as applied to Gases and Vapours, ^ '^' 519 

 The variation of this expression being of opposite sign to the 

 variation of ^ ', shows that any small disturbance of the den- 

 sity produces a force tending to restore that distribution to the 

 - state corresponding to the position of equilibrium of the layers, 

 and therefore that the state indicated by equation (5c) is stable. 

 (14.) The integral of equation (5c) is 



'ylru^u^^^e^'bj^ d^'1> (6) 



The arbitrary constant a is determined from the ' equation of 

 condition (2) in the following manner. 



Substituting for yjru in equation (2) its value as given above, 

 we obtain 



,gkb e 



or 





(7) 



which integration having been effected, we shall obtain for the 

 value of the superficial elasticity of the atomic atmospheres, 



p=b^3f{l)=b^J)e' 



M 



M 



(8) 



To obtain an infinite series for approximating to the value of 

 the integral in equation (7), let the following substitutions be 

 made : 



and let the values of the successive differential 

 coefficients of &) with respect to X, when X=0, 

 ^ = 0, and a) = l, be denoted by 



(o-O, K), K'), &c. 



Then 



(9) 



-/". 



</\.e30Xft). 



The value of which (when the function ^ is such as to admit of 

 its having a finite value) is 



