Brcmilccr — Errors Affeding Logarithmic Computations. 461 



S . ' 



Then, -r being put equal to e, the error by which a is af- 



A 

 fected will bo 



- ^{i^-')f 1-^-^/2] 



But sincG 



cZ(log^(a) )=I^S^m da = /Ida * 

 cp{a) 



the error of the lo;^arithm from which a is found by means of 

 the table may be written 



Again, by examination of the various values of e it api^cars 



that the value & = i holds ai]ii0;3t the mean place. Therefore 

 in the change from -any partieuijr logarithm to the number or to 

 the arc the error of the Ivr'ariiLm may be assumed as 



Lastly, if it is ncGC-sarv to ra^s from the loirarithm of one 

 trigonometric function g) [a) to the logarithm of smother trig- 

 onometric function q.' [a)hj the aid of the tables, the error at- 

 taching to log cp" [a) is 



^n ,/ .-. d\o^ cD'{a) ,. , - 

 •^'- "^ '■' cMog q^{a) ^' 



and it does not matter whether a is first found from log9^(^) 

 and then from this log:<?>' [a) , or v,diether the transition is made 

 directly from log q>{(i) to log <p' {a) without reference to the 

 argument a. 



♦According to the notation of the author, d<p (a) t^ei'© denotes the derivative of 

 (p(a) with respect to a.—[E. F. C] 



