or if 



or 



or 



( 203 ) 



C n-\ \ C\C n-\ 



, c( B l \ 16 AB 1 \ 



B 1 (n -J- 3) 2 



C~ 8 n 2 — 1 ' 



a, — a, o n 2 — 1 



— 1 + 



or 



n = — (n — 1) 1 — - 



a„—a % ( (n + 3)* 



In this expression the value of the factor n — 1 always lies between 



and 1 for values of n between 1 and oo. For values of 



a — a,. n* — 1 . . 



<. 1 + 8 — the locus is imaginary. 



n + 3 



The point at which the locus disappears, lies at x = 



(4n+l) 

 db 



and so always between — and — , and at v — b == or v= % 



2 4 4n-fl 2 



By substitution in ( — J = we find the value of MET equal to: 



MRT = 



(q I -|a i -2a M ) (n-1, 3 (n + 3) t 3n+l) 

 ft, — ft, 16(rc-fl) 5 ~ 



This is not the point in which the curve — - = disappears. Al- 

 ready the circumstance that the latter curve disappears between 



1 1 



x = jr and ae = - , whereas in the same cases the discussed point 



1 1 



disappears between a? = — and # = — , shows this. We may, however 



4 2 



conclude, from this, that as n draws nearer to 1, the two points will 



approach each other as regards the value of x. 



Thus (cf. Contribution III These Proc. IX p. 829) x g = 0,48 for 



—- = 5.04, whereas with se = - -— nearly 0.477 is found. But 

 n—1 4(n f 3) 



14 



Proceedings Royal Acad. Amsterdam. Vol. XI. 



