Napierian, that is to say, logarithms to the base e where e = 2-7182818 . . . ; but they are closely related to this system, the connexion being expressed by the equation
log Nap. ?i = l 0,000, 000 log, (10,000,000) - 10,000,000 log, n ;
or log Nap. ;i = 10 7 log e f ) .
A translation of the Canon Mirificus into English was made by Edward Wright, and published after his death by his son Samuel Wright, at London, in 1618, under the title A Description of the admirable Table of Logarithmes. Edward Wright, who was a fellow of Caius College, Cambridge, occupies a conspicuous place in the history of navigation. In 1599 he published Certaine errors in Navigation detected and corrected, and he was the author of other works ; to him also is chiefly clue the invention of the method known as Mercator s sailing. He at once saw the value of log arithms as an aid to navigation, and lost no time in preparing a translation, which he submitted to Napier himself. The preface to Wright s edition consists of a translation of the preface to the Canon Mirificus, together with the addition of the following sentences written by Napier himself: " But now some of our Countreymen in this Island well affected to these studies, and the more publique good, procured a most learned Mathematician to translate the same into our vulgar English tongue, whs after he had finished it, sent the Coppy of it to me, to bee scene and considered on by myselfe. I having most willingly and gladly done the same, finde it to bee most exact and precisely conform able to my minde and the originall. Therefore it may please } 7 ou who are inclined to these studies, to receive it from me and the Translator, with as much good will as we recommend it unto you."
There is a short " preface to the reader " by Briggs, and a descrip tion of a triangular diagram invented by Wright for finding the proportional parts. The table is printed to one figure less than in the Canon Mirificus. Edward Wright died in 1615, and his son in the preface states that his father "gave much commendation of this work (and often in my hearing) as of very great use for mariners" ; and with respect to the translation he says that "shortly after he had it returned out of Scotland, it pleased God to call him away afore he could publish it."
In 1617 Napier published his Rabdologia[1] a duodecimo of one hundred and fifty-four pages; there is prefixed to it as preface a dedicatory epistle to the high chancellor of Scotland. The method which Napier terms " Eabdologia " consists in the use of certain numerating rods for the performance of multiplications and divisions. These rods, which were commonly called " Napier s bones," will be described further on. The second method, which he calls the " Promptuarium Multiplications " on account of its being the most expeditious of all for the performance of multi plications, involves the use of a number of lamellae or little plates of metal disposed in a box. In an appendix of forty-one pages he gives his third method, "local arithmetic," which is performed on a chess-board, and depends, in principle, on the expression of numbers in the scale of radix 2. In the Rabdologia he gives the chrono logical order of his inventions. He speaks of the canon of logarithms as "a me longo tempore elaboratum." The other three methods he devised for the sake of those who would prefer to work with natural numbers ; and he mentions that the promptuary was his latest invention. In the preface to the appendix containing the local arith metic he states that, while devoting all his leisure to the invention of these abbreviations of calculation, and to examining by what methods the toil of calculation might be removed, in addition to the logarithms, rabdologia, and promptuary, he had hit upon a certain tabular arithmetic, whereby the more troublesome operations of common arith metic are performed on an abacus or chess-board, and which may be regarded as an amusement rather than a labour, for, by means of it, addition, subtraction, multiplication, division, and even the extraction of roots are accomplished simply by the motion of counters. He adds that he has appended it to the Rabdologia, in addition to the promptuary, because he did not wish to bury it in silence, nor to publish so small a matter by itself. With respect to the calculating rods, Napier mentions in the dedication that they had already found so much favour as to be almost in common use, and even to have been carried to foreign countries ; and that he has been advised to publish his little work relating to their mechanism and use, lest they should be put forth in some one else s name.
John Napier died on April 4, 1617, the same year as that in which the Rabdologia was published, so that his death must have taken place very soon after its appear ance. His will, which is extant, was signed on the fourth day before his death. No particulars are known of his last illness, but it seems likely that death came upon him rather suddenly at last. In both the Canon Mirijicus and the Rabdologia, however, he makes reference to his ill- health. In the dedication of the former he refers to himself as " mihi jam morbis pene confecto," and in the "Admonitio" at the end he speaks of his "infirma vale- tudo "; while in the latter he says he has been obliged to leave the calculation of the new canon of logarithms to others " ob infirmam corporis nostri valetudinem."
It is usually stated that John Napier was buried in St Giles s church, Edinburgh, and there can be no doubt that some of the family of Napier were buried there in the 16th or 17th century, but the late Professor Wallace, in a paper read before the Society of Antiquaries of Scotland in 1832, and quoted by Mr Mark Napier on pp. 425-427 of his Memoirs of John Napier of Merchiston, gives evidence for believing that he was buried in St Cuthbert s church. Professor Wallace s words are
{EB1911 fine print/s}}" My authority for this belief is unquestionable. It is a Treatise on Trigonometry, by a Scotsman, James Hume of Godscroft, Berwickshire, a place still in possession of the family of Huma The work in question, which is rare, was printed at Paris, and has the date 1636 on the title-page, but the royal privilege which secured it to the author is dated in October 1635, and it may have been written several years earlier. In his treatise (page 116) Hume says, speaking of logarithms, L inuenteur estoit mi Seigneur de grande condition, et duquel la posterite est aujour- d huy en possession de grandes dignitez dans le royaume, qiii estant sur 1 age, et grandement trauaille des gouttes ne pouvait faire autre chose que de s adonner aux sciences, et principalment aux mathe- matiques et a la logistique, a quoy il se plaisoit infiniment, et auec estrange peine, a construict ses Tables des Logarymes, im- primees a Edinbourg en 1 an 1614. ... II mourut 1 an 1616, et fut enterre hors la Porte Occidentale d Edinbourg, dans 1 Eglise de Sainct Cudbert. " {EB1911 fine print/e}}
There can be no doubt that Napier s devotion to mathe matics was not due to old age and the gout, and that he died in 1617 and not in 1616 ; still these sentences were written within eighteen years of Napier s death, and their author seems to have had some special sources of information. Additional probability is given to Hume s assertion by the fact that Merchiston is situated in St Cuthbert s parish. It is nowhere else recorded that Napier suffered from the gout. The Canon Mirijicus contains only an explanation tff the use of the logarithms without any account of the manner in which the canon was constructed. In an " Admonitio" on the seventh page he states that, although in that place the mode of construction should be explained, he proceeds at once to the use of the logarithms, "ut preelibatis prius usu, et rei utilitate, caetera aut magis placeant posthac edenda, aut minus saltern displiceant silentio sepulta." He awaits therefore the judgment and censure of the learned " priusquam caetera in lucem temere prolata lividorum detrectationi exponantur"; and in an "Admonitio" on the last page of the book he states that he will publish the mode of construction of the canon " si huius inventi usum eruditis gratum fore intellexero."
Napier, as we have seen, died in 1617, immediately after the appearance of the Rabdologia, and before he had
1 Rabdologiie, seu Numerations per virgulas Libri duo : Cum Appendice de expeditissimo Multiplicationis Promptuario. Quibus accessit < Arithmetics Localis Liber unus. Authore & Inventore loanne Nepero, Barone Merchistonii, &c. , Scoto. Edinburgi, Excu- debat Andreas Hart, 1617.
- ↑ 1
