n 



THE DYNAMICAL THEORY OF O 



Henoe in the equation 



.(92) 



the term j* will vary inversely as the diameter of the hole, while , and u, 

 will not vary considerably with the diameter. 



Hence when the hole is very small the right-hand side of the equation 

 may be neglected, and the flow of either gas through the hole will be inde- 

 pendent of the flow of the other gas, as the term kAp 1 p t (u t u t ) becomes com- 

 paratively insignificant. 



One gas therefore will escape through a very fine hole into another nearly 

 as fast as into a vacuum ; and if the pressures are equal on both sides, the 

 volumes diffused will be as the square roots of the specific gravities inversely, 

 which is the law of diffusion of gases established by Graham*. 



Variation of the invisible agitation (y8). 

 By putting for Q in equation (75) 



(93), 



and eliminating by means of equations (76) and (52), we find 



fdv, 



iT. 



i du\ .. fdu, dv\ _ f d 



.(94). 



In this equation the first term represents the variation of invisible agitation 

 or heat ; the second, third, and fourth represent the cooling by expansion ; the 



* Trans. Royal Society of Edinburgh, Vol. XH. p. 222. 



