CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 455 



Taking the direction of one asymptote for initial line this has the integral 



Since V u is the relative velocity before collision, and p is the perpendicular from the 

 origin on to the asymptote, we have 



so 



that 



f 



= L 



-i/a 



dr - 



The apse is given by the vanishing of the expression in square brackets. If r is 

 the positive root, we have 



since x is the angle between the asymptote and the apsidal radius vector. 



For some purposes it is more convenient to transform the variable of the last 

 integral to ;, where q =p/r- We thus get 



>; being the least positive root of the expression in square brackets. 



No further progress can be made without knowledge of the form of ^' 13 or ^ ia . The 

 simplest and most natural form to consider is that corresponding to the case in which 

 the molecules attract or repel one another with a force varying inversely as the 

 tt la th power of the distance. In this case 



K K 



> ~' (n..- 1)V' ' 



where K is a constant depending on the nature of the molecules. 

 Hence 



where* 



2K, a (m+m ; ) .-, 



-^- (n _ 1 j|v ^" J 



" 



Thus x is now a function of a only. 



* When the forces are attractive the sign of a"" 1 is reversed. In the text the case considered ia that 

 of repulsion. 



