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 Chisholm of Cromlix, who survived him. By her he had five sons and five daughters.

In 1588 he was chosen by the presbytery of Edinburgh one of its commissioners to the General Assembly.

On the 17th of October 1593 a convention of delegates was held at Edinburgh at which a committee was appointed to follow the king and lay before him in a personal interview certain instructions relating to the punishment of the rebellious Popish earls and the safety of the church. This committee consisted of six members, two barons, two ministers and two burgesses—the two barons selected being John Napier of Merchiston and James Maxwell of Calderwood. The delegates found the king at Jedburgh, and the mission, which was a dangerous one, was successfully accomplished. Shortly afterwards another convention was held at Edinburgh, and it was resolved that the delegates sent to Jedburgh should again meet the king at Linlithgow and repeat their former instructions. This was done accordingly, the number of members of the committee being, however, doubled. These interviews took place in October 1593, and on the 29th of the following January Napier wrote to the king the letter which forms the dedication of the Plaine Discovery.

The full title of this first work of Napier’s is given below. It was written in English instead of Latin in order that “hereby the simple of this Iland may be instructed”; and the author apologizes for the language and his own mode of expression in the following sentences:—

Napier’s Plaine Discovery is a serious and laborious work, to which he had devoted years of care and thought. In one sense it may be said to stand to theological literature in Scotland in something of the same position as that occupied by the Canon Mirificus with respect to the scientific literature, for it is the first published original work relating to theological interpretation, and is quite without a predecessor in its own field. Napier lived in the very midst of fiercely contending religious factions; there was but little theological teaching of any kind, and the work related to what were then the leading political and religious questions of the day.

After the publication of the Plaine Discovery, Napier seems to have occupied himself with the invention of secret instruments of war, for in the Bacon collection at Lambeth Palace there is a document, dated the 7th of. June 1596 and signed by Napier, giving a list of his inventions for the defence of the country against the anticipated invasion by Philip of Spain. The document is entitled “Secrett Inventionis, proffitabill and necessary in theis dayes for defence of this Iland, and withstanding of strangers, enemies of God’s truth and religion,” and the inventions consist of (1) a mirror for burning the enemies’ ships at any distance, (2) a piece of artillery destroying everything round an arc of a circle, and (3) a round metal chariot, so constructed that its occupants could move it rapidly and easily, while firing out through small holes in it. It has been asserted (by Sir Thomas Urquhart) that the piece of artillery was actually tried upon a plain in Scotland with complete success, a number of sheep and cattle being destroyed.

In 1614 appeared the work which in the history of British science can be placed as second only to Newton’s Principia. The full title is as follows: Mirifici Logarithmorum Canonis descriptio, Ejusque usus, in utraque Trigonometria; ut etiam in omni Logistica Mathematica, Amplissimi, Facillimi, ''& expeditissimi explicatio. Authore ac Inventore Ioanne Nepero, Barone Merchistonii, &c., Scoto. Edinburgi, ex officinâ Andreae Hart Bibliopolae, CIↃ.DC.XIV.'' This is printed on an ornamental title-page. The work is a small-sized quarto, containing fifty-seven pages of explanatory matter and ninety pages of tables.

The nature of logarithms is explained by reference to the motion of points in a straight line, and the principle upon which they are based is that of the correspondence of a geometrical and an arithmetical series of numbers. The table gives the logarithms of sines for every minute to seven figures. This work contains the first announcement of logarithms to the world, the first table of logarithms and the first use of the name logarithm, which was invented by Napier.

In 1617 Napier published his Rabdologia, 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 “Rabdologia” 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 Multiplicationis” on account of its being the most expeditious of all for the performance of multiplications, 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 chronological 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 arithmetic 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 arithmetic are performed on an abacus or chess-board, and which may be regarded as an amusement