In 1617 Napier published his Rabdologia, 4 a duodecimo of one hundred and fifty-four pages; there is prefixed to it as preface a dedicatory epistle to the high chancellor of Scotland.
The method which Napier terms "Rabdologia" consists in the use of certain numerating rods for the performance of multiplications and divisions.
In the Rabdologia he gives the chronological order of his inventions.
In the preface to the appendix containing the local arithmetic he states that, while devoting all his leisure to the invention of these abbreviations of calculation, and to examining by what methods the toil of calculation might be removed, in addition to the logarithms, rabdologia and promptuary, he had hit upon a certain tabular arithmetic, whereby the more troublesome operations of common arithmetic are performed on an abacus or chess-board, and which may be regarded as an amusement A facsimile of this document is given by Mark Napier in his Memoirs of John Napier (1834), p. 248.
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.
John Napier died on the 4th of April 1617, the same year as that in which the Rabdologia was published.
In both the Canonis descriptio and the Rabdologia, however, he makes reference to his ill-health.
These treatises were probably composed before Napier had invented the logarithms or any of the apparatuses described in the Rabdologia; for they contain no allusion to the principle of logarithms, even where we should expect to find such a reference, and the one solitary sentence where the Rabdologia is mentioned ("sive omnium facillime per ossa Rhabdologiae nostrae") was probably added afterwards.
The Rabdologia attracted more general attention than the logarithms, and as has been mentioned, there were several editions on the Continent.
Napier also describes in the Rabdologia two other larger rods to facilitate the extraction of square and cube FIG.
In the Rabdologia the rods are called "virgulae," b'ut in the passage quoted above from the manuscript on arithmetic they are referred to as "bones" (ossa).
In the Rabdologia Napier gives an "Admonitio pro Decimali Arithmetica," in which he commends the fractions of Stevinus and gives an example of their use, the division of 861094 by 43 2.
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.
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 Ioo,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 multo praestantiorem nunc etiam invenimus, & creandi methodum, una 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 vero doctissimo viro D.
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 o.
To complete the early history of logarithms it is necessary to return 1 In the Rabdologia (1617) he speaks of the canon of logarithms as " a me longo tempore elaboratum."