Bremiher — Errors Affecting Logarithmic Computations. 459 



Since m can receive all values from to s, the extreme limits 



are — 1 and + 1. By substituting these values in IVm we shall 



havo 



f 7n3 — (m— l-}-£)3-f(m— 1)3— .... 



6£(1 — E) 



■'I ^ — (w— l)3+(r/i— 1— £)3 



But in this formula several terms in which the quantities are 

 negative are to be omitted since m assumes only those values 

 which lie between and 1 ; and thus it is changed into 





W.m = ^^^^;^]m^-im-l+er 



—{m—ef f 



in which m and « receive all values between and 1, and all 

 powers of negative quantities are necessarily excluded. So 

 1 — 2 Wm will be the probability that tlie sum [X—s)f^-ifEf^-\-f^ 

 lies between the limits ±(1 — m). Below are the values which 

 1 — 2 Wm takes for each decimal division of the values of m 

 and « indicated in the table; 



m (2— 2/n)x «=0,1 £=0,2 £=03 e=0,4 c=0,5 



0,1 0,9 0,996 0,993 0,993 0,998 0,998 



There is no need to extend the table further, since for c = 0.6, 

 O.T, etc., 1 — 2 Wm takes on the same values that it has for 

 e =0.4, e=0.3, etc. If we let « = or 1 we shall have 

 Wm-V^ ni^ and so if 



{2—2m)r = 0,1 then 1 —2 Wm = 0,190 



