as* Mr. Ivory's Theory of the Velocity of Sound. 



The equation (D) does not coincide with what is elsewhere 

 given for expressing the relation of the same quantities. It is 

 different from the equation published by M. Poisson in the 

 Conn, des Tems 1826, p. 264. In order to clear away all 

 clouds of obscurity from a matter of considerable importance, 

 I shall now examine particularly', what it is that occasions the 

 difference. For this purpose I shall set out from M. Poisson's 

 equation (6), p. 263, viz. 



Here w is the variation of latent heat corresponding to the 

 small condensation y ; and, in our notation, «j = di, y =. — - 

 k — \ = -J- : the equation may now be put in this form, viz. 



dg /3dt 



which is nowise different from what M. Poisson obtains in 

 p. 264, except that he writes d^ = to, instead o^ di = «;. Dif- 

 ferentiate the second of the formulae (C), changing the sign 

 of i in order to agree with M. Poisson's supposition, that the 

 density increases ; then, 



(Z f Pidi 



^ 1 -j-a^— lii 



Now this equation is identical with M. Poisson's only at one 

 point, namely, when i = 0. The latter is therefore true only 

 in a particular state of the variables, and is inexact in all other 

 circumstances. When the density and latent heat of a mass 

 of air vary together, M. Poisson's equation expresses the true 

 relation of the differentials only initially ; and it ceases to be 

 exact when the variable quantities have changed their original 

 magnitudes. The integral formulae deduced from such a pro- 

 cess cannot be accurate results, although they may be ap- 

 proximations. The truth of what has been observed must 

 be so evident to any one that will consider with attention the 

 manner in which the author obtains the equation in question, 

 that it would be a waste of words to attempt any further ex- 

 planation. 



The investigation I have given in pp. 7 and 8 of the Phil. 

 Mag. for June 1825, is liable to the same objection that has 

 just been urged against M. Poisson. The relation of the dif- 

 ferentials is obtained only in a particular state of the variables. 

 The experiment of MM. Clement and Desormes, although it 



enables us to ascertain the value of ~, is, nevertheless, in- 

 sufficient 



