Napier, John

, baron of Merchiston in Scotland, and the celebrated inventor of the Logarithms, was the eldest son of sir Archibald Napier of Merchiston, and born in 1550. After going through the ordinary course of education at the university of St. Andrew’s, he made the tour of France, Italy, and Germany. On his return he applied himself chiefly to the study of mathematics, to which he joined that of the Scriptures; and in both discovered the most extensive knowledge and profound penetration. His “Essay upon the book of the Apocalypse” indicates the most acute investigation; though time has discovered that his calculations concerning particular events had proceeded upon fallacious data. But what his fame now solely rests upon is his great and fortunate discovery of logarithms in trigonometry, by which the ease and expedition in calculation have so wonderfully assisted the science of astronomy and the arts of practical geometry and navigation. Napier, having much attachment to astronomy and spherical trigonometry, had occasion to make many numeral calculations of such triangles, with sines, tangents, &c. which being expressed in large numbers, occasioned a great deal of labour and trouble: To spare themselves part of this labour, Napier, and other authors about his time, endeavoured to find out certain short modes of calculation, as is evident from many of their writings. To this necessity, and these endeavours it is, that we owe several ingenious contrivances; particularly the computation by Napier’s Rods, or Bones, as they are called, and several other curious and short methods that are given in his “Rabdologia” and at length, after trials of many other means, the most complete one of logarithms, in the actual construction of a large table of numbers in arithmetical progression, adapted to a set of as many others in geometrical progression. The property of such numbers had been long known, viz. that the addition of the former answered to the multiplication of the latter, &c. but it wanted the necessity of such very troublesome calculations as those abovementioned, joined to an ardent disposition, to make such a use of that property. Perhaps also this disposition was urged into action by certain attempts of this kind which it seems were made elsewhere; such as the following, related by Wood ‘in his “Athenae Oxonienses,” under the article Briggs, on the authority of Oughtred and Wingate, viz. “That one Dr. Craig, a Scotchman, coming | out of Denmark into his own country, called upon John Neper baron of Marcheston near Edinburgh, and told him, among other discourses, of a new invention in Denmark, (by Longomontanus as ‘tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it, than that it was by proportionable numbers. Which hint Neper taking, he desired him at his return to call upon him again. Craig, after some weeks had passed, did so, and Neper then shewed him a rude draught of that he called ’ Canon Mirabilis Logarithmorum.’ Which draught, with some alterations, he printed in 1614; it came forthwith into the hands of our authorBriggs, and into thoseof William Oughtred, from whom the relation of this matter came.”

Whatever might be the inducement, however, Napier published his invention in 1614, under the title of “Logarithmorum Canonis Descriptio,” &c. containing the construction and canon of his logarithms, which are those of the kind that is called hyperbolic. This work coming presently to the hands of Mr. Briggs, then Professor of Geometry at Gresham College in London, he immediately gave it the greatest encouragement, teaching the nature of the logarithms in his public lectures; and at the same time recommending a change in the scale of them, by which they might be advantageously altered to the kind which he afterwards computed himself, which are thence called Briggs’s Logarithms, and are those now in common use. Mr. Briggs also presently wrote to lord Napier upon this proposed change, and made journeys to Scotland the two following years, to visit Napier, and consult him about that alteration, before he set, about making it. Briggs, in a letter to archbishop Usher, March 10, 1615, writes thus: “Napier lord of Markinston, hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it please God; for I never saw a book which pleased me better, and made me more wonder.” Briggs accordingly paid him the visit, and staid a month with him.

The following passage, from the life of Lilly the astrologer, contains a curious account of the meeting of those two illustrious men. “I will acquaint you,” says Lilly, “with one memorable story related unto me by John Marr, an excellent mathematician and geometrician, whom I | conceive you remember. He was, servant to king James and Charles the First. At first when the lord Napier, or Marchiston, made public his logarithms, Mr. Briggs, then reader of the astronomy lectures at Gresham college in London, was so surprised with admiration of them, that he could have no quietness in himself until he had seen that noble person the lord Marchiston, whose only invention they were: he acquaints John Marr herewith, who went into Scotland before Mr. Briggs, purposely to be there when these two so learned persons should meet. Mr. Briggs appoints a certain day when to meet at Edinburgh; but failing thereof, the lord Napier was doubtful he would not come. It happened one day as John Marr and the lord Napier were speaking of Mr. Briggs; `Ah, John,‘ said Marchiston, `Mr. Briggs will not now come.’ At the very instant one knocks at the gate; John Marr hasted down, and it proved Mr. Briggs, to his great contentment. He brings Mr. Briggs up into my lord’s chamber, where almost one quarter of an hour was spent, each beholding other almost with admiration before one word was spoke. At last Mr. Briggs began: ‘My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms; but, my lord, being by you found out, I wonder no body else found it out before, when now known it is so easy.’ He was nobly entertained by the lord Napier; and every summer after that, during the lord’s being alive, this venerable man Mr. Briggs went purposely into Scotland to visit him.”

Napier made also considerable improvements in spherical trigonometry, &c. particularly by his Catholic or Universal Rule, being a general theorem, by which he resolves all the cases of right-angled spherical triangles in a manner very simple, and easy to be remembered, namely, by what he calls the Five Circular Parts. His construction of Logarithms too, beside the labour of them, manifests the greatest ingenuity. Kepler dedicated his Ephemerides to Napier, which were published in 1617; and it appears from many passages in his letter about this time, that he accounted Napier to be the greatest man of his age in the particular department to which he applied his abilities.

The last literary exertion of this eminent person was the publication of his “Rabdology and Promptuary,” in | 1617; soon after which he died at Marchiston, the 3d of April in the same year, in the 68th year of his age. The list of his works is as follows: 1. “A Plain Discovery of the Revelation of St. John,” 1593. 2. “Logarithmorum Canonis Descriptio,” 1614. 3. “Mirifici Logarithmorum Canonis Constructio; et eorum ad Naturales ipsorum nu*­meros habitudines; una cum appendice, de alia eaque praestantiore Logarithmorum specie condenda. Quibus accessere propositiones ad triangula sphserica faciliore calculo resolvenda. Una cum Annotationibus aliquot doctissimi D. Henrici Briggii in eas, et memoratam appendicem.” Published by the author’s son in 1619. 4. “Rabdologia, sen Numerations per Virgulas, libri duo,” 1617. This contains the description and use of the Bones or Rods; with several other short and ingenious modes of calculation. 5. His Letter to Anthony Bacon (the original of which is in the archbishop’s library at Lambeth), entitled, “Se­”cret Inventions, profitable and necessary in these days for the Defence of this Island, and withstanding strangers enemies to God’s truth and religion" dated June 2, 1596. ¹