98-101] Maxwell's Treatment of Equipartition 89 



From this it follows that in equation (206) the decrease in p l caused by 

 the formation of double molecules of any specified kind is exactly counter- 

 balanced by the increase caused by the dissolution of double molecules of 

 the same kind. Hence in equation (206), dp l jdt may be taken to be the 

 change in p caused solely by the continuous motion of the fluid, and may be 

 treated as p 2 has been treated, leading to the result that p l must be constant 

 along every stream line. 



100. We have found, therefore, that the conditions for steady motion, 

 on the hypothesis of binary encounters, may be expressed as follows : 



(a) Throughout the 2n + 3 dimensional space, p 1 must be constant 

 along every stream line. 



(/3) Throughout the 4>n + 9 dimensional space, p 2 must be constant 

 along every stream line. 



(7) At every point on the boundary of the 4n, + 9 dimensional space 

 we must have 



p a = pipi- 

 To these may be added a fourth condition : 



(8) At every point on the boundary of the 2n + 3 dimensional space 

 (i.e. at infinity) the flow across the boundary must be nil, or what is the 

 same thing, we must have 



Pi = 0, 



this last condition securing that steadiness is maintained without a supply of 

 new systems from infinity. 



These conditions are necessary and sufficient for steady motion. 



Ternary and Higher Encounters. 



101. By a simple extension of the method already explained, the 

 possibility of encounters of ternary and higher orders may be con- 

 sidered. For instance, to take ternary encounters into account we imagine 

 systems of triple molecules, these being represented in a suitable space, 

 in which the number of dimensions will be 6w + 15, namely 2n + 6 for each 

 constituent molecule, less three for the position of the centre of gravity 

 of the whole system. The density in this space being p s> we have as con- 

 ditions additional to those just given : 



(e) Throughout the 6w + 15 dimensional space, p 3 must be constant 

 along every stream line. 



() At every point on the boundary of the 6ft + 15 dimensional 

 space we must have 



