Napier, John (DNB00)
NAPIER or NEPER, JOHN (1550–1617), laird of Merchiston, inventor of logarithms, was the eldest son of Sir Archibald Napier (1534–1608) [q. v.], by his first wife, Janet Bothwell. He was born in 1550, before his father had completed his sixteenth year, at Merchiston Castle, near Edinburgh. There he resided during his childhood with his youthful father and mother, a younger brother Francis, and a sister Janet. The only brother of his mother, Adam Bothwell [q. v.], elected bishop of Orkney in 1559, wrote to his father on 5 Dec. 1560, 'I pray you, sir, to send John to the schools either to France or Flanders, for he can learn no good at home.' This advice was afterwards followed. In the beginning of 1561 the bishop executed a will in favour of his nephew, but nothing came of it, as he subsequently married and had a son (Mark Napier, Memoirs, p. 63, &c.) At the age of thirteen John went to St. Andrews, his name appearing in the books of the college of St. Salvator for the session 1 Oct. 1563 to July 1564. He was boarded with John Rutherford, the principal of his college (ib. pp. 91-5). On 20 Dec. 1563 his mother died, and in the inventory of debts due by her is a sum of 18l. (Scots) to John Rutherford for her son's board (ib. p. 93). In the address to the 'Godly and Christian Reader' prefixed to his work on ' Revelation,' Napier states that, while at St. Andrews, he, 'on the one part, contracted a loving familiarity with a certain gentleman, a papist, and on the other part, was attentive to the sermons of that worthy man of God, Master Christopher Goodman [q. v.], teaching upon the Apocalypse.' He 'was so moved,' he continues, 'in admiration against the blindness of papists that could not most evidently see their seven-hilled city of Rome painted out there so lively by St. John as the mother of all spiritual whoredom, that not only bursted [he] out in continual reasoning against [his] said familiar, but also from thenceforth [he] determined with [himself] by the assistance of Gods spirit to employ [his] study and diligence to search out the remanent mysteries of that holy book.' The absence of his name from the list of determinants for 1566, or of masters of arts for 1568, makes it probable that after one or perhaps two sessions Napier was sent abroad to prosecute his studies; Mackenzie (Scots Writers, iii. 519) says he stayed for some years in the Low Countries, France, and Italy; but nothing definite is known. By 1571 Napier had returned home. On 24 Oct. 1571 his uncle, Adam Bothwell, now commendator of Holyrood House as well as bishop of Orkney, assigned to Sir Archibald and his sons, John and Francis, the teinds of Merchiston for nineteen years (Memoirs, p. 129), and, immediately after, negotiations began for John's marriage with Elizabeth, daughter of Sir James Stirling of Keir. In December 1571 a contract was entered into by the respective fathers, Sir Archibald ap-parently undertaking to infeft his son in the baronies of Edenbellie-Napier and Merchiston, and Sir James agreeing to pay Sir Archibald three thousand merks in name of tocher. Other deeds, dated 16 and 23 Feb. following, are in the Stirling and Napier charter chests; and on 2 April 1572 a deed was signed at Merchiston by John Napier and Elizabeth Stirling, preliminary to their marriage (Stirling of Keir, p. 43; Memoirs, p. 130) After some delays due to the political disturbances in which Napier's father was involved, a royal charter, on 8 Oct. 1572, granted to Napier and his future wife, in conjunct fee, the lands of Edenbellie, Gartnes, while Napier also received 'the lands of Merchiston with its tower and the Pultrielands; half the lands of Ardewnan, &c., half the lands of Rusky, Thorn, &c., with the house of Barnisdale; the third of the lands of Calziemuck ; and the lands of Auchinlesh.' The life-rent of all the lands save those in conjunct fee was reserved to Sir Archibald and his wife.
The couple being thus provided for, the marriage followed, and Napier and his wife settled on their property. A castle, beautifully situated on the banks of the Endrick, was built at Gartnes, with garden, orchard, and suitable offices; it was completed in 1574, as appears from a sculptured stone bearing that date, still preserved in a wall of one of the buildings of an adjacent mill. Two sundials from the castle have been recently taken to Helensburgh, and these are now almost the sole remnants of Napier's home. On the opposite side of the Endrick was a lint mill, and the old 'Statistical Account of Scotland ' (xvi. 107) records that the clack of this mill greatly disturbed Napier, and that he would sometimes desire the miller to stop the mill so that the train of his ideas might not be interrupted. His residence at Gartnes extended from 1573 to 1608, when the death of his father put him in possession of Merchiston Castle. Towards the end of 1579, after bearing two children, his wife died, and he subsequently married Agnes, daughter of Sir James Chisholm of Cromlix, Perthshire.
The political activity of his father-in-law, Sir James Chisholm, involved Napier in some anxieties. In February 1592-3 the conspiracy known as 'the Spanish Blanks' was discovered, and Chisholm, 'the king's master of the household,' was deeply implicated, along with the popish earls Angus, Huntly, and Erroll. The king, disinclined to proceed to extremities, desired that the conspirators should keep out of the way for a time. With this view, apparently, a bond of caution in 5,000l. (Scots) was signed, on 28 July and 3 Aug. 1593, by John Napier and another, that Chisholm, 'during his absence furth the realm, conform to his majesty's licence, shall do nothing to hurt his majesty, the realm, or the true religion' (Reg. Privy Council, v. 610). Chisholm and the earls, however, remained in the country. Accordingly, a small deputation of commissioners of the church followed the king to Jedburgh in October, and urged their speedy trial and punishment. One of the deputies was, according to Rymer (Foedera, 1715, xvi. 223-5), 'the laird of Markiston younger,' that is John Napier, who is thus represented as urging the king to take proceedings against his father-in-law (Memoirs, p. 162). Calderwood (Hist. Church of Scotl. 1678, p. 292) calls the deputy, however, 'the Laird of Merchistoun,' that is, Napier's father.
As a landlord Napier also had his troubles. There had been disputes of long standing, occasionally leading to violence (see Reg. Mag. Sig. 2 Nov. 1583), between his father's tenants of Calziemuck and the Grahams of Boquhopple and other feuars of neighbouring lands in Menteith. In August 1591 matters came to a crisis, with reference to the ploughing and sowing by Napier's tenants of land which the feuars alleged to be commonalty; and on the 20th of that month Napier, who appears to have managed the Menteith property for his father, wrote to him from Keir describing how the feuars had summoned him and his tenants to find law burrows (i.e. sureties that they would not harm the person or property of the complainers) and had put an arrestment on their crops, 'so that there is certainly appearance of cummer to fall shortly betwixt them and our folks.' As he had no mind 'to mell with na sik extraordinar doings,' he prayed his father to find caution for him in a thousand merks (Memoirs, p. 148). This was accordingly done on 23 Aug. (Reg. Privy Council, iv. 673). Disputes between the same parties were repeated in 1611, 1612, and 1613 (ib. vols. ix. and x.), but at length on 14 June 1616 Napier obtained a disposition of the lands of Boquhopple in favour of himself and his son Robert (Douglas, Peerage, ii. 291). In July 1594 he entered into a curious contract with Robert Logan of Restalrig. The document is in Napier's handwriting throughout. After referring to divers old reports of a treasure hidden in Logan's dwelling-place of Fast Castle, he agreed to go thither, and 'by all craft and ingyne endeavour to find the same, and by the grace of God, either shall find it, or make sure that no such thing is there so far as his utter diligence may reach.' Should the treasure be found, Napier was to have a third as his share, and he further bargained that Logan was himself to accompany him back to Edinburgh to insure his safe return without being robbed, a contingency not unlikely if the laird of Restalrig were absent and free to give a hint to his retainers that money might be got by robbery (Memoirs, p. 220). That Napier's experience of Logan was unsatisfactory seems proved by the terms of a lease granted by him at Gartnes, on 14 Sept. 1596, in which it was expressly stipulated that the lessee should neither directly nor indirectly suffer or permit any person bearing the name of Logan to enter into possession. At the same time a like exception was made with reference to Napier's nearest neighbour at Gartnes, Cunningham of the house of Drumquhassil, with whom he , had a dispute respecting crops in 1591 (ib. pp. 148, 223). Towards the close of 1600 his half-brother Archibald was murdered by the Scotts of Bowhill, and Napier and his father had much trouble in restraining the dead man's family from taking the law into their own hands (Memoirs, p. 302; Pitcairn, Crim. Trials, ii. 339; Reg. Privy Council, vi. 259, 267). On 30 April 1601 he became cautioner for his father's brother, Andrew Napier, 'touching the mass which was said in his house' (Reg. Privy Council, vi. 632). On 11 March 1602 he brought a complaint against the provost and baillies of Edinburgh that they had caused 'build scheillis and ludgeis to their seik personis infectit with the pest upoun the said complenaris yairdis of his proper lands of the schenis' (ib. vi. 359). On 20 Jan. 1604 Napier's turbulent neighbours, Allaster McGregor of Glenstrae, Argyllshire, and four of the Macgregor clan, were brought to trial at Edinburgh for making a raid on their foes the Colquhouns, and Napier was one of the assize of fifteen persons who found them guilty of capital crimes (Crim. Trials, ii. 430). On 30 July 1605 he and another were named arbitrators by Matthew Stewart of Dunduff concerning the slaughter of his brother (Reg. Privy Council, vii. 106).
On Sir Archibald's death, on 15 May 1608, Napier, who came into full possession of the family estates, at once took up his abode in the castle of Merchiston. His position as laird was first publicly recognised by the lords of the privy council on 20 May, when he was appointed a commissioner to fix the price of boots and shoes twice a year for Edinburgh (ib. viii. 93). A bitter quarrel followed between Napier and his half-brother Alexander and his half-sisters as to their respective rights over the family property (Memoirs, p. 317). Alexander disputed Napier's title to the lands of Over-Merchiston, and a long litigation, which was not concluded until 9 June 1613, was necessary before Napier was served heir to that property (ib. p. 313). In another dispute regarding the teind sheafs of Merchiston, the privy council was informed on 1 Sept. 1608 that Napier and his relatives each intended to convoke their kin and friends and such as will do for them in arms, for leading and withstanding of leading of the said teinds.' Consequently the lords appointed William Napier of Wrichtishousis as a neutral person to lead said teinds in his own barnyard (Reg. Privy Council, viii. 159), and Napier, in a letter to his son, expressed himself satisfied with this arrangement (Memoirs, p. 315).
In 1610 Napier sold the Pultrielands to Nisbet of Dean for seventeen hundred merks (Douglas, Peerage ii. 291); and to protect his property at Gartnes he entered, on 24 Dec. 1611 into an agreement with Campbell of Lawers, Stirling, and his brothers that 'if the Macgregors or other hieland broken men should trouble his lands in Lennox or Menteith,' the Campbells should do their utmost to punish them (Memoirs, p. 326).
A man of wide intellectual interests and great versatility, Napier, as a landowner, gave considerable attention to agriculture, which, owing to the disturbed state of the country, was at a low ebb, resulting in frequent scarcity of corn and cattle. He appears to have instituted experiments in the use of manures, and to have discovered the value of common salt for the purpose. The details of his method are explained in a pamphlet nominally written by his eldest son Archibald [q. v.], to whom a monopoly of this mode of tillage was granted on 22 June 1598 (ib. p. 283). His son's share in these experiments— he was only twenty-three— cannot have been great. With somewhat similar ends in view he invented an hydraulic screw and revolving axle, by which, at a moderate expense, water could be kept down in coal-pits while being worked, and many flooded pits could be cleared of water and recovered, to the great advantage of the country. In order that he might in part reap the profits of his invention, the king, on 30 Jan. 1596-7, granted him a monopoly for making, erecting, and working these machines (Reg. Mag. Sig. vi. 172). In 1599 Sir John Skene published his 'De Verborum Significatione,' in which he mentions that he had consulted Napier whom he there styles 'a gentleman of singular judgement and learning, especially in mathematic sciences' in reference to the proper methods to be used in the measuring of lands. To mathematics Napier chiefly devoted his leisure through life; but soon after settling at Gartnes he interrupted his favourite study in order to cross swords with Roman catholic apologists. In 1593 he completed with that object a work on ' Revelation,' which had occupied him for five years. He had thought at first to write it in Latin, but the 'insolency of Papists determined him to haste [it] out in English.' It was entitled 'A Plaine Discovery of the whole Revelation of St. John,' and appeared at Edinburgh early in 1594. In his dedication to James VI, dated 29 Jan. 1593-4, Napier urged the king to see 'that justice be done against the enemies of God's church,' and counselled him 'to reform the universal enormities of his country, and first to begin at his own house, family, and court.' The volume includes nine pages of English verse by himself. It met with success at home and abroad (Memoirs, p. 326). In 1600 Michiel Panneel produced a Dutch translation, and this reached a second edition in 1607. In 1602 the work appeared at La Rochelle in a French version, by Georges Thomson, revised by Napier, and that also went through several editions (1603, 1605, and 1607). A new edition of the English original was called for in 1611, when it was revised and corrected by the author, and enlarged by the addition of 'A Resolution of certain Doubts proponed by well-affected brethren;' this appeared simultaneously at Edinburgh and London. The author stated that he still intended to publish a Latin edition, but, 'being advertised that our papistical adversaries were to write largely against the editions already set out,' he deferred it till he had seen their objections. The Latin edition never appeared, and his opponents' works proved unimportant. A German translation, by Leo de Dromna, of the first part of Napier's work appeared at Gera in 1611 (some copies are dated 1612), and of the whole by Wolfgang Meyer at Frankfort-on- the-Maine, in 1615 (new edit, 1627).
But other instruments besides the pen suggested themselves to Napier as a means of confounding the foes of his religion and country. On 7 June 1596 he forwarded to Anthony Bacon [q. v.], elder brother of Francis, lord Verulam, 'Secret Inventions, profitable and necessary in these Days for Defence of this Island, and withstanding of Strangers, Enemies of God's Truth and Religion' (the manuscript is at Lambeth). Four inventions are specified : two varieties of burning mirrors, a piece of artillery, and a chariot of metal, double musket proof, the motion of which was controlled by those within, and from which shot was discharged through small holes,' the enemy meantime being abased and altogether uncertain what defence or pursuit to use against a moving mouth of metal' (Memoirs, p. 247). A curious story of a trial of the last invention in Scot- land is given by Sir Thomas Urquhart in 'The Jewell ' (London, 1652, p. 79). Napier desired that these instruments of destruction should be kept secret unless necessity compelled their use.
Napier's permanent fame rests on his mathematical discoveries. His earliest investigations, 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 Napier'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 Briggsi.' 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, 'Rabdologiae 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 multiplication and division can be performed by simple addition and subtraction, the extraction of the roots of numbers by division, and the raising of them to any power by multiplication. By these simple processes the most complicated problems in astronomy, navigation, and cognate sciences can be solved by an easy and certain method. The invention necessarily gave a great impulse to all the sciences which depend for their progress on exact computation. Napier's place among great originators in mathematics is fully acknowledged, and the improvements that he introduced constitute a new epoch in the history of the science. He was the earliest British writer to make a contribution of commanding value to the progress of mathematics.
The original portraits of Napier, known to the author of the 'Memoirs' in 1834, were six in number, all in oil, viz. : (1) three-quarter length, seated, dated 1616, set. 66, presented to Edinburgh University by Margaret, baroness Napier, who succeeded in 1686, engraved in 'Memoirs;' (2) three-quarter length, seated, with cowl, set. 66, belonging to Lord Napier, and never out of the family, engraved in 'De Arte Logistica;' (3) half-length, with cowl, in possession of Mr. Napier of Blackstone; (4) a similar one in possession of Aytoun of Inchdairnie; (5) half-length, without cowl, acquired by Lord Napier, the history of which is unknown; (6) half-length,with cowl , belonging to Professor Macvey Napier, and attributed to Jameson (Memoirs, pp. ix, x). There is also an engraving by Francisco Delaram dated 1620, a half-length, with ruff, using his 'bones,' of which an original impression is at Keir. From this a lithographic reproduction was executed for Sir William Stirling-Maxwell, which, however, appears never to have been published.[Mark Napier's Memoirs, 1834; Registrum Magni Sigilli Regum Scotorum; Register of the Privy Council of Scotland; Exchequer Rolls of Scotland; Douglas's Peerage, 1813, vol. ii.; Crawford's Peerage, 1716; Mackenzie's Eminent Writers of the Scots Nation, vol. iii. 1722; Earl of Buchan's (D. S. Erskine) Life of Napier, 1787. In an appendix to the English translation of the Mirifici Logarithmorum Canonis Constructio (Edinburgh, 1889) appear full details of the editions of Napier's works, as well as an account of works by other authors, interesting from their connection with the works of Napier.]