284 M. Blot's Abstract of Mr Napier's 



testible when we consider the number of years which the 

 calculation of those tables must of necessity have occupied. 

 Their whole construction is founded upon the adoption of that 

 notation, and thus they attest the anterior usage, probably much 

 anterior to Pitiscus, who had not employed it in his former edi- 

 tion in 1599. 



The system of logarithms adopted by Napier was the most 

 simple and the most commodious which could then be conceived 

 for the formation of the successive terms of the geometrical 

 progression. The tables which he had constructed already 

 offered, in place of the multiplications and divisions, those im- 

 mense advantages of simplification which we have explained 

 above. Kepler adopted them, and published a copy of them 

 with his Rudolphine tables, of which, as we have observed, he 

 transformed the plan in order to adapt them to the usage of 

 logarithms. But that invention once found, it was easy to 

 see that the particular logarithmic system selected by Napier 

 was not that which adapted itself the most perfectly to our deci- 

 mal mode of numeration. Professer Briggs of Oxford, a cotem- 

 porary of Napier's, conceived a modification which afforded this 

 advantage, and which is the same we now use. It appears that 

 he received that idea from Napier himself, to converse with 

 whom he made several expeditions into Scotland. At the end 

 of Napier's posthumous work, there is an appendix, in which we 

 find the indication of the method employed by Briggs.-)- Be this 



• Mr Napier shews (p. 364.), that the subject of his biography was busy 

 with the invention of logarithms, and consequently his use of decimal frac- 

 tions* at least as early as 1594. See also pp, 451, 452, 454. for the history of 

 decimal fractions, as first operated with, and written in the present form of 

 notation, by Napier. — Translator. 



-f- M. Biot says, " Briggs, &c. en imagina un autre,'* &c., but immediately 

 adds, " il parait qu'il regut cette idee de Napier meme," &c. The fact is more 

 fully explained in the memoirs, and appears incontestibly to be this. Briggs, 

 whenever he had studied Napier's invention, saw the practical advantage of 

 a modification of the system to suit, for practical purposes, the decimal scale 

 in use ; and he commenced his calculations to efl^ect that advantage. But he 

 journeyed into Scotland (a very interesting fact) to consult the inventor him- 

 self upon the subject. There he learnt that Napier had long previously 

 conceived the same principle of modification, and intended to realize it by a 

 method which, when he shewed it to Briggs, the latter instantly acknowledg- 

 ed was superior to his own method of that modification. Therefore Briggs 



