ox MATHEMATICAL TABLES, '49 



can bo readily expressed as a decimal (to seven places) of a day, and vice 

 versa by means of it. 



Tlic following are tables described in § -1 : — 



Tables for the conversion of Time into Space, and vice versa. — -Cross- 

 well, 1791, T. XIII.; BowDixcir, 1802, T. XII.; Ilios, 1809, T. XYI.- 

 I'u^iiiGAN, 1821, T. XIII. ; Stansbuky, 1822, T. I. ; Pearson, 1824 [T. I.] ; 

 Galbraith, 1827, T. XII. (Introd.); Warnstorff's Schumacher, 1845 TT II- 

 KiinLER, 1848 [T. I.] ; Gordon, 1849, T. XI. ; Domke, 1852, T. XLVll. and 

 XLVIII. ; Bremiker, 1852, T. II. ; Thomson, 1852, T. I. ; Bremiker's Veg\, 

 1857, T. III. ; HouEL, 1858, T. I. ; Peters, 1871 [T. II.]. 



Tables to express Degrees, Minutes, S,-c. as decimals of a rir/M angle, 

 or Hours, Minnies cj-c. as decimals of a day, and vice versa, 6,-c. — IIobert 

 and Ideler, 1799, C. I.-IV., D. I.-III., E. I.-IV., F. ; Galbraith, 1 827, 

 T. XI, (Introd.); Hantschl, 1827, T. XII.; Beverle\- (1833?), T. VI, 

 (p. 127) ; KiiHLER, 1848, T. IX. ; Peters, 1871 [T, I.], 



Art. 13. Tables of {Briygian) Logarithms of Numbers. 

 The facts relating to the invention of Briggian (or decimal) logarithms arc 

 as follows: — In 1614 Napier published his 'Canon ilirificus ' (see § 3, 

 art. 17), which contained the first announcement of the invention of logarithms, 

 and also a table of logarithmic sines, calculated so as to be very similar to what 

 are now called hyperbolic logarithms. HenrtBriggs, then Professor of Geo- 

 metry at Gresham College, London, and afterwards Savilian Professor of Geo- 

 metry at Oxford, admired this work so mucli that he resolved to visit Napier. 

 " Naper, lord of Markinston, hath set my head and hands at work with his 

 new and admirable logarithms. I hope to see him this summer, if it please 

 God ; for I never saw a book which pleased me better, and made me more 

 wonder," This he says in a letter to Usher (Usher's ' Letters,' p. 3G, accord- 

 ing to Ward). Briggs accordingly visited Napier, and stayed with him a 

 whole month (in 1615), He brought with him some calculations he had 

 made, and suggested to Napier the advantages that would result from the choice 

 of 10 as a base, having publicly explained them previously in his lectures 

 at Gresham College, and written to Napier on tlie subject. Napier said that 

 he had already thought of the change, and pointed out a slight improvement, 

 viz. that the characteristics of numbers greater than unity should be posi- 

 tive,^ and not negative, as Briggs suggested. Briggs visited Napier again in 

 1016, and shoAved him the work he had accompHshcd, and, as he himself says, 

 would have gladly paid a third visit in 1617, had Napier's life been spared 

 (he died April 4, 1617). The work alluded to is Briggs's ' Logarithmorum 

 Chilias Prima,' which was published (privately, we believe) in 1617, after 

 Napier's death, as in the short preface he states that why his logarithms are dif- 

 ferent from those introduced by Napier " spcrandum, ejus librum posthumum, 

 abunde nobis propediem satisfacturum." The liber postlmmus was Napier's 

 ' Constructio,' which appeared in 1619, edited by his son (see § 3, art. 17). 

 Briggs continued to labour assiduously, and in 1624 published his 'Arith- 

 nietica Logarithmica,' giving the logarithms of the numbers from 1 to 

 20,000, and from 90,000 to 100,000 (and in some copies to 101,000), to 14 

 places. 



To the above facts we must add that Napier made a remark, both in Wriglit's 

 translation of the ' Uescriptio ' (1010) and in the ' llabdologia' (1617), to (lie 

 effect that lie intended in a second edition to make an alteration equivalent 

 to taking the logarithm of 10 equal to unity. 



We have thought it proper to give the circumstances attending the inveu- 

 1873. ]5 



