23* MAXWELL'S LAW 403 



in which the function <p' is connected with the potential energy <j> 

 of the atom by the relation 



and a, b, C, I) i, fy 2 > fys are constant coefficients. 



The first three formulae need not be again investigated. We 

 deduce at once, from their holding good in this case too, that 

 Maxwell's law of distribution in composite molecules also is 

 not disturbed by motions of translation or rotation of the gas as a 

 whole. 



If we integrate the last three differential equations we find 

 that the function F contains a factor depending on it, tt, tt), which 

 may also be brought into the form 



25 is here again a constant, and x has now the meaning 

 X = m j(u - a) 2 + (t) - b) 2 + (n> - c) 2 } + 2f , 



where / has the value just given. 



On the same grounds as those given before in 22*, all terms 

 drop out of the expression for r which contain uneven powers of 

 U, t>, VD or of F, t), 5, at least if the supposition is realised that the 

 gas is free from external forces, electrical or magnetic for 

 instance, which cause a definite orientation or a definite direction 

 of rotation of the molecules ; for on our supposition each direc- 

 tion is as probable as that which is its exact opposite. Hence it 

 follows that 



a = 0, b = 0, c = 0, 



so that the function x takes again the simple form 

 x = m(u 2 + \3 2 + n> 2 ) + 2</>, 



in which denotes the potential energy of the atom m. 



The introduction, therefore, of the theorem of the conservation 7 

 of areas alters nothing in the result of the calculation ; and we \ 

 may therefore be convinced that, in the formulae before developed, ( 

 the energy of the rotatory motion of the molecules has already- 

 been taken into account. 



The case would, however, be probably different if the gas were 

 dielectrically polarised or encircled by electric currents. 



D D 2 



