12 
DE. G. H. BEYAN ON THE KINETIC THEOEY 
centrifugal force. On the kinetic theory, this limitation finds its interpretation in 
the fact that the density of the atmosphere according to the above law of distribution 
is proportional to 
exp — hm{Y — + t)) = ~ hm{'V — l-Qb’'} where yf . . (19). 
If clYjdr > the density decreases as we proceed outwards from the axis of 
the planet, it becomes a minimum when dVjdr = Ddr, and begins to increase again 
outwards when dY;'dr < Ob*. Hence the point at which centrifugal force is just 
balanced by the planet’s attraction is the point of minimum density in the atmo¬ 
sphere according to the above law of permanent distribution. And since the 
atmosphere does not extend to infinity, we conclude that it cannot be permanent 
unless the density at the point of minimum density is infinitesimal, and practically 
zero. 
This may be made clearer by drawing the meridian sections of the surfaces of 
equal density, and thus reproducing the results first obtained by Edouard Eoche, of 
Asymptotes. 
0-6 O-a 10 12 1-4 l-t 1-8 2-0 
Montpellier. In the case of a spherical planet of mass M (astronomical units), these 
curves are given in cylindrical co-ordinates by the equation 
