On the Velocities of Sound in different Bodies. 261 



the same, a part only of the caloric which it receives is employed 

 to produce that effect. The other part which remains latent 

 serves to dilate its volume ; and it is this which develops itself 

 when the air thus dilated is reduced by compression to its original 

 volume. The heat disengaged by the approximation of two 

 neighbouring particles of an aerial vibrating fibre, increases their 

 temperature, and spreads itself gradually over the air and sur- 

 rounding bodies : but this diffusion and irradiation taking place 

 with an extreme slowness relatively to the svv'iftness of the vibra- 

 tions, it nifiy be reasonably supposed that during the period of a 

 vibration the quantity of heat remains the same between two 

 adjoining particles. Tlius tiiese particles in approximating re- 

 pel each other more at first, because, their temperature being 

 supposed constant, their mutual repulsion augments in an inverse 

 ratio to their distance; and afterwards, because the latent ca- 

 loric which develops itself raises their temperature. Newton 

 had only regarded the first of these two causes of repulsion ; but 

 it is evident that the second cause ought to increase the swift- 

 ness of sound, since it augments the elasticity of the air. By 

 taking this into the calculation, I arrive at the following theorem : 



" The real swiftness of sound is equalized to the product of 

 swiftness which the Newtonian formula gives by the square root 

 of the affinity of the specific heat of air submitted to the con- 

 stant pressure of the atmosphere and to difl^erent temperatures, 

 to its specific heat when its volume remains constant." 



If we suppose, with many philosophers, that the heat con- 

 tained in a mass of air submitted to a constant pressure and to 

 different temperatures is proportional to its volume (which would 

 be deviating a Httle from the truth), the preceding square root 

 will become that of the affinity of the difference of two pressures 

 to the difference of the quantities of heat which two equal volumes 

 of atmospheric air submitted respectively to these pressures de- 

 velops, in passing from a given temperature to an inferior tem- 

 perature ; the smallest of these quantities of heat and the smallest 

 of these pressures being taken for unities. 



Being desirous of comparing this theorem with experience, 1 

 have fortunately found the data of the observation which it sup- 

 j)oses among the numerous results of the interesting work of 

 M.M. La Roche and Berard upon the specific heat of gas. These 

 able philosophers have calculated the quantities of heat which 

 two cfjual bodies of atmospheric air emit by a reduction in tem- 

 perature of about eighty degrees ; the one compressed by the 



weight of the atmosphere, the other by the same weiglit aug-^ 

 mented I'Vu. Tiiey liave found that the heat ilisen.;age(i, rela- 

 tive to the greatest pressure, was 1'24 ; the heat relative to the 

 sipallest pressure being unity. It is necessary then according to 



