72 KEPORT — 1873. 



the logarithms therefore decrease as the sines increase. A hrief explanation 

 of the principle of Napier's own method is given by Professor Wackerbarth 

 in vol. xxxi. p. 263 (1871) of the 'Monthly Notices of the Royal Astro- 

 nomical Society.' The anthor of that communication there points out that 

 the description in most elementary books of Napierian logarithms, as loga- 

 rithms to the base e, is incorrect ; but this criticism appears to us irrelevant, 

 as by calling certain logarithms Napierian it is not asserted that they arc 

 used at present in the exact form in whicli they were presented by Napier. 

 A glance at the formula written above shows that all the essential features 

 of logarithms to the base e arc contained in Napier's system, and that there 

 is no impropriety in calling the former by his name. De Morgan says that 

 " Delambre proposed to call them [Napier's logarithmsj Napierian logarithms, 

 and to restrict the term hj-pcrbolic to the modern or e logarithms ; but 

 custom has refused," — and no doubt very properly, as, except in mathematical 

 histories &e., there is no occasion to distinguish the two systems from one 

 another. For our own part, we should much prefer to see natural or ' 

 hyperbolic and common logarithms universally called Napierian uni Brigr/ian, 

 after the two great founders of logarithmic tables. 



A translation of Napier's ' Canon Mirificus ' was made by Edward "Wright 

 (well known in connexion with the history of navigation), and, after his death, 

 published by his son at London in 1616, under the title " A Description of 

 the admirable Table of Logarithmes, &c." (12mo). Ou account of the rarity 

 of this work and the ' Constructio,' the full titles of both are given in § 5. 

 There is a short " Preface to the Reader " by Briggs, and a description of a 

 triangular diagram invented by Wright for finding the proportional parts. 

 Napier's table, however, is printed to one figure less than in the ' Canon 

 Mirificus ' throughout. The edition was revised by Napier himself. On 

 Wright, see Introduction to Button's ' Mathematical Tables.' The ' Canon 

 Mirificus ' was also rej)rinted by Maseres in the sixth volume of the ' Scrip- 

 tores Logarithmici ' (1791-1807); and in 1857 Mr. Filipowski published 

 at Edinburgh a translation of the same work (full title given in § 5 ; the tone 

 of the Introduction renders any comment on it unnecessary). 



Both the ' Deseriptio ' (the ' Canon Mirificus ') and the ' Constructio ' 

 were reprinted by Bartholomew Vincent at Lyons in 1620 (who thus first 

 published logarithms on the Continent), the title of the former appearing on 

 the titlepage as " Logarithmorum Canonis Deseriptio, sen Arithmeticarum 

 supputationura mirabilis abbreviatio. Ejusquc ususin utraque Trigonometria 

 ut etiam in omni Logistica Mathematica, amplissimi, facillimi &, expeditissimi 

 cxplicatio. Authore ac Inventore Joanne Nepero, Barone Merchistonii, &c., 

 Scoto. [Printer's device with word Vincenti.'] Lugduni. Apud Barth. Vin- 

 centium, M.DC.XX. Cum privilegio Cffisar. Majest. & Christ. Galliarum 

 Regis." The full title of Napier's original edition of 1614 is given in § 5 ; 

 and it will be seen that it is very difi'erent from that written above. Yery 

 many writers (including Montucla) give the title of Vincent's reprint as that 

 of the original work. There is an imperfect copy of Vincent's reprint, 

 containiug only the * Deseriptio ' (the * Constructio ' having been torn out), 

 in the British Museum ; but the Royal Society has a perfect copy. Wright's 

 translation of 1616 is in the British Museum. 



On the accuracy of Napier's Canon see Delambre, * Astron. Mod.,' t. i. 

 p. .501. Mr. Mark Napier's 'Memoirs of John Napier' gives nearly all that 

 is known with regard to Napier's life, MSS., &c. ; but it is told in a verbose 

 and diff'use manner, and written in a partisan spirit as regards Briggs. 



A manuscript on arithmetic and algebra, written by Napier and left by 



