57] ON THE VALUES OF THE NAPIERIAN LOGARITHMS, ETC. 469 



I have now succeeded in tracing and correcting the errors which vitiated 

 the later decimals in my former calculations, and have extended the com- 

 putations to a few more decimal places. The computations of the fundamental 

 logarithms a, b, c, d, e have now been carried to 276 decimal places, of 

 which only the last two or three are uncertain. 



The equation of condition, a 2b + c = d + 2e, by which the accuracy of 

 all this work is tested, is now satisfied to 274 places of decimals. 



The parts of the several logarithms concerned which immediately follow 

 the first 260 decimal places as already given in my paper in the Proceedings, 

 are as follows : 



a 05700 33668 72127 8 



b 67972 72775 92889 4 



c 42038 01732 39184 3 



d 08865 93150 99834 1 



e 01463 48349 12851 7 



Whence a-2b+ c = 11792 89849 25533 3 



and d + 2e = 11792 89849 25537 5 



Difference = 42 



Also the corresponding parts of the logarithms which are derived from 

 the above are 



log 2 30070 95326 36668 7 



log 3 68975 60690 10659 1 



log 5 13580 59722 56777 3 



log 7 74183 10810 25196 7 



Whence log 10 43651 55048 93446 



And the correction to the value of log 10 which was formerly employed 

 in finding the Modulus is 



-(263) 33 69426 01554 



where the number within brackets denotes the number of cyphers which 

 precede the first significant figure. 



The corresponding correction of M, the Modulus of common logarithms, 

 will be found by changing the sign of this and multiplying by M\ the 

 approximate value of which is 



0-18861 16970 1161 



