NAPIER, JOHN, Baron of Merchiston in Scotland, and the inventor of the Logarithms, was the eldest son of Sir Archibald Napier of Edinbush and Merchiston, by his first wife Janet Bothwell, and was born near Edinburgh, in the year 1550. Having given early indications of great natural parts, his father was careful to have them cultivated by a learned education. After passing through the ordinary
courses of liberal study at the University of St Andrews, he is said to have made the tour of France, Italy, and Germany. Upon his return to his native country, his literature and other accomplishments soon rendered him conspicuous, and might have raised him to the highest offices of the state; but declining all civil employments, and avoiding the bustle of the court, he retired from active life to pursue scientific and literary researches, in which he made such uncommon progress, as to favour mankind with divers useful discoveries. He applied himself chiefly to the study of mathematics, and to that of the Holy Scriptures; and in regard to both, he has evinced the most extensive knowledge and profound penetration. His Commentaries upon the Apocalypse indicate the most acute investigation, and an uncommon strength of judgment; and though time has discovered that his calculations concerning particular events proceeded upon fallacious data, his reasonings are not on that account the less ingenious. This work was printed abroad in several languages; particularly in French at Rochelle in the year 1602, in a quarto volume, announced in the title as revised by himself. Nothing, it has been observed, could be more agreeable to the people of Rochelle, or the Huguenots of France, at this time, than the author's annunciation of the pope as antichrist, which in this book he has endeavoured to set forth with much zeal and erudition. But what has rendered his name for ever illustrious was his great and fortunate discovery of the logarithms, by which the science of astronomy and the arts of practical geometry and navigation have been wonderfully aided and advanced. 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 Neperianam 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 Oxoniensis, and explains it in a way perfectly consonant to the rights of Napier as the inventor.
When Napier had communicated to Mr Henry Briggs, mathematical professor in Gresham College, his wonderful Canon for the Logarithms, that learned professor set himself to apply the rules in his Imitatio Neperæ; 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 Napier. 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 Hoennburg. This passage occurs in Gassendi's observations on a letter from Tycho to Herwart, written on the last day of August 1599. "Dixit Hervatus nihil morari se solvendi cujusquam trianguli difficultatem; solere se enim multiplicationum ac divisionum vice additiones solum, subtractiones 93 usurpare quod ut fieri posset, docuit postmodum suo logarithmorum Canone Neperus." But Herwart here alludes to the work afterwards published in the year 1610, which solves triangles by prostapheresis, a mode totally different from that of the 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. "And, indeed," to use the words of one of his biographers, "if we consider that Napier's discovery was not, like those of Kepler or of Newton, connected with any analogies or coincidences which might have led him to it, but the fruit of unassisted reason and science, we shall be vindicated in placing him in one of the highest niches in the temple of fame. Kepler had made many unsuccessful attempts to discover his canon for the periodic motions of the planets, and hit upon it at last, as he himself candidly owns, on the 15th of May 1618; and Newton applied the palpable tendency of heavy bodies to the earth to the system of the universe in general; but Napier sought out his admirable rules by a slow scientific progress, arising from the gradual evolution of truth." But to quote this, or any other similar observations of an ordinary biographer, may here be considered as worse than superfluous; for the Dissertation on the History of Mathematical and Physical Science, by the late Professor Playfair, prefixed to this work, contains a view of the nature and value of Napier's great discovery, and the character of his genius, which at once satisfies scientific curiosity, and throws into the shade all the slighter sketches of less weighty authorities.
The last literary exertion of this eminent person was the publication, in the year 1617, of his Rabdology and Promptuary, which he dedicated to the Chancellor Seton, and soon afterwards died at Merchiston, on the 4th of April of the same year, in the sixty-eighth year of his age.
This renowned discoverer was twice married. By his first wife, who was a daughter of Sir James Stirling of Keir, he had only one son, named Archibald. He was appointed a privy counsellor 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 the 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. The biographical notice in the preceding editions of this work seems to have been compiled from the former; and we have not seen reason to make any material change, particularly as the Dissertation above referred to, and the article LOGARITHMS, contain all that is most deserving of attention in regard to the life of this great man. It may, however, be proper to subjoin a correct list of his different publications.
1. A plaine Discovry 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 Napeir L. of Marchistoun 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-meme"), 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 Andreae Hart, 1614, 4to.
3. Rabdologie, seu Numerationis per Virgulas libri duo: cum Appendice de expeditissimo Multiplicationis Promptuario. Quibus accessit et Arithmetice Localis liber unus. Edinburgh, excudebat Andreas Hart, 1617, 12mo. Reprinted at Lyons in 1626, and again in 1628, 12mo.
4. Mirifici Logarithmorum Canonis Constructio, et eorum ad naturales ipsorum numeros habitudines; una cum Appendice, de alia eaque praestantiore Logarithmorum specie condenda. Quibus accessere Propositiones ad triangula sphaerica 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 Maseres's large collection entitled "Scriptores Logarithmici," vol. vi.; London, 1807, 4to.
It is not necessary to specify the English translations or other works illustrative of these several publications.
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 (fig. 2) against 5 in the index, we find this number by adding, according to the rule.
Total product..... 1835680
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 five 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 six in the quotient. Thus,