( 430 ) 



and 



A + (!-«) ; = A 



t/,#' (1— .r-j- //".'■ )./-|l — .1?) rt 1— .(•-//. 



Hence 



c 



(n— i) - / — {l— « /<v; 



must be negative. 



Now it' we write a = a, il -a?) + a s tf — ex J — ./■■ and - 



c (n-1)" 



and -^ — n 1 — i •• tl,cn 



1 — x -f- •'"•'' 

 (n-l)-(n-l)l/ ( i _^ (i 4 fi j^jl .,„■■= (1 :"ö-(„-l)» .*(!-.'■> 



must be negative. This will be the case it' under the radical sign 

 the numerator is larger than the denominator, or if: 



(l_. t .)(14 fi ) 4-nV(l ."J - (n -If .r(l -.*•)< l-.r + ""•'' 

 or 



(1— «) £, + n*me, - (n-1) 9 £ (1 -*) < 

 or 



(*-i) 2 I (n-i)"l 



The extreme values of # of the closed curve are given by the 

 equation : 



1 / i \ *> V 



(n-1) 2 | (n-1)' 



If the first member of this equation is negative, the values of < 



satisfying the same value, are nearer together, as was to be expected. 



We have reduced the condition that tp m be negative in its minimum 



value to : 



6, i f l n2f 2 ) . A 



(n-1) 2 I (n-1) 2 



if L is a positive quantity. If this is to be the case for real values of 

 x, then (e, and s, positive . 



in 



nst be, or 



(„_!)» | -(„-1)' 



i _ K'' + "*■ > o. 



rc — 1 



This condition is fulfilled when the points of which g, and g a are 



