24 On the Values of Napierian Logarithms, fyc. [Jan. 13, 



putations 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— 26 + c = d+2e, by which the accu- 

 racy 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 = 4 2. 



Also the corresponding parts of the logarithms which are derived 

 from the above are — 



losr 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 loga- 

 rithms, will be found by changing the sign of this and multiplying by 

 M 2 , the approximate value of which is 



0-18861 16970 1161 



Hence this correction is 



(264) 6 35513 15874 7 



And finally the corrected value of the Modulus is 



