286 



Free Path Phenomena 



[CH. XV 



where 



CL = 



.(675). 



(m^ + m^K 



The apse is of course given by the vanishing of the denominator in the 

 integral of equation (674). If the corresponding positive root for ij is v) , the 

 angle between the asymptotes, being twice the angle between either asymptote 

 and the apsidal line, is given by 



= 2 f 

 J o 



(676). 



o Vl - ff - XV ' 



After collision the velocities parallel and perpendicular to the initial 

 line are of course 



and Fsin0'. 



343. There is naturally a doubly infinite series of possible orbits corre- 

 sponding to different values of p and V. Except for a difference of linear 

 scale, however, these may be reduced to a singly infinite system corresponding 

 to the variation of p*V. In fig. 23, which is taken from Maxwell's original 

 paper*, some members of this singly infinite system are shewn. 



FIG. 23. 



344. Let us consider a collision between two molecules, the velocities 

 before collision being u, v, w and u, v', w. The relative velocity V is 



given by 



V* = (u'-u)* + (v'-v) 2 + (w'-w)* (677), 



and V is here the same as the V of 342. 



Collected Works, n. p. 42. I am indebted to the University Press for the use of the original 



block. 



