NAPIER, John, Baron of Merchiston, the distinguished inventor of logarithms, was the eldest son of Sir Archibald Napier of Edinbelle and Merchiston, by his first wife Janet Bothwell, and was born at Merchiston Castle, near Edinburgh, in 1550. After passing through the ordinary courses of liberal study at the university of St Andrews, he travelled in France, Italy, and Germany. Upon his return to his native country, his accomplishments soon rendered him conspicuous, and might have raised him to the highest offices of state; but declining all civil employments, he retired from active life to pursue those scientific and literary researches in which he subsequently made such uncommon progress. He applied himself chiefly to the study of mathematics, and of the Holy Scriptures; and in A Plain Discovery of the Revelation of St John, his first publication, he displayed great acuteness and striking ingenuity, but did not succeed in fathoming the mysteries of the Apocalypse. This work was printed abroad in several languages, particularly in French at Rochelle in the year 1602, in a quarto volume, revised by himself. But what has rendered his name for ever illustrious was his discovery of logarithms. That he had begun before the year 1594 the train of inquiry which led to this great achievement, appears evident from a letter to Crugerus, written by Kepler in the year 1624, wherein, mentioning the Canon Mirificus, he writes thus:—"Nihil autem supra Nepierianam rationem esse puto; etsi Scotus quidem literis ad Tychonem, anno 1594, scriptis jam spem fecit canonis illius mirifici." This allusion agrees with the idle story mentioned by Wood in his Athenæ Oxonienses, and explains it in a way perfectly consonant to the rights of Napier as the inventor.
When Napier had communicated to Henry Briggs, mathematical professor in Gresham College, his wonderful Canon for Logarithms, that learned professor set himself to apply the rules in his Imitatio Nepiærea; and in a letter
to Archbishop Usher, written in the year 1615, he thus expresses himself:—"Napier, Baron of Merchiston, 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." The following passage from the Life of Lilly the astrologer gives a picturesque view of the meeting between Briggs and the inventor of the logarithms, at Merchiston, near Edinburgh:—"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 I. and Charles I. When Merchiston first published his logarithms, Mr Briggs, then reader of the astronomy lectures at Gresham College in London, was so much surprised with admiration of them, that he could have no quietness in himself until he had seen that noble person whose only invention they were. He acquaints John Marr therewith, 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, Merchiston was fearful he would not come. It happened one day as John Marr and the Baron Napier were speaking of Mr Briggs; 'Ah, John,' said Merchiston, 'Mr Briggs will not come.' At the very instant one knocks at the gate: John Marr hastened down, and it proved to be Mr Briggs, to his great contentment. He brings Mr Briggs up to the Baron's chamber, where almost one quarter of an hour was spent, each beholding the other with admiration, before one word was spoken. At last Mr Briggs began:—'Sir, 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, Sir, being by you found out, I wonder nobody else found it out before, when now being known it appears so easy.' He was nobly entertained by the illustrious baron; and every summer after that, during the baron's life, this venerable man, Mr Briggs, went purposely to Scotland to visit him."
There is a passage in the Life of Tycho Brahe by Gassendi, which might lead some to suppose that Napier's method had previously been explored by Herwart at Hoensburg. But Herwart's work, published in 1610, solves triangles by prostaphæresis, a mode totally different from that of logarithms. Kepler, who was ignorant that Napier had been deceased for more than two years, addressed a letter to him, dated 28th of July 1619 (prefixed as a dedication to his Ephemerides for the year 1620), in which he expresses his high admiration of the Canon Mirificus, and his astonishment and delight on first becoming acquainted with the importance of Napier's great discovery. In the archiepiscopal library of Lambeth the original of a letter still exists, addressed by Baron Napier to Anthony Bacon in 1596, entitled "Secret Inventions necessary in those days for the Defence of this Island, and withstanding Strangers, Enemies to God's Truth and Religion." These inventions consisted of burning mirrors designed to fire the enemies' ships at a distance, by reflecting the sun's rays, or "the beams of any material fire or flame," to a focus. It does not appear that the invention attracted much notice at the time, owing probably to the modesty or humanity of the author, who, in relation to this matter, remarked on his death-bed, that the instruments of human destruction "should never be increased by any new conceit of his."
Baron Napier's last work was his Rabdology and Promptuary, published in 1617, and dedicated to the Chancellor Seton. He died at Merchiston on the 4th of April of the same year, in the sixty-eighth year of his age.
Napier was twice married. By his first wife, who was a daughter of Sir James Stirling of Keir, he had only one son,
named Arnevaud. He was appointed a privy councillor by James VI., under whose reign he also held the offices of treasurer-depute, justice-clerk, and senator of the college of justice; and by Charles I. he was raised to the peerage. By his second wife, a daughter of Sir James Chisholm of Cromlix, he had a numerous family of sons and daughters.
We have two Lives of the inventor of logarithms; one by the late Earl of Buchan, with an analysis of Napier's printed works by Dr Walter Minto, published in 1787; the other by Mr Mark Napier, advocate, published in 1834; both in 4to. (For additional information respecting this illustrious mathematician, see LOGARITHMS.) The following is a correct list of his different publications:—
1. A plaine Discouery of the whole Reuelation of Saint Iohn; set downe in two treatises: the one searching and prouing the true interpretation thereof; the other applying the same paraphrastically and historically to the text. Set forth by Iohn Napier L. of Merchiston younger. Edinburgh, printed by Robert Waldegrave, 1593, 4to. In republishing this work in 1611, the author subjoined "A resolution of certaine doubts, mooved by some well-affected brethren." The "fifth edition" was printed at Edinburgh, 1645, 4to. It was translated into French by George Thomson, and printed at Rochelle, 1602, in 4to. On the title, it is said to have been revised by the author himself ("reueue par lui-même"), and was reprinted in 1605, and again in 1607, in 8vo.
2. Mirifici Logarithmorum Canonis Descriptio, ejusque usus, in utraque Trigonometria, ut etiam in omni Logistica Mathematica amplissimi, &c., explicatio. Edinburgh, ex officina Andree Hart, 1614, 4to.
3. Rabdologia, seu Numerationis per Virgulas libri duo: cum Appendice de expeditissimo Multiplicationis Promptuario. Quibus accessit et Arithmetico Localis liber unus. Edinburgh, excudebat Andreas Hart, 1617, 12mo. Reprinted at Lyons in 1626, and again in 1629, 12mo.
4. Mirifici Logarithmorum Canonis Constructio, et eorum ad naturales ipsorum numeros habitudines; una cum Appendice, de aliis eaque prestantiore Logarithmorum specie condenda. Quibus accessere Propositiones ad triangula spherica faciliore calculo resolvenda, &c. Edinburgh, excudebat Andreas Hart, 1619, 4to. This posthumous work was published by the author's third son, Robert Napier. Some copies of it occur, along with the Canonis Descriptio, having a general title-page for both, dated 1619, the original title of 1614 being cancelled. Both works were reprinted at Lyons in 1620, 4to; and the first, followed with copious "Observations," was included in Baron Masere's large collection, entitled Scriptores Logarithmici, vol. vi., London, 1807, 4to.
NAPIER'S RODS, or Bones, an instrument invented by Baron Napier, whereby the multiplication and division of large numbers is much facilitated. Suppose the common table of multiplication to be made upon a plate of metal, ivory, or pasteboard, and then conceive the several columns, standing downwards from the digits on the head, to be cut asunder; these are what are called Napier's Rods of Multiplication. But then there must be a good number of each; for as many times as any figure is in the multiplicand, so many rods of that species, or with that figure on the top of it, must we have, though six rods of each species will be sufficient for any example in common affairs. There must also be as many rods of 0's. But before we explain the mode of using these rods, there is another thing to be known, namely, that the figures on every rod are written in an order different from that in the table. Thus the little square space or division in which the several products of every column are written is divided into two parts by a line across from the upper angle on the right to the lower on the left; and if the product is a digit, it is set in the lower division; but if it has two places, the first is set in the lower, and the second in the upper division. The spaces on the top are not divided. There is also a rod of digits not divided, which is called the index-rod, and of this we require only one single rod.
Multiplication by Napier's Rods.—First lay down the index-rod; then on the right of it set a rod whose top is the figure in the highest place of the multiplicand; next to this again set the rod whose top is the next figure of the multiplicand, and so on in order to the first figure. Then the multiplicand is tabulated for all the nine digits; for in the same line of squares standing against every figure of the index-rod, we have the product of that figure; and therefore we have no more to do but to transfer the products and sum them. But in taking out these products from the rods, the order in which the figures stand obliges us to employ a very easy and small addition. Thus, begin to take out the figure in the lower part or units' place of the square of the first rod on the right, add the figure on the upper part of this rod to that in the lower part of the next, and
so on, which may be done as fast as we can look on them. To make this practice as clear as possible, take the following example:—To multiply 4768 by 385. Having set the rods together for the number 4768 against 5 in the index, we find this number by adding, according to the rule
To render the use of the rods yet more regular and easy, they are kept in a flat square box, the breadth of which is that of ten rods, and the length that of one rod, as thick as to contain six, or as many as may be required, the capacity of the box being divided into ten cells for the different species of rods. When the rods are put up in the box (each species in its own cell distinguished by the first figure of the rod set before it on the face of the box near the top), as much of every rod stands without the box as shows the first figure of that rod; also upon one of the flat sides without, and near the edge upon the left hand, the index-rod is fixed; and along the foot there is a small ledge, so that the rods when applied are laid upon this side, and supported by the ledge, which makes the practice very easy. But in case the multiplicand should have more than nine places, the upper face of the box may be made broader. Some make the rods with four different faces, and figures on each for different purposes.
Division by Napier's Rods.—First tabulate the divisor; then we have it multiplied by all the digits, out of which we may choose such convenient divisors as will be next less to the figures in the dividend, and write the index answering in the quotient, and so continually till the work is done. Thus 2179788 divided by 6123 gives in the quotient 356. Having tabulated the divisor 6123, we see that 6123 cannot be had in 2179; therefore take five places, and on the rods find a number that is equal or next less to 2179, which is 18369; that is, three times the divisor. Wherefore set 3 in the quotient, and subtract 18369 from the figures above, and there will remain 3428; to which add 8, the next figure of the dividend, and seek again on the rods for it, or the next less, which will be found to be five times; therefore set 5 in the quotient, and subtract 30615 from 34288, and there will remain 3673, to which add 8, the last figure in the dividend, and finding it to be just six times the divisor, set 6 in the quotient. Thus,