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 rather than a labour, for, by means of it, addition, subtraction, multiplication, division and even the extraction of roots are accomplished simply by the motion of counters. He adds that he has appended it to the Rabdologia, in addition to the promptuary, because he did not wish to bury it in silence nor to publish so small a matter by itself. With respect to the calculating rods, he mentions in the dedication that they had already found so much favour as to be almost in common use, and even to have been carried to foreign countries; and that he has been advised to publish his little work relating to their mechanism and use, lest they should be put forth in some one else’s name.

John Napier died on the 4th of April 1617, the same year as that in which the Rabdologia was published. His will, which is extant, was signed on the fourth day before his death. No particulars are known of his last illness, but it seems likely that death came upon him rather suddenly at last. In both the Canonis descriptio and the Rabdologia, however, he makes reference to his ill-health. In the dedication of the former he refers to himself as “mihi jam morbis pene confecto,” and in the “Admonitio” at the end he speaks of his “infirma valetudo”; while in the latter he says he has been obliged to leave the calculation of the new canon of logarithms to others “ob infirmam corporis nostri valetudinem.”

It has been usually supposed that John Napier was buried in St Giles’s church, Edinburgh, which was certainly the burial-place of some of the family, but Mark Napier (Memoirs, p. 426) quotes Professor William Wallace, who, writing in 1832, gives strong reasons for believing that he was buried in the old church of St Cuthbert.

Professor Wallace’s words are—

There can be no doubt that Napier’s devotion to mathematics was not due to old age and the gout, and that he died in 1617 and not in 1616; still these sentences were written within eighteen years of Napier’s death, and their author seems to have had some special sources of information. Additional probability is given to Hume’s assertion by the fact that Merchiston is situated in St Cuthbert’s parish. It is nowhere else recorded that Napier suffered from the gout. It has been stated that Napier’s mathematical pursuits led him to dissipate his means. This is not so, for his will (Memoirs, p. 427) shows that besides his large estates he left a considerable amount of personal property.

The Canonis Descriptio on its publication in 1614, at once attracted the attention of Edward Wright, whose name is known in connexion with improvements in navigation, and Henry Briggs, then professor of geometry at Gresham College, London. The former translated the work into English, but he died in 1615, and the translation was published by his son Samuel Wright in 1616. Briggs was greatly excited by Napier’s invention and visited him at Merchiston in 1615, staying with him a whole month; he repeated his visit in 1616 and, as he states, “would have been glad to make him a third visit if it had pleased God to spare him so long.” The logarithms introduced by Napier in the Descriptio are not the same as those now in common use, nor even the same as those now called Napierian or hyperbolic logarithms. The change from the original logarithms to common or decimal logarithms was made by both Napier and Briggs, and the first tables of decimal logarithms were calculated by Briggs, who published a small table, extending to 1000, in 1617, and a large work, Arithmetica Logarithmica, containing logarithms of numbers to 30,000 and from 90,000 to 100,000, in 1624. (See .)

Napier’s Descriptio of 1614 contains no explanation of the manner in which he had calculated his table. This account he kept back, as he himself states, in order to see from the reception met with by the Descriptio, whether it would be acceptable. Though written before the Descriptio it had not been prepared for press at the time of his death, but was published by his son Robert in 1619 under the title Mirifici Logarithmorum Canonis Constructio. In this treatise (which was written before Napier had invented the name logarithm) logarithms are called “artificial numbers.”

The different editions of the Descriptio and Constructio, as well as the reception of logarithms on the continent of Europe, and especially by Kepler, whose admiration of the invention almost equalled that of Briggs, belong to the history of s (q.v.). It may, however, be mentioned here that an English translation of the Constructio of 1619 was published by W. R. Macdonald at Edinburgh in 1889, and that there is appended to this edition a complete catalogue of all Napier’s writings, and their various editions and translations, English and foreign, all the works being carefully collated, and references being added to the various public libraries in which they are to be found.

Napier’s priority in the publication of the logarithms is unquestioned and only one other contemporary mathematician seems to have conceived the idea on which they depend. There is no anticipation or hint to be found in previous writers, and it is very remarkable that a discovery or invention which was to exert so important and far-reaching an influence on astronomy and every science involving calculation was the work of a single mind.

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 deliberately set himself to abbreviate multiplications and divisions—operations of so fundamental a character that it might well have been thought that they were in rerum natura incapable of abbreviation; and he succeeded in devising, by the help of arithmetic and geometry alone, the one