9;u 



(ji)j. _ /; j2 . j^j^ ^j.^ which we shall call /3 for a inoment, we find 

 further : 



which becomes for %: 



^k — ^ it 



from- which immediately follows b't = (?, ie. the value given b} 

 (24). And with i-egard to h"k, from 



b' /^^-^« Y~^ — _ ^ '^ ^~* 



- .r«-^ — 



+ 





follows after a second differentiation, and substitution of vz=V]c and 

 b^=hk (see also above): 



- b"k {bk - ^oJ - 0* — 1) ^V = 



+ .r-t"-! [2 .vk' — 2 6't .VI,' + 6";t (6^ — ^) -c/cj 



(n-l).rA;«--('^V-6Wr + 



(«-l)(.ri-/?)+2.ri. 



yiekling, when i? is written for b'k- 



- ^>"/.- (/>/. - ^) f 1 H- -^%1 == ('' - 1) i^' + .'^ 



or - b"k {bk — b,) Xk =- ^ (-rt — /?) • (/^ + ^ ) ■^'i-- 



Now according to (30"^ (?i+l) (.r^— ,'?) = (1— e^^^-) + (.t^— /?)=! — ^; 



hence 



- h"k {bk -b„) = ^{l^^) = b'k (1 - b'k) , 



and now (24) is again satisfied. 



After having thus carried out these control calculations, we return 



to equation (30). 



The quantity b'^ cannot be computed from the above equation 



{a) for b', as the latter gives = for t\, b,. No more could b" , 



be calculated from the general equation for b" . But since in the 



neighbourhood of v^.b^: 



b—b " 



evidently b', = Lim = .?■„, and hence according to (306) = \/a. 



When we represent {b—b^) : {bk—bo) by é, 



b'J'-' = 



^ 



a;k"{^k—^) 



r.Ji-1 _ 



^ _ b\^\ 

 Ö Ö ) 



