Memoirs of John Napier of Merchiston. 285 



as it may, Briggs skilfully constructed, on this new plan, excel- 

 lent tables, the most exact, the most abundant in decunals that 

 have been published even to this day. It is a work to be esteemed, 

 not merely for its patience of labour, but for the skilful in- 

 genuity displayed in numerical approximations. On the strength 

 of this amelioration, however, some have occasionally assigned to 

 Briggs a share in the invention itself. Truly this is to confound 

 two very different merits, genius and labour. But an ardent 

 reverence for discoveries, however, is not a common faculty, 

 and is too often replaced by another less honourable, and 

 that is, the secret inclination of ordinary minds to lower the 

 exalted. 



Independently of the merit of the invention, Napier's tables 

 are a prodigy of laborious patience. When we reflect upon the 

 time and toil it must have cost to calculate all those numbers, 

 we shudder at the chances there were of his being arrested in 

 the progress of realizing his idea, and of its dying with him. It 

 has been said, and Delambre repeats the remark, that the 

 last figures of his numbers are inaccurate ; this is a truth, but 

 it would have been a truth of more value to have ascertained 

 whether the inaccuracy resulted from the method, or from some 

 error of calculation in its applications. This I have done, and 

 thereby have detected that there is in fact a slight error of this 

 kind, a very slight error, in the last term of the second progres- 

 sion which he forms preparatory to the calculation of his table. 

 Now all the subsequent steps are deduced from that, which 

 infuses those slight errors that have been remarked. I corrected 

 the error ; and then, u^ing his method, but abridging the opera- 

 tions by our more rapid processes of development, calculated 

 the logarithm of 5000000, which is the last in Napier'*s table, 

 and consequently that upon which all the errors accumulate ; I 

 found for its value 6931471.808942, whereas by the modern 

 series, it ought to be 6931471.805599; thus the difference 

 (who tells the story himself), casts away all his own calculations made be- 

 fore he had conversed with the inventor, and adopted Napier's. This in 

 every sense gives to Napier the right of having himself deduced the common 

 logarithms from the parent system. Dr Charles Hutton*s extraordinary 

 view of the point in question, as well as his general exposition, so unjust to 

 Napier, of the original invention of logarithms, will be found very thoroughly 

 refuted in the memoirs, p. 383. et ir^fra. — Translator. 



