Born at Merchiston, near Edinburgh, 1550: died there, April 4, 1617. A Scottish mathematician, famous as the inventor of logarithms. He was the eldest son of Archibald, the seventh Napier of Merchiston, hereditary justice-general of Scotland. He matriculated at St. Salvator’s College, St. Andrews, in 1563, and probably completed his education at the University of Paris. His “Mirifici logarithmorum canonis descriptio,” in which his discovery was announced, appeared in 1614. Napier’s bones or rods, constructed to simplify multiplication and division, were introduced in the “Rabdologia” (1617). The “Constructio,” or method by which the canon was constructed, was published in 1619 by his son Robert, edited by Henry Briggs.

  This admirable invention added to the ingenious algorithm of the Indians, by reducing to a few days the labour of several months, doubles—if we may so speak—the life of astronomers, and spares them the errors and disgust inseparable from long calculations; an invention, too, which is the more satisfying to the human mind from its having been entirely deduced from its own resources. In the arts man makes use of the materials and the forms of nature to increase his powers; but in this case it is all his own work.

  Many inventions have been eclipsed or obscured by new discoveries, or they have been so altered by subsequent improvements that their original form can hardly be recognized, and, in some instances, has been entirely forgotten. This has almost always happened to the discoveries made at an early period in the progress of science, and before their principles were fully unfolded. It has been quite otherwise with the invention of logarithms, which came out of the hands of the author so perfect that it has never yet received but one material improvement—that which it derived, as has just been said, from the ingenuity of his friend in conjunction with his own. Subsequent improvements in science, instead of offering anything that could supplant this invention, have only enlarged the circle to which its utility extended. Logarithms have been applied to numberless purposes which were not thought of at the time of their first construction. Even the sagacity of the author did not see the immense fertility of the principle he had discovered: he calculated his tables merely to facilitate arithmetical, and chiefly trigonometrical computation; and little imagined that he was at the same time constructing a scale whereon to measure the density of the strata of the atmosphere and the heights of mountains, that he was actually computing the areas and the lengths of innumerable curves, and was preparing for a calculus which was yet to be discovered many of the most refined and most valuable of its resources. Of Napier, therefore, if of any man, it may safely be pronounced, that his name will never be eclipsed by any one more conspicuous, or his invention be superseded by anything more valuable.

  The invention of logarithms is one of the rarest instances of sagacity in the history of mankind; and it has been justly noticed as remarkable, that it issued complete from the mind of its author, and has not received any improvement since his time.

  We have few examples, indeed, of truly great men pursuing simultaneously their own peculiar studies and the critical examination of the Scriptures. The most illustrious have been the ornaments of our own land, and England may well be proud of having had Napier, and Milton, and Locke, and Newton, for the champions both of its faith and its Protestantism.

  Napier’s great invention of logarithms has from his own day to the present hour been one of the most active and efficient servants of all the sciences dependent upon calculation; nor could those of them in which the most splendid triumphs have been achieved have possibly been carried to the height they have reached without its assistance.

  The more one considers the condition of science at the time, and the state of the country in which the discovery took place, the more wonderful does the invention of logarithms appear. When algebra had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known. It is to be noticed also that the invention was not the result of any happy accident.

  Napier appears, in the fragmentary records that have survived, as a man both just in his dealings with his neighbours and firmly resolved to obtain like justice from them. In his disputes with his father, his step-brothers, the Grahams of Boquhopple, and the magistrates of Edinburgh, he seems invariably to have carried his point. He was a strict Calvinist, and a resolute opponent of papal aggression. His powerful intellect and determined will are best indicated in his prolonged and successful efforts to facilitate numerical calculation which resulted in his discovery of logarithms. The advantage of a table of logarithms are that by its employment multiplication and division can be performed by simple addition and subtraction, the extraction of the roots of numbers by division, and the raising of them to any power by multiplication. By these simple processes the most complicated problems in astronomy, navigation, and cognate sciences can be solved by an easy and certain method. The invention necessarily gave a great impulse to all the sciences which depend for their progress on exact computation. Napier’s place among great originators in mathematics is fully acknowledged, and the improvements that he introduced constitute a new epoch in the history of the science. He was the earliest British writer to make a contribution of commanding value to the progress of mathematics.