73-75] Extension to Complex Molecules 65 



and let the number of molecules for which x lies between ^ and i + d!i, 

 etc., be 



Then, if ) is defined by 



.../.log/.dfcdfc .................. (138), 



where the summation extends over all types of molecules, it can be shewn, 

 precisely as before, that for all except an infinitesimal fraction of that part 

 of the space for which (S has a given value, ) has the minimum value which 

 is consistent with this value of (. 



Let E a be the energy of a molecule of type a specified as a function of 

 the 2n a coordinates (136). Then equation (135) may be written in the form 



Eafad&dga (139), 



in which the summation extends over all the types of molecules. In addition 

 to the functions f a ,ffi being subject to the constraint expressed by equa- 

 tion (139), they are subject also to separate constraints expressing that the 

 number of molecules of each type remains constant. The equation expressing 

 this constraint in the case of/ is 



The equations resulting from the variation of equations (138), (139) and 

 (140), keeping (S and N a , Np ... constant, are 



(141), 



\d& (143). 



The most general variation possible, subject to the constancy of 

 N a y Np ..., is therefore given by the equation 



rr v - ,.. ,,. /! A A\ 



O6 = 2 N, a II . .. (1 + log fa. + \E a + fJi a ) Ojad^id^ 2 (I 1 **)) 



a JJ 



where X, /* a , ^ ... are undetermined multipliers. 



The minimum value for ) is accordingly given by the system of equations 



1 + log/a + ^E + P* = 0> I ...(145). 



= 0, etc.) 



, . 

 Changing the constants, the solution of these equations is given by 



j. 



