Bremilcer — Errors Affecting Logarithmic Computations. 437 

 Thus we must put 



r ^ 



in order that everything may be included in the quantity 'p, 

 Furthermore, if we put for brevity 



^(^ +«i-f«8+ .... + ay) — m 



and instead oiu^, u^, .... w^, write the corfespondiug values 

 2na:i+l, 2na.^-\-l, .... 2na^ +1 ^e have 



and in general 



t—s u = 2nlm—s a) 



in which i- a denotes the sum of// cleraentfe in the series 



<Xi, tTg, (^3, .... <X^ 



By these substitutions we have 



(2»)""^^m— 1 



-2{m—s^af -^+2(771— Sg^)^ —....{ 



(K-i)! 

 as the coefficient of the pov/ex 



1 2m— {a j^ H-o's + . . . . Q^^) | r. 



a: 



this then is the number that indicates how many times among 

 the total number of combinations, 



{2n)^aj^aza^ .... a^ , 



that one is found whose sum is 



^2m-ia,-\-a^+....-\-cx^)jr 



