gations, begun soon after his first marriage, seem to have been directed to systematising and developing the sciences of algebra and arithmetic, and the fragments published for the first time in 1839, under the title 'De Arte Logistica,' were the result of his initial studies. He here mentions that he was considering imaginary roots, a subject he refers to as a great algebraic secret, and that he had discovered a general method for the extraction of roots of all degrees. After five years' interruption, while engaged on his theological work, Napier again, in 1594, resumed his mathematical labours. A letter, presumably from a common friend, Dr. Craig, to Tycho Brahe, indicates that in the course of 1594 he had already conceived the general principles of logarithms (*Epistolæ ad Joannem Kepplerum*, Frankfort, 1718, p. 460; *Athenae Oxonienses*, London, 1691, p. 469; *Memoirs*, pp. 361-6) ; and the next twenty years of his life were spent in developing the theory of logarithms, in perfecting the method of their construction, and in computing the canon or table itself. While thus engaged he invented the present notation of decimal fractions.

Napier's earliest work on logarithms explained the method of their construction, but was written before he had invented the word logarithms, which were there called artificial numbers, in contradistinction to natural numbers, or simply artificials and naturals. This work, known as the 'Constructio,' was not published till after his death. The description of the table (known as the ' Descriptio '), throughout which the name logarithms is used, was composed later, but was given to the world in his lifetime. This famous work, 'Mirifici Logarithmorum Canonis Descriptio,' which embodied the triumphant termination of Napier's labours, contained, besides the canon or table, an explanation of the nature of logarithms, and of their use in numeration and in trigonometry. Published in 1614, with a dedication to Prince Charles, afterwards Charles I, it soon found its way into the hands of two enthusiastic admirers, Edward Wright [q. v.] and Henry Briggs fq. v.] The former at once translated it into English, and sent his version for revision to the author, who found it 'most exact and precisely conformable to his mind and the original.' The translation was returned to Wright shortly before the latter's death in 1615, and was next year seen through the press by Wright's son.

Briggs received the work with delight, and made it his constant companion. While expounding it to his students in London at Gresham College, he observed that it would facilitate its use were the canon altered so that '0 still remaining the logarithm of the whole sine or radius, the logarithm of one-tenth thereof should become 10 000 000 000' instead of 23025850, as in Napier's table. He wrote to Napier concerning this change, and, having computed some logarithms of this kind, proceeded to Edinburgh to visit the 'Baron of Merchiston.' in his own house, in the summer of 1615. There, being hospitably entertained, he lingered a month. Napier told Briggs that he had himself for a long time determined on the same change as Briggs suggested, but that he had preferred to publish the logarithms already prepared, rather than wait for leisure and health to re-compute them. But he was of opinion that the alteration should be made thus: that 0 should become the logarithm of unity, and 10 000 000 000 the logarithm of the whole sine; which, adds Briggs, 'I could not but acknowledge to be far the most convenient.' Briggs undertook the heavy task of computing the new canon, and Napier promised to write an explanation of its construction and use, but this he did not live to accomplish. In the following summer (1616) Briggs proceeded to Edinburgh a second time, and showed Napier so much of the new canon as he had completed. The first thousand logarithms of the new canon were published by Briggs, without place or date (but at London before 6 Dec. 1617), after Napier's death (Briggs, *Logarithmorum Chilias Prima*, 1617, title-page; Briggs, *Arithmetica Logarithmica*, 1624, 'To the Reader;' Napier, *Mir. Log. Can. Constructio*, 1619, 'To the Reader,' by Robert Napier). The original edition of Napier's 'Descriptio' was reprinted at Lyons, 1620, and in London, 1807 (in Maseres's 'Scriptores Logarithmici'). Copies of the 1620 edition are known, with date 1619, and the remainder-copies were reissued in 1658, with title-page and preliminary matter reset. Wright's English translation, which first appeared in 1616, was reissued with additional matter and a substituted title-page in 1618 another English translation was published at Edinburgh in 1857.

In the 'Descriptio' Napier had promised to publish his previously completed 'Constructio'--i.e. his method of constructing the table should his invention meet with the approval of the learned. Kepler, who largely helped to extend the employment of logarithms, had expressed a desire to see this work published, in a letter to the author dated 28 July 1619, before news of Napier's death had reached him. Kepler's letter was prefixed to his 'Ephemerides' for 1620 (*Memoirs*, pp. 432, 521). Shortly after Na-