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0312) 3 syy !;*40 seja, of the French philosophers just named make the cube of the pressure proportional to the 4.1244 power of the density, (as is evident by using 4.1244 in place of 4 in art. 5). -Hence, n=2.1244; and, therefore, the particles should repel leach other with forces inversely as the 2.1244 powers of their distances, a law of which there is no known parallel in nature *. But if the ratio were that of 3 to 4, and consequently, as in art. 5, the cube of the pressure varying as the fourth power of the density, the repulsion between the particles would be inversely as the squares of their distances, which is the only known law of repulsion, and most likely the only one which existsorti ti 111'. - It
appears from experiment, and has been laid down as an ascertained principle, by Marquis Laplace, M. Poisson, and M. Ivory, that the specific heat of air, or the quantity of heat which raises its temperature one degree, under a constant pressure, bears an invariable ratio to its specific heat, when confined in an inextensible vessel. None of these philosophers seem to have been at all aware of the necessary and unavoidable consequences of laying down this principle : one of which, as we have already seen, is, that it requires a very graduation of the air-thermometer from what they assume as the true one. A more obvious consequence is, that the specific heat of the same mass of air, under a constant pressure, must be independent of the intensity of such pressure ; and that when a certain mass of air is confined in an inextensible vessel, its specific heat must be independent of the size of the vessel. This admits of the most rigorous demonstration, and might even have been inferred from the consideration, that the above invariable ratio of the specific heats keeps the quantity of heat which merely raises the temperature quite distinct from what goes to enlarge the volume. Now, the remarkable curiosity
* Newton inferred from Boyle's experiments, that the particles repel each other with forces inversely as their simple distances. In this he was quite excusable, it not being then known that a change of density affects the temperature. It is now certain; that whatever be the true ratio, it must be something very different from the inverse of the simple distance; but I think the French philosophers have gone a little too far to the opposite extreme. It is worthy of remark that this important point may be viewed without any regard to the essence of heat. JAN.-MARCH, 1829.
is, that in the Mécanique Celesté, livre xii,, chap. 3, formula are given for expressing the different values which the specific heat is fancied to have under different constant pressures, and also its supposed different values under different constant vom lumes. The same are given by M. Poisson, Annales de Chimie, for Aug., 1823, and Phil. Mag., Nov., 1823.
Sanctioned by such great names, these formulæ must be received as orthodox by those who never think for themselves, or who do not thoroughly examine the investigations from which the formulæ are deduced. As, however, the point is an important one, I shall, for the satisfaction of the rational inquirer, endeavour to put the matter beyond dispute, by giving a very simple demonstration of what I have now alleged, and which is the more satisfactory as it does not require the law of temperature to be known. For, the very same degree being here used for the several specific heats, it may belong to any scale.
Let the temperature of a given mass of air be reckoned on any scale of which the straight line, BE, is a part, and let CF be a line, no matter to our present purpose whether straight or curved, if it be such that any two ordinates, as BC and EF, may everywhere intercept an area BCFE proportional to the quantity of heat which would raise the temperature of the mass of air, under
f a constant volume, from any point B to any other point E. Let D G be a similar sort of line, so as to make area BDGE proportional to the heat which would raise the temperature of the same mass, if under a constant B pressure from B to E. Now, the chief condition on which we proceed is, that the quantities of heat represented by the areas BCFE and BDGE, may be everywhere to each other in a constant ratio, which call that of 1 to k, and which is obviously the same with the ratio of any ordinate of C F to the corresponding ordinate of DG.
Let the point B denote the original temperature of the given mass ; raise this temperature from B to E, under a constant pressure ; make Ee one degree, and draw the ordinate efg.
Then, area E G ge is the specific heat, at the temperature E, of the same mass of air dilated by heat under the original pressure remaining constant. Now, the specific heat, when the pressure is constant, is always to the specific heat, when the volume is constant, as k to 1; but area E Gge: Effe:: k:1; wherefore, E F fe would be the specific heat, at the temperature E, were the dilated volume now to remain constant. But since area BCFE is the quantity of heat which would raise the temperature from B to E, under the original Folume, and area E Ffe the heat which would raise it one degree more; therefore, E F fe would still have been the specific heat of the same mass of air raised to the temperature E, and all the while under the original volume. Hence, E Ffe is the specific heat of the same mass of air, at the temperature E, whether under the dilated volume remaining constant, or under the original volume constant.
By heating up the air from B to E, under the original volume, its pressure is augmented; also, if area E Ffe were increased as 1 to k, it would become the specific heat, at the temperature E, under the augmented pressure made constant. But E Ffe : EGge :: 1 : k, and therefore, E Gge is the specific heat of the same mass of air, at the temperature E, whether under the augmented pressure remaining constant, or, as in the first case above mentioned, under the original pressure constant. The same conclusions would follow, by a similar process, were the temperature E lower than B.
It is thus clearly established, as a necessary result of laying down the invariable ratio above mentioned, that neither the magnitude of a constant volume, nor the intensity of a constant pressure, have anything to do with the specific heat of a given mass of air. * The contrary errors, even if detached or insulated, would have merited correction; but how much more when it is considered that the eminent French philosophers, as already quoted, have built upon these errors an immense fabric of complex formulæ, and have drawn from them a multitude of conclusions!
The theory of rain proposed by the late ingenious Dr. James Hutton of Edinburgh is by many received as the true explication of the phenomenon, viz, that rain is produced by the mixture of masses of moist air having different temperatures. It is known, from experiment, that the variations in the capacity of air, or rather perhaps of space, for moisture, proceed in a higher ratio than the variations on the common scale of temperature, but still more so with reference to the one we were investigating; and therefore, if the mixture had either the mean' temperature of the whole, or one still lower, its capacity for moisture would come short of the mean. Hence, a deposition of water will ensue, if the air have been sufficiently moist. There can be no question, that this theory is a possible one, but it would be no easy matter to prove that it is the actual and ordinary mode in which rain is produced. I therefore propose adducing some reasons, countenanced by experiment, which seem to render it very probable that clouds, and rain too, may often be traced to a nearer and more 'natural source. The Huttonian theory does not readily explain why rain is more commonly preceded or attended with a falling barometer. For it is as easy to conceive mixtures of air occurring whilst the barometer rises as when it falls, and the like objection attaches to the electrical theory of rain. This prognostic did not long escape notice after the Torricellian experiment was made* ; and the explanation then given, and for long after received, was, that the air from its rarity was unable to buoy up or support the dense vapours, and so of course down they came. It was not then known that, at the same temperature and pressure, moist air, especially if transparent, is lighter than dry. Yet the observers of that period certainly inferred, on very probable grounds, that there existed a connection between the concomitant circumstances of decreasing pressure and depositions of rain, &c. from the atmosphere. They are further to be commended for seeking a solution in a principle supposed to be known, because reason and facts are
* I am aware that some of the first observers are said to have coupled rain with a rising or high barometer, and indeed there are exceptions. When the wind is shifting from west to east, the barometer generally rises, though followed with copious rain; and when the wind shifts from east to west, the barometer usually falls, though it remain dry. The motion of the barometer, in these cases, is, to a certain extent, connected with the earth's diurnal rotation,
always preferable to hypothesis. I am far from reckoning their statical explanation to have no share in the phenomena, though I think there are other and more powerful causes.
We are indebted to M. Deluc, Idées sur la Météorologie, tom. i. 26, and Phil. Trans. 1792, for the first conjectures regarding that theory of the mixture of air and moisture which has since been so ably extended and defended by Mr. Dalton and M. Gay-Lussac, viz. that the quantity of vapour contained in a given space is independent of the presence or density of any other elastic fluid with which it forms no intimate combination; or, that the maximum quantity of vapour which can exist in a given space is the same at the same temperature as it would be did that space contain nothing else. This view of the subject was at first questioned by Saussure, and occasionally since by others, though most of the arguments opposed to it are not much to the purpose. But, as it is pretty well supported by experiments, and is very generally received, I shall adopt it at present as correct. When, therefore, the bulk of a mass of air increases, its entire capacity for moisture should increase at the same rate, were the temperature to remain the same. But when air dilates from a diminution of pressure, its temperature always falls, if there be no accession of heat from some other source* ; and this diminution of temperature lessens the capacity of the air for moisture far more than the increase in bulk enlarges it. If, therefore, the air be sufficiently moist, a fall in the barometer should tend to produce clouds or rain,
Such at least would be the result, calculating from the foregoing principles; but the following simple experiment affords a more direct proof, that sufficient rarefaction will always change common undried air into a cloud. Connect a small glass flask, containing such air, with the receiver of an airpump, by means of an intervening stopcock. Exhaust the receiver, with the cock shut; then, looking attentively at the
* A fall in the barometer may not produce a reduction of temperature near the earth's surface. The temperature there may often be preserved, or even raised, by the evolution of the latent heat of the condensing vapour, and by the retention of the heat which formerly escaped upward, but which ceases to do so after the atmosphere is occupied by dense clouds,