Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/192

180 N A P I E K [OF MERCHISTON. published the promised account of the method of construc tion of the canon. This work was, however, issued by Robert Napier, his second son by his second marriage, in 1619. 1 The Construct consists of a preface of two pages, followed by sixty-seven pages of text. In the preface Robert Napier says that he has been assured from undoubted authority that the new invention is much thought of by the ablest mathematicians, and that nothing would delight them more than the publication of the mode of construc tion of the canon. He therefore issues the work to satisfy their desires, although, he states, it is manifest that it would have seen the light in a far more perfect state if his father could have put the finishing touches to it ; and he mentions that, in the opinion of the best judges, his father possessed, among other most excellent gifts, in the highest degree the power of explaining the most difficult matters by a certain and easy method in the fewest possible words. It is important to notice that in the Constructio log arithms are called artificial numbers; and Robert Napier states that the work was composed several years (aliquot annos) before Napier had invented the name logarithm. The Constructio therefore may have been written a good many years previous to the publication of the Descriptio in 1614. 2 The Canon Mirificus, on its appearance in 1614, at once attracted the attention of perhaps the two most eminent English mathematicians then living Edward Wright and Henry Briggs. The former, as we have seen, translated the work into English, but died in 1615 before he could publish his translation. The latter was concerned with Napier in the change of the logarithms from those originally invented to decimal or common logarithms, and it is to him that the original calculation of the logarithmic tables now in use is mainly due (see BRIGGS). He died on January 26, 1631, aged about seventy-four years, so that at the time of the publication of the Canon Mirificus he was about fifty-seven years of age. In a letter to Archbishop Ussher, dated Gresham House, March 10, 1615, Briggs wrote, " Napper, lord of Markinston, hath set my head and hands a work with his new and admirable logarithms. I hope to see him this summer, if it please God, for I never saw book which pleased me better, or made me more wonder. 3 I purpose to discourse with him 1 The full title was Mirifici logarithmorum canonis constructio; Et eorv.m ad naturales ipsorum numeros habitudines; und cum Appen- dice, de alia eaque priestantiore Logarithmorum specie condendd. Quibus accessere Propositiones ad trianyula sphserica faciliore calculo resolvenda: Und cum Annotationibus aliquot doctissimi D, Ilenrici Briggii, in eas & memoratam appendicem. Authore & Invcntore loanne Nepero, Barone Merchislonii, &c. Scoto. Edinburgi, Excude- bat Andreas Hart, Anno Domini 1619. There is also preceding this title-page an ornamental title-page, similar to that of the Canon Miri ficus of 1614; the words are different, however, and run Mirifici logarithmorum canonis dcscriptio . . . Accesserunt Opera Posthuma: Primo, Mirifici ijisius canonis constructio, & Logarithmorum ad naturales ipsorum numeros habitudines. Secundd, Appendix de alia, eaque pr&stantiore Logarithmorum specie construenda. Tertio, Pro positiones qusedam eminentissimas, ad Triangula sphs&rica mira facili tate resohenda It would thus appear that the Canonis Descriptio and the Canonis Constructio were issued together in 1619, or that at all events this was the intention. 2 Both the Descriptio and Constructio were reprinted by Bartholomew Vincent at Lyons in 1620, and issued together under the title Logarith morum Canonis JJcscriptio, sen Arithmeticarum supputationum mirabilis abbrematio. Ejusque usus in utraque Trigonometria ut etiam in omni Logistica Mathematica, amplissimi, facillimi & expeditissimi explicatio. Authore ac Inventore Joanne Nepero, Earone Merchistonii, <Lc. Scoto. Lugduni. ... It will be seen that the title of the translation is very different from that of Napier s work of 1614; very many writers have, however, erroneously given it as the title of Napier s original publication. 3 Dr Thomas Smith thus describes the ardour with which Briggs studied the Canon Mirificus : " Hune in dcliciis habuit, in sinu, in rnanibus, in pectore gestavit, oculisque avidissimis, et mente attentis- sima, iterum iterumque perlegit, ..." Vitx quorundam cruditissi- morum et illustrmm virorum (London, 1707). concerning eclipses, for what is there which we may not hope for at his hands" ; and he also states " that he was wholly taken up and employed about the noble invention of logarithm?, lately discovered." In the summer of 1615 he went to Merchiston and stayed with Napier a whole month; he repeated his visit in 1616, and, as he states, he " would have been glad to make him a third visit, if it had pleased God to spare him so long." William Lilly, the astrologer, in his Life and Times, 1721, gives the fol lowing account of the meeting between Napier and Briggs on the occasion of the first visit : " I will acquaint you with one memorable story, related unto me by Mr John Man 1 , an excellent mathematician and geometrician, whom I conceive you remember: he was servant to King James and Charles I. At first, when the Lord Napier, or Marchiston, first made publick his logarithms, Mr Briggs, then reader of the Astro nomy lecture at Gresham College in London, was so surprised with admiration of them that lie could have no quietness in himself, until he had seen that noble person the Lord Marchiston whose only invention they were : he acquaints John Marr herewith, who went into Scotland before Mr Briggs, purposely to be there when these two so learned persons should meet. Mr Briggs appoints a certain day when to meet at Edinburgh : but failing thereof, the Lord Napier was doubtful he would, not come. It happened one clay as John Marr and the Lord Napier were speaking of Mr Briggs ; Ah, John, saith Marchiston, Mr Briggs will not now come ; at the very instant one knocks at the gate ; John Marr basted down and it proved Mr Briggs to his great contentment. He brings Mr Briggs up into my Lord s chamber, where almost one quarter of an hour was spent, each beholding the other almost with admira tion, before one word was spoke. At last Mr Briggs began My Lord, I have undertaken tins long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help unto Astronomy, viz. , the Logarithms ; but my Lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy. He was nobly entertained by the Lord Napier, and every summer after that, during the Lord s being alive, this venerable man, Mr Briggs went purposely into Scotland to visit him." With respect to the change of the logarithms to decimal logarithms, the concluding paragraph of the "Admonitio" which appears on the last page of the Canon of 1614 is " Verum si huius inventi usum eruditis gratum fore intel- lexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia, limatior tandem et accuratior, quam unius opera fieri potuit, in lucem prodeat. Nihil in ortu perfectum." In some copies, however, this "Admonitio" is absent. In Wright s translation of 1616 Napier has added the sentence "But because the addition and subtraction of these former numbers may seeme somewhat painfull, I intend (if it shall please God) in a second Edition, to set out such Logarithmes as shall make those numbers above written to fall upon decimal numbers, such as 100,000,000, 200,000,000, 300,000,000, &c., which are easie to be added or abated to or from any other number" (p. 19); and in the dedication to the Eabdologia (1617) he wrote " Quorum quidem Logarithmorum speciem aliam multo prasstan- tiorem nunc etiam invenimus, & creandi methodum, una cum eorum usu (si Deus longiorem vitae & valetudinis usuram concesserit) evulgare statuimus; ipsam autem novi canonis supputationem, ob infirmam corporis nostri valetudinem, viris in hoc studii genere versatis relin- quimus : imprimis vero doctissimo viro D. Henrico Briggio Londini publico Geometriee Professori, et amico mihi longe charissimo." Briggs published in 1617, after Napier s death, his Logarithmorum Chilian Prima, containing the decimal logarithms of the first thousand numbers to 14 places of decimals. This is the first table of common (or Briggian) logarithms calculated or published. In 1624 he published his Arithmetica Loyarithmica, containing the logarithms of the first 20,000 numbers and of the numbers from 90,000 to 100,000 to 14 places of decimals. In the short preface