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 parts 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; 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 its 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 figures, 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 4785 by 385. Having set the rods together for the number 4785 against 5 in the index, we find this number by adding, according to the rule

\[ \begin{align*} \text{Against } 5, \text{ this number} & = 38144 \\ \text{Against } 3, \text{ this number} & = 14304 \\ \end{align*} \]

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 two rods, and the length that of one rod, as thick as to contain six, 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 multiplication 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 21797, 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,

\[ 6123 \times 2179788 = 356. \]

Napier, Macreey, descended from an ancient and respectable family in the west of Scotland, was born in 1776. He received his elementary education in the public school of his native parish; and subsequently studied in the Universities of Glasgow and Edinburgh, at both of which he attracted the favourable notice of some of the most distinguished professors. Being destined for the profession of the law, he was apprenticed to a member of the Society of Writers to the Signet. But the literary and philosophical studies to which he had early attached himself, withdrew his attention from the less interesting though more lucrative business of the law; and he speedily began to regard the latter as being, in his case at least, subsidiary only to his advancement in the former.

When yet very young, he was elected to the responsible situation of librarian to the Writers to the Signet. In this capacity Napier discovered an extensive knowledge of books, and a judicious discrimination in the selection of those best suited to the establishment over which he presided. At a subsequent period, the Writers to the Signet gave a marked proof of the increased estimation in which he was held, by selecting him for a lectureship on conveyancing, founded by the society, and shortly afterwards converted into a professorship in the university of Edinburgh. When the late Mr Constable purchased, in 1814, the copyright of the Encyclopaedia Britannica, he at once fixed upon Napier as the individual best qualified to carry into effect the great improvements he projected in that publication. He was not disappointed in his expectations; and it is not going too far to say that the appearance of the Supplement to the Encyclopaedia Britannica, edited by Napier, forms a memorable era in the history of British literature. Such was the confidence placed in the discretion and good taste of the editor, that the names of a host of individuals distinguished for learning, philosophy, and science are to be found among the contributors to this great work; which in consequence became the depository of a lengthened series of original and profound disquisitions in most departments of human knowledge.

The experience he had acquired in conducting the Supplement, his extended acquaintance with literature and literary men, and the confidence placed in him by the latter, naturally pointed Napier out as the proper, or rather as the only, person to undertake the task of editing a new edition of the Encyclopaedia itself which should be worthy of the age and of the country. The misfortunes by which Mr Constable was unhappily overtaken made no change in this respect. The proposed edition was completed under its present publishers on the same scale on which it had been originally projected.

A vacancy in the situation of principal clerk of session having occurred some time after, when the Whig party came into power in 1830, Napier was appointed to the vacant place; and on receiving this appointment, he resigned his office of librarian.

Mr Napier had for a lengthened period been an occasional contributor to the Edinburgh Review; and on the appointment of Jeffrey to be dean of the Faculty of Advocates in 1829, he succeeded him as editor. Though he wrote little himself; his contributions are remarkable for ability, research, and perspicuity of statement; and he commanded in a high degree the confidence and esteem of those whose assistance was most necessary to sustain and extend the reputation of the leading Whig journal. Those who knew Napier only through the works he edited, or even through his lectures, could form no just idea of the man. He was at once a firm, an intelligent, and an honest friend.

For many years previously to his death, his health was very indifferent, and he occasionally suffered much. But his habitual cheerfulness never forsook him; and he continued to the last in the full enjoyment of his intellectual powers and of the society of his friends. He died in his seventy-first year, on the 11th February 1847.