Bremlker — Errors Affecting Logarithmic Computations. 4:^jo 



Then according to the formulas [11], [12] and [13] the ap- 

 proximate values y, F", V are easily derived which are com- 

 pared in the following table with the corresponding values 1 — 

 2 W computed according to the rigorous formulas [6] of § 5. 

 These are indeed the same as those which were shown in § 6 

 giving the number of diflerences between and 1, and 1 and 2, 

 etc., for cy with regard to integers only. 



It is needless to continue this fartlicr; for the value-s which 

 1 — 2 \V and Y receive evidently agree closely and this happens 



because the quantity y which we have assumed equal to 20 is 



sufficiently large. For values i^ = 2 or v =3 they would 



a^ree less exactlv. 



Accordii:g to formula [15] of § 10, the probable error is 



ny = 2y6fj^/ ^——-—=^—{l-%p^) 

 V 6 lo]/ 6k(53 



or, if we substitute for y, 6, 6\ and y the same values that 

 they had above, and 0.^76030 for p 



Ax =0, 87076 -h0,00554 =0.87630. 

 The corresponding value of m is 



m = — 2- = 9,12370 



If this value of m is substituted in Wm its value (according to 

 § 7) ought to be ^4:- ^7 making the substitution we actually 

 obtain TVVn = 0.25002, which may be considered perfect agree- 

 ment. 



