342-344] Collisions with Law of Inverse Fifth Power 287 



Let us imagine the first molecule to be at rest, and the second to approach 

 it with a velocity of components u' it, v v, w w. Let the direction of 

 this velocity meet a plane perpendicular to it through the centre of the 

 second molecule in a point of which the polar coordinates referred to the 



FIG. 24. 



second molecule as origin are p, e. Then p is the same as the p of 342. 

 Let e be measured from OR, the intersection of the plane normal to NP 

 with a plane through containing the directions of PN and of the axis of x. 



In fig. 25, every point except is on a unit sphere having as centre. 



FIG. 25. 

 Thus if OG, OG' are directions of motion before and after collision, 



RGG'=e, GG' = 0', 

 therefore cos G'X = cos GX cos GG' + sin GX sin GG' cos e. 



But 



cos 



u u 



cos 



u u 



where u, u', etc. are components of velocity after collision, so that 



u' -u=(u'- u) cos & + VF 2 -(u' -uf sin & cos e ...... (678). 



