on some early Logarithmic Tables. 505 



facts will become geDerally known apart from Hutton^s gloss*. 

 One copy of the Canon Mirificns of 1614 that I have seen, viz. 

 that in the Greenwich Observatory Library, is without the final 

 Admoniiio, in which Napier apologizes for any errors that may 

 have crept into the Tables on the ground of his health and the 

 work having been done all by himself, &c. ; and there is no pos- 

 sibility of its having been torn out, as in other copies it is printed 

 on the back of the last page of the Tables f. Mr. Mark Napier 

 mentions in a note that he has seen such a copy ; but in the text 

 he assumes Briggs to have had one with the Admonitio. There 

 are signs that Hutton had not seen this Admonitio. I have col- 

 lected together the few statements in Napier, Briggs, &c. that 

 bear upon the invention of decimal logarithms, but refrain from 

 publishing them till 1 have completed the bibliography of the 

 period, so as incidentally to reproduce as i'aw errors as possible ; 

 but the most important quotations on the matter are to be found 

 in Hutton. 



It is scarcely necessary to mention that in the note on p. 296 of 



* Since this was written, Mr. Sang, of Edinburgh, has circulated some 

 specimen pages of his proposed nine-figure logarithmic Table, in which he 

 states that " John Nepair, the illustrious inventor of logarithms, having 

 computed trigonometrical Tables according to that particular system which 

 bears his name, perceived and announced the far greater advantages to be 

 derived from the Denary system. He carefully explained the process to 

 be followed, and delegated the actual calculation to his friend Henry 

 Briggs, of the University of Oxford." This certainly conveys an incorrect 

 impression. Briggs's own words on the title-page of the Arithmetica, 

 1624(1 quote the English translation of 1631), are: — "These numbers 

 were first invented by the most excellent John Neper, Baron of Marchiston ; 

 and the same were transformed and the foundation and use of them illus- 

 trated with his approbation [ex ejusdem sententia] by Henry Briggs." 

 Elsewhere Briggs states that when he suggested the advantage of decmial 

 logarithms to Napier, the latter told him lie had already thought of them, 

 and pointed out a slight improvement (viz. that the characteristics of num- 

 bers greater than unity should be positive, instead of negative as Bi'iggs pro- 

 posed). Briggs was a distinguished mathematician and not a mere computor. 

 Decimal logarithms doubtless occurred to Napier and Briggs independ- 

 ent y; but it was the latter who developed the idea and formed the Tables; 

 and that he would have done so even it he had never visited or corresponded 

 with Napier, there is good reason to believe. The statement that Napier 

 " carefully explamed the process to be followed," is supported by no evi- 

 dence. That Napier did give Brig-gs assistance is likely enough ; and the 

 probability is increased by the fact that Briggs's method of calculation 

 differs very little from that explained in Napier's Construdio ; but such as- 

 sistance must have been given privately, if at all, as Briggs's Chilias appeared 

 in 1617, and Napier's Construdio not till 1619 ; Briggs also was quite 

 mathematician enough to have been able to investigate the method of com- 

 puting logarithms for himself after reading the Descriptio. I may men- 

 tion that Briggs, though Professor at Oxford towards the close of his life, 

 was educated at Cambridge. 



t Of four other copies of the Canon Mirificus of 1614 that I have seen, 

 three have the Admonitio, and the other has the last page torn out. 



