Mr. Ivory's Theory of the Velocity qfSoimd. 251 



infringed by adopting the explanation deduced, by tliis in- 

 verted procedure, from the phsenomenon itself. In 1816 La- 

 place published the following theorem, without the demon- 

 stration : — The velocity of sound is equal to the velocity accord- 

 ing to Ne-di'to?i's fornmla, imdtiplied by the square root of the 

 proportion of the specific heat of air under a constant pres- 

 siire, to the specific heat under a constant volume. The in- 

 vestigation was first given in the Conn, des Terns 1825, and af- 

 terwards in the xiith book of the Mccaniqne Celeste. This 

 theorem left nothing more to be done than to find a certain 

 ratio in numbers ; and this was accomplished by the ingenious 

 experiment of MM. Clement and Desormes, from which we 

 have deduced the proportion of the latent, to the free, heat, 

 when air varies under a constant pressure. MM. Gay-Lussac 

 and Welter improved a little the original procedure of the in- 

 ventors, and repeated the experiment in a great variety of cir- 

 cumstances; by which means they not only determined the 

 number sought more exactly, but they likewise showed that 

 it was constant, or nearly so, in considerable diversity of tem- 

 perature and pressure. The result of this long investigation, 

 protracted for so many years, was a complete solution of the 

 difficulty, and a satisfectory reconcilement of the theoretical, 

 with the experimental, estimate of the velocity of sound. 



The numerical value of the proportion indicated in Laplace's 

 theorem is immediately deducible from what has been shown 

 respecting the manner in which heat combines with elastic 

 fluids. When air varies under a constant pressure, the ab- 

 solute heat requisite to produce the rise of temperature t, is 

 T + i, i being the latent heat. But t is the heat that causes 

 an equal rise of temperature when the volume is constant. 

 It is manifest therefore that the proportion of the two specific 



heals in the theorem, is t + e to t, or 1 H to 1, that is, 



1 + -^ to 1 : and / 1 + -^ is the factor by which the New- 

 tonian velocity of sound must be multiplied, in order to ob- 

 tain the true velocity. 



But the whole difficulty respecting the velocity of sound is 

 overcome, when it has been found how much heat is extricated 

 from air condensed in a given degree. This is the loading 

 principle on which the investigation must turn, by whatever 

 process the result is brought out. In Newton's formula the 

 pressure and density are supjiosed to follow the law of Boyle 

 and Mariotte ; and the computation will be best rectified by 

 searching out the true relation of the same ([uantities, and 

 substituting it in the place of that inaccurately employed. It 

 2 K 2 remains, 



