114-116] System of Loaded Spheres 103 



The sum of the values of c 2 is, however, 



Zv 



vc-, or K, 

 in 



so that the change in time dt is 



2 - * dt (249). 



m dt 



Equating expressions (248) and (249), 



<^K 8/-W /27T , 



TT = -KIT- \ r (H - ^K) 



dt Mr V lim 



- l6 ^\/iS^^-^ (25o) - 



On. V \Oill / 



Or if, for the sake of brevity, we write 



7 ....(251), 



3 2 V 3m 



so that ft is a constant depending only on the structure of the molecules, 



Since the total energy of the gas is unaffected by collisions, and since also 

 the energy of rotation about the axis of symmetry of the molecules is 

 unaffected by collisions, it follows that H + K is unaffected by collisions. 

 Thus 



ar a;--^ 



116. From equations (252) and (253), 



-iK) .................. (254). 



Since VK is always to be taken positively, it is clear that 



is always negative, so that log(H f K) continually decreases, until finally 



H-fK = ................................. (255). 



This equation, then, expresses the relation between H and K in the steady 

 state. Now H is the energy of two momentoids, of which the separate 

 energies in the steady state must be equal from symmetry, and similarly K is 

 the energy of three momentoids, of which the separate energies are equal in 

 the steady state. Hence equation (254) expresses that, in the steady state, 

 the energies of the five momentoids are equal, agreeing with the result 

 predicted by the general dynamical theory. 



The general result that the ratio of distribution of energy is independent 

 of the structure of the molecule leads sometimes to striking results. In 



