Bremiher — Errors Affecting Logarithmic Computations. 451 



Thus we compute c as a first approximation to li; then on put- 

 ting c-Ydc = h we shall have dc from the equaiion 



dVcdc = Vc or dc=J^» 



dV 



in which the value just found is to be substituted in place of a. 

 Thus, since 



V 



6^1c 



dF'c = -^l.e~2»'^', 



we shall have 





and 



A = 2, /^+^^i- (1-%P^ ) [15, 



Then hy is the probable error ; but the second term either van- 

 ishes for very large values of v or is negligible. 



The mean error, defined in § 7, can in general be computed in 

 the same way as the probable error was computeu in § 9. For 

 we may start from the equation [8] which expresses the proba- 

 bility of the error -7^, 



1 I 



(2/i) a^a^ a 



— TC 



and substitute for (p^ (z) the expressions involving 



sines, and substitute for the prodr.ct of sines the function of the 

 exponents. Then we shall have 



180 n 



* In the notation of the author, dV here denotes the derivative of V with respect to 

 0. [E. F. C.J 



