DEPENDING ON THE HEIGHT ABOVE THE EARTH'S SURFACE. 451 



the increment of pressure due to an equal increase of density without 

 change of temperature. It may be supposed that the temperature is 

 in both cases before the alteration of density, for in the above 

 expression may be taken as small as we please. The experiment of 

 Clement and Desormes, which is in fact a practical imitation, as near 

 as may be, of what takes place in the sonorous vibrations of the air, 

 may consequently be used for determining 1 + ^. In this experiment 

 as described by Poisson (Traite de 3Iecanique, Tom. II. p. 6-11. 2d. Edit.) 

 p — jj is the difference of pressure due to a sudden alteration p" — p of 

 density, accompanied by a change of temperature ; and p" — p is the 

 difference of pressure due to the same difference of density, the tem- 

 perature being the same as it was before the sudden alteration in the 

 first case. Hence, 



p -p 



The numerical values of j>, p', and p", given by the experiment, are 

 respectively 0,7665, 0,7527, and 0,7629. The value of 1 + * derived 

 from these is 1,3529. A similar experiment by Gay-Lussac, gives 

 1,3795. These values fall short of that derived from the observed 

 velocity sound, probably because the experiment cannot be performed 

 so exactly as to avoid all variation of temperature by communication 

 with surrounding bodies. The above expression for 1 + ^ is a little dif- 

 ferent from that of Poisson, and something larger in numerical value. 



It appears both from experiments of the same kind as that above 

 mentioned, and from the observed velocity of sound in different tem- 

 peratures and at diflFerent heights, that the constant k is independent 

 of the temperature and density. 



Recurring now to equation (c), we may derive from it, 



^ = A(i^aa,)-^. 



up ap 



This equation gives the variation of temperature from one point to an- 

 other at a given time, depending on variation of density only; or it 

 gives the difference of temperature of two contiguous elements, which, 

 Vol. VI. Pabt III. sM 



