74 The Law of Distribution [OH. v 



molecular forces between them becomes appreciable, and let us suppose 

 encounters to be possible in which more than two molecules are engaged 

 at once. 



Instead of being written in the form (133) the total energy of the gas 

 may be put in the form 



= E a + E b + ...+W ab +...+W cde + ............... (171), 



in which W ab is the potential energy of the intermolecular forces between 

 the molecules A and B, supposed engaged in an encounter in which no 

 other molecules are engaged, W C d e is the potential energy of the inter- 

 molecular forces between the three molecules C, D, and E, supposed engaged 

 in an encounter in which no other molecules are engaged, and so on. This 

 equation only differs from equation (133) in that the intermolecular energy 

 <I> is expressed as the sum of the intermolecular energies of the various 

 encounters. 



Let us now regard the molecules A and B as forming a single dynamical 

 system, which we shall refer to as a " double-molecule." Let the molecules 

 C, D, and E form a single dynamical system a " triple-molecule " ; and so 

 on. The energy E ab of the double molecule AB may be supposed to be 

 given by 



E^ = E a + E b + W ab , 



that of the triple molecule GDE by 



and so on. The whole energy of the gas at any single instant is now 

 given by 



3 E+ ..................... (172), 



where ^E is the sum of the energies of all the single molecules, i.e., mole- 

 cules which are not engaged in encounter at all, ^E is the sum of the 

 energies of all the double molecules, and so on. The energy has now been 

 expressed as the sum of the energies of a number of molecules of different 

 kinds, regarding multiple molecules merely as new species of molecules. To 

 this extent the problem is the same as the problem already dealt with in 75. 

 There is, however, an important difference. In the former case a molecule 

 belonged to the same type for ever: in the present case single molecules are 

 always combining into multiple molecules, and vice versd. In fact we cannot 

 assume that the total number of molecules of each, or even of all, kinds is 

 constant. 



All the constituent molecules A, B,... of the gas must be represented 

 separately in the generalised space, as before. A double molecule AB comes 

 into existence when certain relations are satisfied between the coordinates of 

 A and those of B. We shall find it convenient to make a slight alteration 



