ON MATHEMATICAL TABLES. 51 



computer ; and in these terms Mr. Sang has also recently spoken of the latter. 

 Mr. Napier attributes Huttou's assertions to national jealousy (!) ; and it will 

 be a matter of regret if any other writers should follow his example in at- 

 tempting to glorify Napier by depreciating Briggs. The words of the latter, 

 in the 1031 translation (and amplification, see below) of his ' Arithmetica ' of 

 1G24, are : — " These numbers were first invented by the most excellent John 

 Neper, Baron of Marchiston ; and the same were transformed, and the founda- 

 tion and use of them illustrated with his approbation [ex ejusdem sententia] 

 by Henry Briggs." No doubt the invention of decimal logarithms occurred 

 to both Napier and Briggs independently ; but the latter not only first an- 

 nounced the advantage of the change, but actually completed tables of the 

 new logarithms. Thus, as regards the idea of the change, Napier and 

 Briggs divide the honour equally ; while, on the principle that " great points 

 belong to those who make great points of them," nearly all belongs to Briggs. 



On the subject of Briggs and the invention of logarithms, see the careful 

 and impartial life of Briggs in Ward's ' Lives of the Professors of Gresham 

 College,' London, 1740, pp. 120-129, and also ' Vitfe quorundam eruditis- 

 simorum et illustrium virorum' &c., scriptore Thoma Smitho, Londini, 1707 

 (Vita Henrici Briggii), as well as ' Memoirs of John Napier of Merchiston,' by 

 Mr. Mark Napier, Edinburgh, 1839, and the same author's ' Naperi libri qui 

 supersunt' (see § 3, art. 17). See also Hutton's account (reference given above) 

 and Phil. Mag., October and December (Supplementary No.) 1872, and May 

 1873. It is proper to add that the date we have given for Briggs's first visit 

 to Napier, viz. 161.5, is diflferent from that assumed by other writers, viz. 1616; 

 ■\ve have, however, little doubt that the former is correct, as it in all respects 

 {fgrees with the facts. The reason that Ward, Hutton, &c. assign Briggs's 

 first visit to 1616, and the publication of the ' Chilias' to 1618, is, no doubt, 

 due to the fact that they supposed Napier to have died in 1618 ; but Mr. Mark 

 Napier has shown that the true date is 1617 ; and this brings all the facts into 

 agreement (see Phil. Mag. December 1872, Supp.). 



Like Napier, Briggs was not very particular about the spelling of his name. 

 In Wright's translation it appears as Brigs on the titlepage, Brigges on the 

 first page of the preface, and Briggs in the eulogistic verses. 



Although we have spoken of logarithms to the base 10 &c., we needscarcely 

 observe that, although exponents and even fractional exponents were in a sort 

 of way introduced by Stevinus, neither Napier nor Briggs, nor any one tiU 

 long after, had any idea of connecting logarithms with exponents. 



To return to the original calculation of the logarithms of numbers. Briggs, 

 ns has been stated, published the logarithms of the numbers from 1 to 

 20,000 and from 90,000 to 100,000 to fourteen places, in his ' Arithmetica.' 

 There was thus left a gap from 20,000 to 90,000, which was filled up by 

 Adrian Vlacq (although Briggs had in the mean time nearly completed the 

 necessary calculations ; see Phil. Mag. May 1873), who published at Gouda, 

 in li)28, a table containing the logarithms of the numbers from unity to 

 100,000 to 10 places of decimals. Having calculated 70,000 logarithms and 

 copied only 30,000, Vlacq would have been quite entitled to have called his 

 a new work. He designates it, however, only a second edition of Briggs, 

 the title running, "Arithmetica logarithmica sive logarithmorum chiliadca 



centum, pro numeris naturali serie crescentibus ab TJnitate ad 100000 



Editio socuuda aucta per Adrianum Vlacq, Goudanum Gouda), excudebat 



Petrus Eammasenius. 1628." This table of Vlacq's was published, with an 

 English explanation prefixed, in London in 1631, under the title, " Logarith- 

 micall Arithmctike, or Tables of Logaritbmes for absolute numbers, from au 



£ 2 



