Comte - The positive philosophy. Vol. 1

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that they form with each surface.—The last consideration, and the most important, is the difference of temperatures between the two bodies. When this difference is not very great, the intensity of the action is in precise proportion to it: but this relation appears to cease when the temperatures become very unequal.

When the radiation is not direct, but transmitted through an intermediate body, the conditions just noticed become complicated with new circumstances relating to the action of the interposed body. We owe to Saussure a fine series of experiments—hardly varied enough however,— upon the effect of a set of transparent coverings in changing remarkably the natural mode of accumulation or dispersion of heat whether radiant or obscure. More recently, M. Melloni has pointed out an essential distinction between the bans mission of heat and that of light, in proving that the most translucent bodies are not always those through which heat passes most easily; as was previously supposed.

It is well for physicists to separate the radiation of heat from its propagation by contact, for analytical purposes; but it is evident that the separation cannot be found in nature. They are always found in connection, however unequally. Besides that the atmosphere can hardly be absent, and is always establishing an equilibrium of heat between bodies that are apart, it is clear that it is only the state of the surface that can be determined by radiation. The interior parts, which have as much to do with the final condition as the surface, can grow warmer or cooler only by contiguous and gradual propagation. Thus, no real case can be analysed by the study of its radiation alone. And again, the action by contact of two bodies can take place only in those small portions which are in contact, while the bodies are acting upon each other by the radiation of all the rest of their surfaces. Thus, though the two modes of action are really distinct, the analysis of either is rendered extremely difficult by their perpetual combination.

Of the three conditions noticed above, relating to the action exerted at a distance, the only one which applies equally to the propagation of heat by contact is the difference of temperatures. The temperature of the parts in question can have so little inequality, that the law which makes the action increase in proportion to the difference may be regarded almost as an exact expression of the fact. As for the law relating to direction, it probably subsists here too, though we cannot be perfectly assured of it. But that law which relates to the distance must be totally changed; for, on the one hand, the action of the almost contiguous par-

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ticles cannot be nearly so great as the variations which we are able to estimate would lead us to suppose; and, on the other hand, when we compare the various small intervals between them, the diminution is certainly much more rapid than in the case of distant bodies.

Whatever may be the mode of the warming and cooling of respective bodies, the final state which is established under the laws just noticed is numerically determined by three essential coefficients, proper to every natural body, as its specific gravity is in barology.

Under the old term conductibility, two properties were confounded, which Fourier separated, giving them the names of penetrability and permeability; 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 through the interior. Permeability 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 pervades 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 permeability 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 modifications: 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 marked 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 breal; 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

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very important to measure the value of these two coefficients for all bodies under study: 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.

One consideration, that of specific heat, remains to be noticed, as concurring to regulate the results of thermological action. Whether under 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 temperature 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 measurement. The quantity of heat consumed by any body at a determinate 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 conductibility as identical in all directions, in all bodies, however their structure may vary in different directions; and specific heat probably 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.

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Section II

Constituent Changes by Heat

The second part of thermology is that which relates to the alterations caused by heat in the physical constitution of bodies. These alterations are of two kinds, changes of volume, and the production of a new state of aggregation; and this is the part of thermology of which we are 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.

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 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 procure 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, contrary 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

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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 produced by heat able to melt equal weights of ice at zero. This is the only 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; vet they all dilate uniformly and equally, their volume increasing three-eighths, from the temperature of melting ice to that 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 GayLussac at Paris, and Dalton at Manchester.

Next, we have to notice the changes produced by heat in the state of aggregation of bodies.

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, and 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 the fusion of solids and in the evaporation of liquids. All

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these changes have been brought by the illustrious Black under one fundamental law, which is both from its importance and its universality, one of finest discoveries in natural philosophy. It is this: that in the passage from the solid to the liquid state, and from that to the gaseous, every substance always absorbs a more or less distinguishable quantity of heat, without raising its temperature; while the inverse process occasions a disengagement of heat, precisely correspondent to the absorption. These disengagements and adsorptions 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 principle.

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 hydrometry. 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 chemical fact, occasioned by the dissolving action of air upon liquids. He showed that the action of the air was adverse to evaporation, except 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 were 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, whereas is, appears that no degree of co suffices to stop the process entirely, since ice itself produce a vapour appreciable 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 equal to the atmospheric pressure; a fact which can be ascertained by direct experiment. Proceeding from this point, Dr. Dalton discovered the important law that the vapours of different liquids have tensions always equal between

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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 vapours, 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 temperatures of different liquids and their other properties; but this remains to be done, and these temperatures 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 hygrometrical equilibrium between moist bodies seems a natural adjunct to the theory of evaporation. Saussure and Deluc have given us a valuable instrument for this inquiry; but we know scarcely anything of the laws which regulate the equilibrium of moisture. Prevision, which is the exact measure of science of every kind, is almost non existent in the case of hydrometry. The small part that it plays in the inorganic departments of nature is, no doubt the reason of the little attention that physicists have de voted to it: but we shall hereafter find how important is its share in vital phenomena. According to M. de Blainville hydrometrical action constitutes the first degree and ele mentary mode of the nutrition 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. To 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

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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 theory.

Section III

Connection with Analysis

This theory relates to the first class of cases,—those in which an equalization of 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 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 his- tory,—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.

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Section IV

Terrestrial Temperatures

The temperature of each point of our globe is owing (putting aside local or accidental influences) to the action of three general and permanent causes variously combined: first, the solar heat, affecting different parts unequally, and subieeted to periodical variations: next, the interior heat proper to the earth since its formation as a planet: and thirdly, the general thermometricalstate 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 the globe were not pervaded by a heat of its own, independent of the action of the sun; a heat which tends to dispersion from the surface, by radiation towards the planets, though the atmosphere must considerably retard this dispersion. 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, in proportion to the depth.—As to the third cause, Fourier was the first to conceive of it. He was wont to give, in a simple and striking form, the results of his inquiries in the saying that if the earth left a thermometer behind it in any part of its orbit, the instrument (supposing it protected frown 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 considering the interior heat, if the

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surrounding space had Lot 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 this interior mass through future ages. This rapid sketch will suffice to show what a sudden scientific consistcany 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.

Chapter IV

Acoustics

This 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.

By studying sonorous vibrations, we obtain some insight into the interior mechanical constitution of natural bodies, manifested by the