calculation of the tables. It now remains to refer in more detail to the invention itself and to examine the claims of Napier and Briggs to the capital improvement involved in the change from Napier’s original logarithms to logarithms to the base 10.

The Descriptio contained only an explanation of the use of the logarithms without any account of the manner in which the canon was constructed. In an “Admonitio” on the seventh page Napier states that, although in that place the mode of construction should be explained, he proceeds at once to the use of the logarithms, “ut praelibatis prius usu, et rei utilitate, caetera aut magis placeant posthac edenda, aut minus saltem displiceant silentio sepulta.” He awaits therefore the judgment and censure of the learned “priusquam caetera in lucem temerè prolata lividorum detrectationi exponantur”; and in an “Admonitio” on the last page of the book he states that he will publish the mode of construction of the canon “si huius inventi usum eruditis gratum fore intellexero.” Napier, however, did not live to keep this promise. In 1617 he published a small work entitled Rabdologia relating to mechanical methods of performing multiplications and divisions, and in the same year he died.

The proposed work was published in 1619 by Robert Napier, his second son by his second marriage, under the title Mirifici logarithmorum canonis constructio.... It consists of two pages of preface followed by sixty-seven pages of text. In the preface Robert Napier says that he has been assured from undoubted authority that the new invention is much thought of by the ablest mathematicians, and that nothing would delight them more than the publication of the mode of construction of the canon. He therefore issues the work to satisfy their desires, although, he states, it is manifest that it would have seen the light in a far more perfect state if his father could have put the finishing touches to it; and he mentions that, in the opinion of the best judges, his father possessed, among other most excellent gifts, in the highest degree the power of explaining the most difficult matters by a certain and easy method in the fewest possible words.

It is important to notice that in the Constructio logarithms are called artificial numbers; and Robert Napier states that the work was composed several years (aliquot annos) before Napier had invented the name logarithm. The Constructio therefore may have been written a good many years previous to the publication of the Descriptio in 1614.

Passing now to the invention of common or decimal logarithms, that is, to the transition from the logarithms originally invented by Napier to logarithms to the base 10, the first allusion to a change of system occurs in the “Admonitio” on the last page of the Descriptio (1614), the concluding paragraph of which is “Verùm si huius inventi usum eruditis gratum fore intellexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia, limatior tandem et accuratior, quàm unius opera fieri potuit, in lucem prodeat. Nihil in ortu perfectum.” In some copies, however, this “Admonitio” is absent. In Wright’s translation of 1616 Napier has added the sentence—“But because the addition and subtraction of these former numbers may seeme somewhat painfull, I intend (if it shall please God) in a second Edition, to set out such Logarithmes as shall make those numbers above written to fall upon decimal numbers, such as 100,000,000, 200,000,000, 300,000,000, &c., which are easie to be added or abated to or from any other number” (p. 19); and in the dedication of the Rabdologia (1617) he wrote “Quorum quidem Logarithmorum speciem aliam multò praestantiorem nunc etiam invenimus, & creandi methodum, unà cum eorum usu (si Deus longiorem vitae & valetudinis usuram concesserit) evulgare statuimus; ipsam autem novi canonis supputationem, ob infirmam corporis nostri valetudinem, viris in hoc studii genere versatis relinquimus: imprimis verò doctissimo viro D. Henrico Briggio Londini publico Geometriae Professori, et amico mihi longè charissimo.”

Briggs in the short preface to his Logarithmorum chilias (1617) states that the reason why his logarithms are different from those introduced by Napier “sperandum, ejus librum posthumum, abunde nobis propediem satisfacturum.” The “liber posthumus” was the Constructio (1619), in the preface to which Robert Napier states that he has added an appendix relating to another and more excellent species of logarithms, referred to by the inventor himself in the Rabdologia, and in which the logarithm of unity is 0. He also mentions that he has published some remarks upon the propositions in spherical trigonometry and upon the new species of logarithms by Henry Briggs, “qui novi hujus Canonis supputandi laborem gravissimum, pro singulari amicitiâ quae illi cum Patre meo L. M. intercessit, animo libentissimo in se suscepit; creandi methodo, et usuum explanatione Inventori relictis. Nunc autem ipso ex hâc vitâ evocato, totius negotii onus doctissimi Briggii humeris incumbere, et Sparta haec ornanda illi sorte quadam obtigisse videtur.”

In the address prefixed to the Arithmetica logarithmica (1625) Briggs bids the reader not to be surprised that these logarithms are different from those published in the Descriptio:—