106 THE FUNCTION <j> AND 



(343) 

 whence 



(344) 



Now it has been proved in Chapter VII that 



7 - ^ _ 2 



( 6 ~~ e ) ~ ~r~ P ' 

 n de p p 



We have therefore 



approximately. The order of magnitude of rj < is there- 

 fore that of log n. This magnitude is mainly constant. 

 The order of magnitude of rj + <p Q \ log n is that of unity. 

 The order of magnitude of </> , and therefore of 77, is that 

 of n.* 



Equation (338) gives for the first approximation 



(1^ = _, (346) 





( *-*>(.-0 = ^ = *, W 



/ . __ , Y ( 6 ~ 6 o) 2 = ^ ^f (348) 



ap 



The members of the last equation have the order of magnitude 

 of n. Equation (338) gives also for the first approximation 



d e fi\ ~ \ ^2 / v e o)> 

 * Compare (289), (314). 



