158 SCIENCE PROGRESS 



course, mainly to be ascribed to the early introduction of the 

 more convenient tables computed to the base 10. 



Three editions of the Descriptio were published in the years 

 1614, 1619 and 1620 respectively; an English translation by 

 Edward Wright was published in 1616; a retranslation, to- 

 gether with a table of hyperbolic logarithms, was published 

 in Edinburgh in 1857. A reprint of the Latin text is to be 

 found in the sixth volume of Baron Francis Maseres' massive 

 compilation entitled Scriptores Logarithm ci. (Dates of publica- 

 tion 1791-1807.) 



The Constructio is much less accessible. After the first 

 (Edinburgh) edition of 1619 the only other edition of the 

 Latin text was printed at Lyons in 1620. In 1889, however, 

 a careful translation into English was issued by W. R. Mac- 

 donald, to which was added a very full and complete biblio- 

 graphy of Napier's published works. 



The Constructio was printed in the form of a sequence of 

 propositions, some sixty in number. Starting with a definition 

 of progressions, both arithmetical and geometrical, Napier 

 lays down, in very clear fashion, various rules for obtaining 

 accuracy in computation, e.g. the taking of a large radius in 

 order to get a larger number of significant figures in the 

 numbers for both sines and logarithms ; and, equally important, 

 the annexing to the radius of a number of cyphers following 

 a decimal point, the figures following the decimal point being 

 discarded in the final tables. As Napier expresses himself in 

 Proposition IV., " Thus, in commencing to compute, instead 

 of 10,000,000 we put io,ooo,ooo - ooooooo lest the most minute error 

 should become very large by frequent multiplication." 1 



Then follows a clear discussion on the limits of accuracy 

 obtainable in adding, subtracting, multiplying and dividing 

 two numbers whose limits of accuracy are given and, beginning 

 with Proposition XIII., the methods of forming "easy" geo- 

 metrical progressions are carefully discussed. 



Propositions XVI. — XXI. are concerned with the formation 

 of three tables of fundamental importance. The First Table 

 is a geometrical progression of 100 terms, of which radius 

 forms the first term, consecutive terms being in the proportion 



1 0000000 radius 

 9999999 radius - 1' 



1 Constructio, Prop. IV. 



