908 

 Now 



I [W (t) — A-]'« dt\<^l \iD{t) — .V\m\dt\<\ W (§) 



if, in the if-plane, ^ = ^ is the point on the straight line from to 

 j;, where ui{t] — .c gets it maximum modulus. Thus we have 



1 



ax ^^ Um I a,n \m<\ü) {^) — ic \ 

 and therefore 



«z < I w (t) — § H- I - ^ I < i to (^) — § I + I § - ^1, 



or, since .v is a point of the domain («), 



«r < I 0> (.t:„i) — X,a -\- « 



so that further 



a («) < I w (x,,,) — x,n I + « . 



Thus we have tinally for the number /i,, which, for the series P, 

 corresponds to a, the iiiequalitj' 



/3j < I to {x,„) - .v,n i + 2et 



If this be compared with (66), and if we notice the signification 

 of Xm and .v\n, it will be seen that we have /?, <[ ^, so that point 

 2 of the theorem is verified. 



