138 



H. S. CARSLAW. 



manner, that should become the logarithm of unity, and 

 10,000,000,000 that of the whole sine." And finally in the 

 Appendix we see that he often passes from logarithms of 

 sines, and now drops all reference to the radius. 



In the new system, logarithms were to be defined by the 

 relations: — 



If a : b = c : d, then nl a — nl b = nl c - nl d, 

 with nil = and nl 10 = 10 10 . 

 It need hardly be added that 10 10 was taken for the logarithm 

 of 10 instead of unity, for the same reason that 10 7 (or 10 10 ) 

 was taken for the radius in dealing with the trigonometrical 

 ratios. 



Later Briggs takes the logarithm of 10 as unity, and 

 introduces the notation of decimal fractions in his Tables, 

 a notation employed, probably for the first time, by Napier 

 himself. 



If this account of the growth of the idea of a logarithm 

 in Napier's work is correct, 1 it seems unfortunate that the 

 term Napier's logarithms is usually confined to the loga- 

 rithms 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 textbooks they receive the awkward name 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 loga- 

 rithms as those of his Canon. 



Speidell's New Logarithmes (1619). 



§ 7. In most accounts of the discovery of logarithms 

 reference is made to Speidell's Neiv Logarithmes (London, 



1 See also Gibson's paper in the Napier Tercentenary Memorial Volume, 

 pp. 111-137. 



