THE INVENTION OF LOGARITHMS 197 



Descriptio. But the distinction is of no mathematical importance. 

 The one follows from the other as soon as we determine to make 

 the logarithm of unity zero. This step, which did not at first seem 

 necessary either to Napier or Buergi, was indeed first suggested 

 by Napier in his conversation with Henry Briggs as reported 

 by Briggs himself, and is no doubt part of the improvement 

 which Napier referred to in an Admonition in the Descriptio. 

 Also, according to Briggs, it was Napier who suggested taking 

 the logarithm of 10 to be equal to unity, as it is in all tables of 

 what are known as common logarithms. This choice of a new 

 base, as we now call it, effected a great practical improvement, 

 the carrying out of which we owe to the devoted labours of 

 Briggs. 



A popular notion which long held sway was that Napier in- 

 vented a system of logarithms which would have been of little 

 use if Briggs had not thereafter imagined and calculated an 

 infinitely superior system ; and this tradition was no doubt 

 fostered by the nomenclature adopted in many books. No 

 candid reading of the original documents could ever have led 

 to such a misconception. Napier not only gave to the world 

 the mathematical conception of the logarithmic function with 

 its practical corollary the Natural or Napierian Logarithm, but 

 he also directed Briggs to calculate the common logarithm to 

 base 10, which is what the ordinary computer is content to use 

 without troubling his mind about the niceties of transcendental 

 functions. In fact, we owe to Napier the only two systems of 

 logarithms in use. 



All this and much more will be found in the pages of the 

 Memorial Volume ; for the Congress did not limit its activities 

 to consideration merely of things logarithmic. Although his 

 chief fame rests on the discovery of the logarithm, John 

 Napier's mathematical genius had other issues. He was led to 

 construct his logarithmic tables so as to facilitate trigonometrical 

 calculations ; and although he soon found that the conception 

 of the logarithm was far wider than the original problem he set 

 before him, nevertheless in his Descriptio he demonstrates the 

 value of his method by applying it to trigonometrical questions. 

 Thus in the fourth chapter of the second book he gives his 

 Rules for Circular Parts for right-angled and quadrantal spherical 

 triangles. Again in the Constructio we find one of the celebrated 

 propositions known as Napier's Analogies, in which the angles 



