pier's death his son Robert transmitted the manuscript to Briggs, by whom it was edited and published at Edinburgh in 1619 under the title 'Mirifici Logarithmorum Canonis Constructio, una cum Annotationibus aliquot doctissimi Henrici Briggii.' Along with it were printed some very remarkable propositions for the solution of spherical triangles, which Napier was engaged in perfecting at the time of his death; there are also added 'Remarks' and 'Notes' by Briggs, and a preface by the author's eldest son by his second wife, Robert Napier. The volume was reprinted at Lyons in 1620, and appeared in an English translation at Edinburgh in 1889.
Napier probably commenced his last work, 'Rabdologiæ seu numerationis per virgulas libri duo,' in 1615, that date being appended to his first example. He published it in Latin at Edinburgh early in 1617, with a dedication to Chancellor Seton, earl of Dunfermline; he there stated that he had always endeavoured, according to his strength and ability, to do away with the tediousness of calculations. With that aim he had published the 'Canon of Logarithms.' He explains the title ' Rabdologia ' as 'numeration by little rods.' These rods, being usually made of bone or ivory, were familiarly called 'Napier's bones' (cf. Butler, Hudibras, ed. Grey, 819, iii. 48). By means of them multiplication and division could be performed by methods which, though they now seem cumbrous enough, were received throughout Europe as a valuable aid to the rude arithmetic of the day. The extraction of the square and cube root could also be performed by their help, in conjunction with two larger rods, the method of constructing which is described. In an appendix, 'de expeditissimo Multiplications Promptuario,' he explains another invention for the performance of multiplication and division—'the most expeditious of all'—by means of metal plates arranged in a box. This is the earliest known attempt at the invention of a calculating machine [see Morland, Sir Samuel and Babbage, Charles]. There is also added his 'Local Arithmetic,' wherein he describes how multiplication and division, and even the extraction of roots, may be performed on a chessboard by the movement of counters. The 'Rabdologia ' was reprinted at Leyden (1626), and copies of this are found, with substituted title-page, dated 1628. An Italian translation was issued at Verona (1623), and a Dutch one at Gouda (1626). In 1667 William Leybourn [q. v.]] published 'The Art of Numbering by Speaking Rods, vulgarly termed Napier's Bones.' An enlarged account by Leybourn of 'the Use of Nepiar's Bones' was appended to his 'Description and Use of Gunter's Quadrant ' (2nd edit. London, 1721).
Continuous study and the arduous work of computation, which, Napier says, 'ought to have been accomplished by the labour and assistance of many computers, but had been completed by the strength and industry of himself alone,' told severely on his health. In a complaint against the Grahams of Boquhopple, his old opponents, which was presented to the privy council on 28 April 1613, he stated that he was 'heavily diseased with the pain of the gout' (Reg. Privy Council, x. 41). 'Johne Naipper of Merchistoun, being sick in body at the plesour of God, but haill in mynd and spereit,' made his will and signed it on 1 April 1617, 'with my hand at the pen led be the nottars underwrittine at my command in respect I dow not writ myself for my present infirmitie and sickness' (Memoirs, p. 430). Worn out by overwork and gout, he breathed his last at Merchiston on 4 April 1617, and was buried outside the west port of Edinburgh in the church of St. Cuthbert, the parish in which Merchiston is situated (J. Hume, Traité de la Trigonométrie, Paris, 1636, p. 116).
By his first wife, Elizabeth Stirling, he had one son, Archibald (1576-1645) [q. v.], and one daughter, Joanne, to whom he granted an annuity of 100l. (Scots) by charter dated 13 Nov. 1595. By his second wife, Agnes Chisholm, he had five sons: John, Robert (to whom he granted the lands of Ballacharne and Tomdarroch on 13 Nov. 1595), Alexander, William, and Adam; and five daughters: Margaret (who married Sir James Stewart of Rossyth before 1 Jan. 1608), Jean, Agnes, Elizabeth, and Helen. On 13 April 1610 Napier granted the following annuities to the children of his second marriage, viz.: 250 merks to Robert, 200 to Alexander, 300 to Jean, and 200 to Elizabeth (Memoirs, p. 323; Douglas, Peerage, ii. 291).
Napier appears, in the fragmentary records that have survived, as a man both just in his dealings with his neighbours and firmly resolved to obtain like justice from them. In his disputes with his father, his step-brothers, the Grahams of Boquhopple, and the magistrates of Edinburgh, he seems invariably to have carried his point. He was a strict Calvinist, and a resolute opponent of papal aggression. His powerful intellect and determined will are best indicated in his prolonged and successful efforts to facilitate numerical calculation which resulted in his discovery of logarithms. The advantages of a table of logarithms are that by its employment
