38 GANESH PRASAü, 



Therefore it foUows from (1) and (V) that 



9 27t, 

 9, 



(2) 



i.|431/'WI + 67Z, + ||IM|, 



+ (3) 



But it follows, from the suppositions in the beginning o£ Art. 35, that 



Therefore the right side of (2) is greater than the right side of (3). 

 Thus, in order that 



3^+£ 



9 



e 

 9i 



lo-^ 

 lo-^ 



it is sufficient that 



2 ff/' 



i= {43 1 r {7t) I + 676 + 1 2 ^1 < 10" 

 tf [ 1 ) 



The final result , regarding the condition to be satisfied by f{x) , may now 

 be thus stated: 



If it be supposed that 



Aj < 10-^ 

 A,<10-A., 



and 



s 



then, in order that the approximate conditions of the phenomenon be satisfied, 

 it is sufficient that 



-A_|43|/-'(ff)| + 67& + ||lM| be negligible, i. e. <, say, 10- 



38. By a quasi - necessary condition I mean a sufficient condition which, 

 though itself not necessary, is similar to the condition which is both sufficient 

 and necessary. Thus the condition (Pj is a quasi-necessary one. 



If stand for the greater of the two quantities 



3B+£ , e 



and — , 



9 9t 



then 



< 10- 



