THE INVENTION OF LOGARITHMS 193 



there ; and to us nowadays it seems extraordinary that the idea 

 had not been developed in a practical form earlier than it was. 



As we shall see later, Napier's method of constructing a 

 serviceable logarithmic table for trigonometrical purposes was 

 evolved along a different line. Jobst Buergi, however, an in- 

 genious Swiss, constructed along the very lines of the example 

 just given what he called Aritmetische und Geometrische Progress 

 Tabullen. The book, which was printed six years after the 

 publication of Napier's Description is very rare; but, through 

 the kindness of the Town Library of Danzig, the members who 

 attended the Napier Tercentenary Congress had the privilege of 

 seeing one of the few copies extant. In the Bibliography of 

 Books Exhibited at the Celebration which Prof. Sampson con- 

 tributes to the Memorial Volume a clear account is given of 

 the mode of construction of the Progress Tabullen. Beginning 

 with the number 100,000,000, Buergi constructed a geometrical 

 progression with constant ratio roooi. The corresponding 

 terms in the associated arithmetical progression are o, 10, 20, 30, 

 etc., the constant difference being 10. The numbers of this latter 

 series are distinguished by being printed red. They correspond 

 to what we now call logarithms. Thus in Buergi's table we 

 may regard the logarithms as proceeding by a constant difference 

 ten (or by unity if we drop the unnecessary zero) and the 

 corresponding numbers by a constant multiple roooi. By this 

 means the tabulated numbers were near enough together to 

 make the table useful as an antilogarithmic table through a 

 considerable range. It has, however, conspicuous limitations 

 in comparison even with Napier's original form. 



When we turn to Napier's Mirifici Logarithmorum Canonis 

 Descriptio (of which the title page is here reproduced) we 

 come into touch with a new order of thought. In this book 

 the word Logarithm is coined, its meaning explained, and its 

 uses illustrated. But there is no account of the method of 

 calculation of the tabulated numbers which give the logarithms 

 of the trigonometrical sines of angles. For this information we 

 must have recourse to the Constructio, which was published after 

 Napier's death in 1819. It is abundantly evident that the Con- 

 structio was written before the Descriptio, probably many years 

 earlier; and the calculations themselves must have been com- 

 pleted before even the Constructio was composed. 



Now, according to Lord Moulton's theory, Napier seems to 



