57. 



SUPPLEMENTARY NOTE ON THE VALUES OF THE NAPIERIAN LOGARITHMS 

 OF 2, 3, 5, 7, AND 10, AND OF THE MODULUS OF COMMON LOGARITHMS. 



[From the Proceedings of the Royal Society. Vol. XLII. (1886).] 



IN Vol. xxvn. of the Proceedings of the Royal Society, pp. 88 94, I 

 have given the values of the logarithms referred to, and of the Modulus, all 

 carried to 260 places of decimals. 



These logarithms were derived from the five quantities a, b, c, d, e, 

 which were calculated independently, where 



10 , , 25 81 , . 50 . 126 



= log~, d = \og-, and e- 



-, ~, -, 



and a complete test of the accuracy of these latter calculations is afforded 

 by the equation of condition 



In the actual case the values found for a, b, c, d, e satisfied this 

 equation to 263 places of decimals. 



Although this proved that the values of the logarithms found in the 

 above paper had been determined with a greater degree of accuracy than 

 was there claimed for them, yet I was not entirely satisfied with the 

 result, since the calculation of the fundamental quantities had been carried 

 to 269 places of decimals, and therefore the above-cited equation of con- 

 dition shewed that some errors, which I had not succeeded in tracing, had 

 crept into the calculations so as to vitiate the results beyond the 263rd 



place of decimals. 



592 



