as applied to Gases and Vapours. • 521 



(15«.) If we apply to vortices at the surface of contact of the 

 atmospheres of two atoms of the same or different kinds, the 

 conditions of permanency laid down in article 13 for vortices in 

 the same atmosphere, these conditions take the following form : — 



First. The superficial atomic mean elasticities must be the 

 same; in other words, the superficial atomic mean densities 

 must be inversely as the coefficients of elasticity of the atmo- 

 spheres. This is the condition of equilibrium of pressure. 



Second. The law of variation of the elasticity from the centre 

 to the circumference of a vortex, as expressed in equation (5), 

 must be the same for both atoms ; and this law depends on the 



quantity -j- = y-, ; therefore the condition of equilibrium of heat 



is, that the square of the velocity of vortical motion, divided by 

 the coefficient of atmospheric elasticity, shall be the same for 

 each atom. Of this quantity, therefore, and of constants com- 

 mon to all substances, temperature must be a function. 



Taking the characteristics (A) and (B) to distinguish the 

 quantities proper to the two atoms, we have the following equation : 



J^Df{l)(A) = 4^Dt(l)(B) 



S(-^)=S(«) 



!>• (12) 



temperature =<P{tI) universal constants) 

 (16.) In 2i perfect gaSy equation (11) is reduced to 



the pressure being simply proportional to the mean elasticity of 

 the atmospheric part of the gas, multiplied by a function of the 

 heat, which as equation (12) shows, is a function of the tempera- 



ture, from its involving only 77 and universal constants. 



Therefore in two perfect gases at the same pressure and tem- 

 perature, the mean elasticities of the atmospheric parts are the 

 same, and consequently — • 



The mean specific gravities of the atmospheric parts of all perfect 

 gases are inversely proportional to the coefficients of atmospheric 

 elasticity. 



Let n therefore represent the number of atoms of a perfect 

 gas, which fill unity of volume under unity of pressure at the 

 temperature of melting ice, so that nM is the total specific gra- 

 vity of the gas, and n^ji, that of its atmospheric part ; then 



Z>w/i = constant for all gases, . . . (126) 



