using a tall jar, and pouring in more liquor till that in the gauge reached its former level. However, it is easier and more accu rate in practice, to overlook those increments of volume, because they will be proportional to the depressions themselves, and therefore, the ratio of these depressions, which gives the thing wanted, is not altered by this circumstance. For the same reason, it is better to neglect any change in the height of the liquid in the cistern, and only to observe its height when the air-vessel is open. As an error might have been introduced by allowing the liquid in the tube to spring up and displace a portion of the air it contained, or at least to render the volume uncertain by its undulations, a cork was struck in it, immediately above the common level. It was not so tight as to prevent the passage of air, but it operated as a sufficient check to the rise of the denser fluid. Every other precaution I could think of was attended to, and the mean of many experiments with this apparatus gave the ratio of the specific heat of air under a constant volume, to that under a constant pressure, as 1 to 1.334, which is so nearly as 3 to 4, that I am inclined to consider this the true value. However, I intend to repeat these experiments, and to prove them by a different process. The ratio of 3 to 4 does not completely bear out the amendment proposed on the Newtonian theory of sound, by the Marquis La Place. But a complete theory ought to account for the almost absolute control which wind exercises over the intensity of sound. I have often thought that both the intensity and the excess in the experimental over the theoretical velocity, are connected with the reaction of the earth's surface. As an illustration of this, sound is well known to be rendered more intense, by passing along the face of a wall or precipice; and very likely it is at same time accelerated. From the experiments of MM. Desormes and Clement, the ratio of the specific heat of air under a constant volume, is to that under a constant pressure, as 1 to 1.354; and from those of MM. Gay Lussac and Welter as 1 to 1.375. The fractional part of both approaches to, and Mr Ivory has adopted this, and suggested a reason why it should be the true value*. By * Phil. Mag. lxvi. 9. adopting the fraction }, Mr Ivory obtains the following equa tion, . 1 + ar+ai 1+ar Where is the initial temperature, a a constant, and i the change of temperature, produced by changing the density from unit to That this is the true value of i, considered as proportional to the change in the quantity of heat, Mr Ivory thinks pretty certain; because he supposes a consequence of it to be, "that, when air contracts or enlarges its dimensions, the heat disengaged or absorbed follows the proportion in which the linear distance of the particles is lessened or augmented,”—an opinion which he thinks so probable, that it should not be rejected till the contrary be placed beyond all doubt. Now, although my experiments are favourable to Mr Ivory's conjecture regarding the value of this ratio, yet I cannot ac quiesce in the reason which that able mathematician has given for fixing on that quantity. I shall not enlarge on its incompatibility with the law of temperature which I formerly laid down ; but that it may not be urged as an argument against that law, I shall, with every deference to Mr Ivory, shew that his view of this part of the subject is otherwise untenable; because it involves a mistake, in that he has inadvertently taken the linear distance of the particles of a mass of air as proportional to the cube root of the density, in place of the cube root of the volume. For it is obvious, that is not proportional to the linear distance of the particles, but to its reciprocal; and whilst is the 1, that is, as the difference of the resame, i varies as e ciprocals of the linear distances at the beginning and end of the change of density; so that neither the heat of combination nor the quantity i follows the variation of the linear distance of the particles. For, as we formerly saw, the first follows the variation of the logarithm of the volume or cube of the linear dis tance. T The following is a different mode of estimating the ratio of the specific heats, by using great changes of density. Let the density of the external aire, and suppose the air in a close vessel to be rarified till its mass or density =r; and that when it has acquired the common temperature, a communi cation with the atmosphere is opened, restoring the external pressure, whereby the density within is increased from r to m. The density of the air which has re-entered will thus be diminished from e to m, and its mass will be m→ r. Now, from what was formerly shewn of the air-thermometer, the heat evolved by the compression of the rarified mass r, will be to that absorbed by the dilatation of the re-entered mass temperature by the true scale, or the heat evolved by a mass of air = 1, when its density is increased from unit to But the mixed mass is m, and, therefore, the rise in its 1 temperature on the same scale, is — log {(~)"(-)"} m r Hence, i the rise of temperature in the mass m, reckoned on the common scale, is equal to what any mass of air at the temperature would undergo by increasing its density from unit T m = e. Wherefore, if the specific heat of air under " (-) = a constant volume, be to that under a constant pressure, in the constant ratio of 1 to 1 + x, we have i = 1+ ar a To find the value of r when the surplus heat, or 1 m log {(;)"} m =- log is a maximum, we have and a are given, m may in every case be found, from the above formulæ, or from 2.71828' but its minimum, answers to two different values of For instance, r = 1 e. If three-fourths of the air be extracted from a close vessel, and, after the temperature has settled, one-fourth be instantly restored, no change of temperature should ensue. The law of temperature admits of a somewhat simpler investigation than was formerly given. Let t be the temperature, or rather the indication on the common scale of an air-thermometer, p the pressure, and the density of the mass of air; then and b being constants, we have, as before, from the law of Boyle, p=bę (1+at). Now, the specific heat under a constant pressure being to that under a constant volume, in the inverse ratio of the variations of temperature produced in these two different cases by equal variations in the quantities of heat, the following expressions respectively contain all the variables which enter into these specific heats, relatively to the ordinary graduation. $ which are obtained from the above equation, by making p and respectively to vary with t, whilst the other is constant. The variations of the quantities of heat being constant, and, as men 4. tioned above, the same in both terms, are omitted, as also the constant linear degree of the common scale. Let the temperature be reckoned on AB, as on the common scale of an airthermometer commencing at A or — 448° F; and let CF be a line of such a nature, that every ordinate as BC EF, &c. may be proportional to the specific heat of air under a constant E B A F volume, at the respective temperatures B, E, &c. So at the intercepted areas will denote the corresponding variations in the quantity of heat under a constant volume. But if the specific heat of air under a constant pressure exceed that under a constant volume, in the constant ratio of K to 1, and if these ordinates be every where increased in that ratio, another line GD, passing through their extremities, must be of the same nature with CF, and the intercepted areas to the former as K to 1. Again, let the specific heat of a mass of air under a constant pressure be BD x 1°; and let its temperature be raised from B to E under the same pressure; then the area BDGE will denote the increase of heat, and EG × 1 the specific heat under a constant pressure at the temperature E. Now EG: EF:: K: 1, wherefore EF x 1° is the specific heat of the dilated mass at the temperature E, under a constant volume. But EF x 1° would still have been the specific heat, had the air under its original . volume been raised to the temperature E; and because EF : EG 1 K, its specific heat at the temperature E under a constant pressure would have been EG x 1°, as before. Hence, the constant ratio of the specific heats renders them independent of the actual density or pressure, and, therefore and : de are constant quantities. It thus appears, that the above expressions for the specific heats answering to a degree on the common scale, vary inversely as 1+ at; or, that any nate BD, or BC is inversely as AB, which is the well' perty of the hyperbola; and, therefore, CF and hyperbolas, having A for their centre, and AE for We have, then, without going through the pr |