Bremil-er — Errors Affecting Logdriilimic Compulations. 4C0 

 B/ the same method, 



[t—Uj^)'^ , {t—u-if , etc., 



in which t docs not take vahies less than Wj, u^, etc., become 



— (<— mJ^ , —{t — u-i)^ i etc. 



y y 



The siiin of these can be expressed in the form 



V 



Similarly the powers 



{t—u^—u^)^~ , {t — u^—u^)^~ .... {t—u^_^ — u^) ^ 



in which i has as its least values 



can be expressed in the form 



Thus the sum of all the coefScients of the powers from 2^ to 

 2^ will be 



Then, substituting according to the same plan that was used in 

 ^ 4 and dividing by tlij sum of all the coefficients or (which is 

 the same thing) by the number of all the combinations, we have 



v\a^a^a^....a^ \ ^^"^ ~^{m-s^a)^ -^2{m—s^af -....( [G] 



which is the probability that the error is between the limits 



