528 Mr. W. Sutherland on the Viscosity 



where b is four times the volume of the N spheres ; with the 

 usual notation of v for B the volume, the last expression 

 becomes 





We have now to take up the evaluation of v for attracting 

 molecules. In the first place, if we neglect molecular diameter 

 compared to free path and also neglect curvature of path and 

 acceleration of velocity due to molecular force, then the 

 number of encounters per second of each of N molecules 

 in volume B is obtained, according to our principle, from 

 that given for forceless molecules by increasing (2a) 2 to 

 (2a) 2 (l + m/(l/2a)/i; 2 ). But it may not appear legitimate to 

 neglect curvature of path and acceleration of velocity due to 

 molecular force, even although they tend to neutralize one 

 another, so we will prove them to be practically negligible in 

 determining the average time taken by a molecule starting 

 with relative velocity V from distance D to reach distance 

 2a from the centre of attraction. Neglecting m 2 /(l/D), 

 v 2 _ y2 _j_ 2 m f (i/ r ) gives the velocity v at distance r ; but 



©•-©'+-*©* 



and with the usual notation for orbital motion, 



at 



b being the perpendicular from the centre of attraction on the 

 asymptote to the orbit ; hence 



D dr 



-i 



T ( 1+ !2AVi.^ 



Now in the case of molecules collisions occur for all values 

 of b from up to 2a(l + 2w/(l/2a)/V 2 ) 1 , to be denoted by 

 V ; hence the average value of t under these conditions is 



. > D dr 





^i + ™-" 



