398 APPENDIX VI. 



Here a = B and q = l-0;y"; hence, 



C = ^ (I-QF'"- 1) or = ^ (1 - l-Oj^""-) 

 l-OiJ'"-! ' 1 - l-Ojy- • 



Formula IV.-C = '' i^-^P"-^ ) 



This formula is obtained by introducing iit = 1 into Formula III. 



Formula F.-CV = ^ (l-QiJ'""-!) 

 l-0iJ'""(l-0p'«-l) 



1-0^/" ^ l-O/-'- ^ • • • ^ i-o^.- 

 7? 1 



*^o — 1 , which, alter reduction, leads to 



1 - ^ 



Formula V. 



Formula VI.~C, = 'lM^!:zi) is obtained by introducing 

 vi = 1 into Formula V. 



Formula VII.— C, = 1^. 



^<j = 1-7.- +T-r>-> + . • . + -,-,s— Si- Here « — ^ ^, and ^7 = --:- • 



r 



hence 6' = ^^ = Jl 



1 - _L -^p 



Formula VIII.— C,, = ^ 



l-Oj)"-! 



c =^-+^- + ... + JL 



Here a = ^ J' ; </ = —p.— and u = 00 ; hence , 



