1)32 



If for the sake of brevity we write .i- for (6 — bj : {v — 1\), tli 



en 



6 — 6„\" ;r" 



1 , 



a 





which with introduction of vjc and hk passes into 





(«) 



from which b^, can be computed, when a and n are known. Sub- 

 stitution yields: 



( '-] — , ri9a) 



\bk—bj a—.'vjc» 



in which a is therefore Lim x^". Let us derive from this the \'alues 



of b' and b". We find for b' : 



■n I'U 1 



b' /6-6A"-' 

 — n j 



bic—b^ \bk—b^_ 



b-b. b' 



-t- 



a—.vjc" V {^ — b,y ' v—bj' 



hence for b' 



■ b" 



bk — bo'\bk-t)o 



■ b" /6-6„Y-i {b'r /6-6„V-2 



nl I -(- — ;-^^ n (n— 1) 



W(W— l).f"-2/ b-b, 



,.ii-l 



a — A'/-" 



6-6, 



a — .Tjt" 

 6' 



+ 



+ 



{v—b,y v—b, 



b" 



_ {r-by {v-b,r v-bj 



Hence at the critical point aftei- multiplication by bk — ^o > ''^sp- 



- (bk—b.f : 



6V- = ^vk'^-' ''^''~^'^"''^ ; - b"k (6,- 6J - (n-1) (6',)^ = 

 a— A')fc« 



_ (n-1) a;k"~- {xk'- b'k ^vkY + ^^k" '' [2^-^:^—26';^ .rr + b"k jbk—b,) a^k] 

 ~~ a — xk'' 



The first equation yields at once: 



{^) 



b'k[\ + 

 hence b'k ■ (i = '^i-"+' , or 





*-A;" 



6'a 

 -(n-l)(6')tr = 



The second gives : 

 - 6'ï-(6;fc-6„)fl + 



{n~\){b'k)\vk'^—2{n—\)b'kxe+''-2,b'k ^^■"+' -f (// - \)xk'^+^- + 2.^^:"+- 



a — xk^ 



