NAPIER, JOHN (1550-1617), Scottish mathematician, the inventor of logarithms, was born in Merchiston near Edinburgh in 1550, and was the eighth Napier of Merchiston. He matricu lated at St. Salvator's college, St. Andrews, in 1563. Very little is known of his life at this time, but it is plain from the "Discourse" which he prefixed to his Plaine Discovery that he was already a devoted adherent of the Protestant cause. From St. Andrews he went apparently to study in Paris, and travelled in Italy and Ger many. But he was back at Merchiston in 1571, and in the next year married Elizabeth, daughter of Sir James Stirling. The son of this marriage was Archibald, Lord Napier. Elizabeth Napier died in 1579, and soon after Napier married Agnes Chisholm.
Napier was one of the Edinburgh commissioners to the General Assembly in 1588, and on Oct. 17, 1593, was a member of a com mittee nominated by a convention of delegates to make repre sentations to the king at Jedburgh on the safety of the Church and the punishment of the Roman Catholic earls. He was a mem ber of a similar delegation later in the month. On Jan. 29, 1594, Napier addressed to the king the letter which forms the dedication of his Plaine Discovery of the whole Revelation of Saint John: set down in two treatises . . . (Edinburgh, 1593). This book has a great place in the history of theology in Scotland, for it is the first important Scottish work on the interpretation of scripture.
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 June 7, 1596, and signed by Napier, giving a list of his inventions for the defence of the country against the antici pated invasion by Philip of Spain. In 1614 appeared Canonis De scriptio embodying his invention of logarithms. Their nature 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 corre spondence 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. The method which
Napier terms "Rabdologia" consists in the use of certain numer ating rods for the performance of multiplications and divisions. These rods were commonly called "Napier's bones." The second method, which he calls the "Promptuarium Multiplicationis," in volves the use of a number of lamellae or little plates of metal disposed in a box. In an appendix he gives his third method, "local arithmetic," which is performed on a chess-board, and de pends, in principle, on the expression of numbers in the scale of radix 2. In the Rabdologia he gives the chronological order of his inventions.
John Napier died on April 4, 1617, the same year as that in which the Rabdologia was published.
The Canonis Descriptio on its publication in 1614 at once attracted the attention of Edward Wright, whose name is known in connection with improvements in navigation, and Henry Briggs, then professor of geometry at Gresham college, London. The former translated the work into English, but he died in 1615, and the translation was published by his son Samuel Wright in 1616. The logarithms introduced by Napier in the Descriptio are not the same as those now in common use, nor even the same as those now called Napierian or hyperbolic logarithms. The change from the original logarithms to common or decimal logarithms was made by both Napier and Briggs, and the first tables of decimal logarithms were calculated by Briggs, who published a small table, extending to i,000, in 1617, and a large work, Arithmetica Logarithinica, containing logarithms of numbers to 30,00o and from 90,00o to ioo,000, in 1624. (See LOGARITHMS.) Napier's Descriptio of 1614 contains no explanation of the manner in which he had calculated his table. This account he kept back, as he himself states, in order to see from the reception met with by the Descriptio whether it would be acceptable. Though written before the Descriptio it had not been prepared for press at the time of his death, but was published by his son Robert in 1619 under the title Mirifici Logarithmorum Canonis Constructio. In this treatise (which was written before Napier had invented the name logarithm) logarithms are called "artificial numbers." Napier's priority in the publication of the logarithms is unques tioned and only one other contemporary mathematician seems to have conceived the idea on which they depend.