21* MAXWELL'S LAW 395 



operation we must consider not only the velocities u, v, w of the 

 molecules and the atomic velocities u, fc, tt) as variable, but also 

 the distances r and the function </>, since the mode in which the 

 atoms are bound together into molecules and arranged within 

 them is not given. The number of molecules N therefore cannot 

 be taken as absolutely fixed, but we shall have the product 



where H stands for a given constant, which in 53 was thus 

 denoted. 



The variation consequently gives 



= ~L.in(u^u + vlv + wcw) 4- SS. 



= S.mSu, = S.m&>, = 8. 



The variation fy here occurring is not independent of the other 

 variations. For by addition of heat not only does the kinetic 

 energy rise in amount, but also the relaxing of the bonds, which 

 Clausius calls disgregation, increases in continually corre- 

 sponding measure, till at last it leads to dissociation. The 

 regular connection between these phenomena is to be introduced 

 into the calculation. 



Since an increase of the velocity with which the centroid of a 

 molecule moves is conceivable without the internal connection 

 between its component parts needing in any way to be altered, 

 ^ cannot depend on u, v, w. On the contrary, <f> must be 

 considered a function of U, tt, tt> ; for an increase in the atomic 

 motions must cause the distances t between the molecules to 

 increase in consequence both of the collisions between the atoms 

 and of their centrifugal force. Hence we must put 



<ty = S. 



where the sum is to be taken over all the atoms of the molecule 

 which contains the atom subjected to the influence of affinity. 



If now, as before, we denote the probability that an atom 

 possesses the molecular velocities u, v, w, and also the special 

 velocities u, t), w by 



F = F(u t v, w, u, V, tt>), 



