22* MAXWELL'S LAW 399 



In order, further, to find the value of the magnitude 23, a 

 determination is first of all necessary of the limits within which 

 the velocities it, tt, tt> are variable. These magnitudes cannot 

 assume any value between oo and -f oo, as in the case of the 

 molecular velocities u t v, 10 ; for if their values were to increase 

 above a certain amount, the energy of the internal motions would 

 be sufficient to break up the combination of the atoms, which 

 would then move on, either singly as independent molecules or in 

 new molecular groupings : the former atomic motions are there- 

 fore partly transformed into molecular motions when their value 

 exceeds the limits determined by affinity. 



In this view the upper limits of the atomic velocities are 

 determined by the condition that the corresponding kinetic energy 

 of an atom cannot be greater than the energy of affinity which is 

 overcome when the atom considered is to be loosed from the bonds 

 of the molecule. If we denote by $ the maximum value of the 

 energy which can be developed by the combination of the atom 

 with the remaining constituents of the molecule, so that 



* = 8.J"f(r)*, 



then, since the molecule considered is in such a thermal condition 

 and with the disgregation so far advanced that the chemical 

 energy 



has already been overcome by the expansive tendency of heat, 

 there still remains only the difference 



to keep the atom in the molecule. The condition, then, which 

 determines the upper limits of the atomic speeds is therefore 



or, more shortly, with the above definition of 



This equation expresses that the sum of the kinetic and potential 

 energies at any moment within the molecule, or the sum of the 

 heat and chemical affinity within it, must remain smaller than the 



