode of propagalion of sounds: next, their degree of intensity; and thirdly, their nuisical tone. Of these departments, the sci'ond is that of which our lau)wledge is most imperfect.
DIVlSIO^■s: Till': i'kopa(;ation of sound. 279 PROPAGATION OP SOUND.
As to the first, the pi'opagation of souucl, the simplest, most interesting-, and best known ^J ^^Imnd ^"" question is the measurement of the duration, especially Avhen the atmosphere is the medium. Newtou enunciated it very simply, apart from all modifying causes: — that the velocity of sound is that acquired by a gravitating body falling fronx a height eqiuil to half the weight of the atmosplu're, — su]>posing the atmosphere homogeneous. lu an analogous way, we may calcvdate the velocity of sound in the different gases, according to their respective densities and elasticities. By this law the speed of sound in the air must be regarded as independent of atmosi>heric vicissitudes, since, by Mariotte's rules, the density and elasticity of the air alw^ays vary in proportion; and their mutual relation alone influences the velocity iu question. Of Laplace's rectification of Newton's formula, we took notice just now. — One impoi'tant result of this law is the necessary identity of the velocity of different sounds, notwithstanding their varying degi'ees of intensity or of acuteuess. If any inequality existed, we should be able to establish it, from the irregularity which must take place in musical intervals at a certain distance.