BremiJcer — Errors Affecting Logarithmic Cornputations, 453 



and, if the factor 2 bo inserted, the integrals maj have zero £3 

 lower limit. 



But if we multiply bv 2cr and integrate with respect to c 

 between the limits and s we shall have the mean error, or the 

 aggregate of all the errors regardless of sign divided hj the total 

 number of them. 



Bj partial integration according to the formula 



6j ^l 





all parts of the integral can be reduced to the form 



j: 



1 



from which we obtain 



""""lAk (^+2^1 t^ 



3^.2 



if the terms are omitted which have ^ ~'275^^^ ^ factor. And 

 this is the mean error. 



§ 11. 



In formula [6] of § 5 the probability of an error between the 

 limits ±[s — '^m)r was found to equal 1 — 2 W; and in § 



this is shown to equal Vq for limits ±cr * So if ^ be taken 

 equal to ^ — 2 m, 1 — 2 W and V must necessarily express t!,e 

 same pn/oiibility. But V is only an approximation, since, in de- 

 riving it, y was assumed very large. In order that this agree- 

 ment may be subjected to some numerical test, let us employ tho 



