238 SIXTIJ REPORT — 183G. 



when the temperature is t, i the increase of latent heat accom- 

 panying the change of volume from v to v', and u, /3, two con- 

 stants, it will be seen that 



V = v' (1 + « t), and v = v' (1 + (3 ?'). 

 Hence a t = /3 i, or -^ = — . The first of the expressions 



for V supposes the volume to change under a constant pressure ; 

 the other obtains in whatever way the change of volume takes 

 place. The ratio of i to t is the ratio of the heat absorbed by a 

 mass of air, or become latent, by a given sudden rarefaction, 

 to the heat of temperature required to expand the mass to the 

 same degree of rarefaction. This ratio can therefore be in- 

 ferred from the experiment of Clement and Desormes, so often 

 cited ; and as a is known, /3 may also be found. The absolute 

 heat requii'ed to produce a rise of temperature t under a con- 

 stant pressure is, according to this theory, t + ^ ; and that re- 

 quired to cause the same rise of temperature when the volume 



is constant is t. Hence is the ratio of the specific heats ; 



T 



and admitting Laplace's theorem, the factor by which the 

 Newtonian velocity of sound must be multiplied is a / i + - 



1 ^- " . Mr. Ivory finally observes* that the main ele- 



n/ 



ment on which the solution of the problem must turn, by what" 

 ever process the result is brought out, is the quantity of heat 

 extricated from air condensed in a given degree ; and accord- 

 ingly he proceeds to investigate in an independent manner, 

 the relation between the elasticity and density of a mass of air 

 that varies its temperature as it dilates or contracts, without 

 losing or receiving any heat by means of the suiTounding me- 

 dium. This investigation conducts to the following relation 

 between the pressure and the density 



from which the velocity of propagation of sound is arrived at by 



the usual process, the factor being a / 1 + — as before. From 



V /3 



* Pliil. Mag. and An., vol. i. p. 252. 



