476 Peculiarity of the Normal Component of Attraction. 

 But 



a = cos log - = cos i log - 4- loo; ~ I . 



z & t J 



Therefore 



C t(ldt T> fl 1 1 



\ ~Z T~^ = & COS -^ 10 O- f-ry L 



approximately, where 



I t cos log - 

 E, cos 7=1 -om-^, 



rf sin log - 



Again, 

 r a i z tadt | f«/* __tdt__ • f 1 1 ^ 



which can be made as small as we please by choosing z to be 

 sufficiently small and C to be sufficiently large. Thus it is 

 proved that Nx behaves as 



— 27rE cos \ log — +- y L 



as z tends to 0. 



Therefore the limit of N l5 and, consequently, that of N 

 are non-existent. 



Case II. cr= cos %(r). 



4. Take the general case in which <x=cos%(r), where 

 Lim^(r) is infinite. Then the same peculiarity is noticed 



as in Case I, if 



Lim ^O) 



r=0 J" 



is zero or a finite quantity different from zero. For the 

 proof of this statement, see a paper of mine which will 

 appear shortly in the ' Bulletin of the Calcutta Mathematical 

 Society/ vol. ix. 



