

; 

 the Development of his Theory. 483 



term Napier's logarithms is usually confined to the logarithms 

 of his Canon. His " better kind of logarithms " actually 

 consists of the logarithms now in daily use — the logarithms 

 which we call logarithms to the base 10. In some text-books 

 they receive the awkward name of Briggsian logarithms. 

 Certainly Briggs calculated them, and the rapidity and 

 industry with which he performed this immense work in 

 computation will always be the admiration of mathematicians. 

 But the discovery of the system was Napier's, and the 

 logarithms are as much Napier's logarithms as those of his 

 Canon. 



Speidell's New Logarithmes (1619). 



§ 7. In most accounts of the discovery of logarithms 

 reference is made to SpeidelPs ' New Logarithmes ' (London, 

 1619), and it is stated that they contain the first table of 

 logarithms to the base e *. Attention is also usually called 

 to the fact that, while logarithms to the base e are frequently 

 spoken of as Napierean logarithms, they are quite different 

 from the logarithms of Napier's Canon ; and it is pointed 

 out that the place of the number e in the theory of logarithms 

 and the possibility of defining logarithms as exponents were 

 discoveries of a much later day. These two statements, at 

 first sight, seem inconsistent. A word or two regarding 

 SpeidelPs system will make the matter clearer, and will also 

 confirm the view I have taken above as to Napier's final 

 conception of the logarithm. 



SpeidelPs ' New Logarithmes/ like Napier's Canon, refer to 

 the trigonometrical ratios. Using Glaisher's notation sl r # 

 for SpeidelPs logarithm of x when the radius is 10 r , we have 



sl r .t'=10 r+1 — nl r A\ 

 It follows that 



si,, (wo) =sl r zj-fsl r v — sl r l, 



Sl,. (ll/v) = Sl r U — sl r V + S\ r 1, 



and sl r l is not zero. 



The sole advantage of this system was that it avoided the 

 use of negative quantities in calculation with logarithms. 

 Such quantities were then outside the range of the " vulgar 

 and common arithmetic." 



* In Glaisher's paper already referred to, lie published the interesting- 

 discovery that an Appendix (1618) to Wright's English translation of 

 the Descriptio contains a table of hyperbolic logarithms by an anonymous 

 author, whom Glaisher identifies -with Oiu>htred. 



