ton on the 3rd of April, 1617, in the sixty-eighth year of his age. That same year he had published at Edinburgh a small treatise in Latin, of about one hundred and fifty pages, which he entitled, "Rabdologiae seu Numerationis per Virgulas Libri Duo." It contained an account of a method of performing the operations of multiplication and division, by means of a number of small rods, having the digits inscribed upon them according to such an arrangement that, when placed alongside of each other in the manner directed, in order, for instance, to multiply any two lines of figures, the several lines of the product presented themselves, and had only to be transcribed and added up to give the proper result. This was not, however, nearly so convenient a contrivance as that of logarithms, even for multiplication, and it was still less useful in division; on which account it has been supposed that, although given to the world so late, it was probably an expedient which had suggested itself to Napier for the abridgment of calculation before his great invention. It has been thought, too, of so little practical utility as, in all likelihood, never to have been actually employed for the purposes of calculation *. A little tract, however, it may be remarked, appeared at London so late as the year 1684, entitled "Enneades Arithmeticæ," containing, among other things, an account of "the Numbering Rods of the Right Honourable John, Lord Nepeer, enlarged;" and this work bears to be " printed for Joseph Moxon, at the sign of the Atlas in Ludgate street, where also these numbering rods (commonly called Napier's bones) are made and sold." These rods, or bones, we may add, are what Butler alludes to in his Hudibras, where, in the account of the " rummaging of Sidrophel," he speaks of * Montucla, Histoire des Mathematiques, ii. 26. "A moon-dial, with Napier's bones, That over mortals had strange powert." It was principally, as we have seen, with a view to the simplification of operations in trigonometry that Napier proposed the logarithmic calculus. This was not the only improvement which he contributed to that branch of science. Among others, it owes to him a formula of great elegance and convenience, by which the solution of all the cases of spherical trigonometry is comprehended under a single rule. This, with several other new views in the same department of the mathematics, appeared for the first time in his second work on logarithms, published at Edinburgh, as we have already mentioned, in 1619. But his ingenious and contriving mind did not confine itself merely to speculative science, if we may believe the very curious statements which he makes with regard to some of his other inventions, in a paper with his signature, which is preserved among the manuscript collections of Anthony Bacon (the brother of the Lord Chancellor Bacon), in the archiepiscopal library at Lambeth. This paper, which has of late years been several times printed ‡, is en *A correspondent informs us that he has seen at Gartness, the place before-mentioned, globular stones with the circles of the sphere and constellations engraven on them, and concave stones with engravings of a like character, said to have been made by Napier. They were certainly not of modern date, and one is built into the wall of a mill, where it is still to be seen. Part ii. canto 3, v. 1095. See also Part iii. canto 2, v. 409. Professor Napier, of Edinburgh, who is descended from Lord Napier, is in possession of the set of bones used by his great ancestor. In Dr. Anderson's Bee, vol. iii. p. 133,-in Lord Buchan's Life of Napier, and in Tilloch's Philosophical Magazine, vol. xviii. pp. 53, &c. There is also a copy of it in the British Museum, among the MS. collections of Dr. Birch. titled "Secret Inventions, profitable and necessary in these days for the defence of this island, and withstanding of strangers, enemies to God's truth and religion." Of these, the first is stated to be " a burning mirror for burning ships by the sun's beams," of which the author professes himself able to give to the world the "invention, proof, and perfect demonstration, geometrical and algebraical, with an evident demonstration of their error who affirm this to be made a parabolic section." The second is a mirror for producing the same effect by the beams of a material fire. The third is a piece of artillery, contrived so as to send forth its shot, not in a single straight line, but in all directions, in such a manner as to destroy every thing in its neighbourhood. Of this the writer asserts that he can give "the invention and visible demonstration." The fourth and last of these formidable machines is described to be a round chariot in metal," constructed so as both to secure the complete safety of those within it, and, moving about in all directions, to break the enemy's array, "by continual charges and shot of the arquebuse through small holes." "These inventions," the paper concludes, "besides devices of sailing under the water, and divers other devices and stratagems for harassing of the enemies, by the grace of God and work of expert craftsmen, I hope to perform. John Napier, of Merchiston, anno dom. 1596, June 2." 66 From this date it would appear that Napier's head had been occupied with the contrivances here spoken of, long before he made himself known by those scientific labours by which he is now chiefly remembered; and, indeed, we might perhaps have inferred, even from the general nature of the inventions, and the object which the author avows he had in view by them, that they were the produce of that part of his life in which his apprehensions of the encroachments of popery contributed to animate his studies. Some of the announcements are certainly very extraordinary, and would almost lead us to suppose that the writer in this paper rather intended to state what he conceived to be possible, than what he had himself actually performed. Yet several of his expressions will not bear this interpretation; and there are not wanting other attestations which go to confirm what he asserts as to his having really constructed some of the machines he speaks of. There is a passage in a strange work, entitled "The Jewel," written by Sir Thomas Urquhart, and first published in 1652, which seems manifestly to allude to the third invention here enumerated. Sir Thomas, although certainly not the most veracious of authorities, would scarcely, one should think, have ventured to publish what we are now going to quote, only five and thirty years after Napier's death, if there had not been some foundation for his statement. His description may be sufficiently overcharged (for he writes, it will be observed, in an extravagantly bombastic and hyperbolical strain), without being altogether a fiction. After eulogizing Napier's mathematical learning in very high-sounding terms, Sir Thomas proceeds to remark, that he deems him especially entitled to remembrance on account of an almost incomprehensible device, which, being in the mouths of the most of Scotland, and yet unknown to any that ever was in the world but himself, deserveth very well to be taken notice of in this place; "—" and," he adds, "it is this; he had the skill (as is commonly reported) to frame an engine (for invention not much unlike that of Archytas' dove), which, by virtue of some secret springs, inward resorts, with other implements and materials fit for the purpose, inclosed within the bowels thereof, had the power, if proportionable in bulk to the action required of it (for he could have made it of all sizes), 66 to clear a field of four miles circumference, of all the living creatures exceeding a foot of height that should be found thereon, how near soever they might be to one another; by which means he made it appear that he was able, with the help of this machine alone, to kill 30,000 Turks, without the hazard of one Christian. Of this it is said that (upon a wager) he gave proof upon a large plain in Scotland, to the destruction of a great many heads of cattle and flocks of sheep, whereof some were distant from other half a mile on all sides, and some a whole mile*." It were to have been desired, certainly, that our author had been a little more particular in his description of the scene of this devastating exploit among the cattle-" a large plain in Scotland," being rather an unsatisfactory form of expression, even in reference to a country where there are not a great many large plains; but this indefinite mode of writing is only Sir Thomas's usual style. We are not inclined, indeed, to put much faith in the rumour here recorded that Napier actually put the power of his machine to the proof in the manner described; but the whole statement, taken in conjunction with what we have found the alleged inventor asserting under his own hand, seems to put it beyond doubt that he had at least imagined some such contrivance as that alluded to in the above passage, and even that his having done so was matter of general notoriety in his own day, and for some time after. Sir Thomas Urquhart was born in 1613, some years before Napier's death, and his " Jewel," was first published in 1652. Napier, he informs us, when requested on his death-bed to reveal the secret of this engine of such extraordinary potency in the destruction of cattle, sheep, and Turks, refused to do so, on * The Discovery of a most rare Jewel, &c. second edit. Edinburgh, 1774, pp. 57, 58. |