136 H. S. CARSLAW. 



of a geometrical series and the terms of an arithmetical 

 series was left far behind. This is the third and final stage 

 of his work. 



Briggs and Napier. 



§ 5. In the change from the logarithms of the Canon to 

 this "better kind of logarithms" Briggs was associated 

 with Napier; but, chiefly because of the unsatisfactory 

 account of the matter given by Hutton in his History of 

 Logarithms, 1 the share of the former in the discovery has 

 been exaggerated. The fault is not due to Briggs; and, 

 though his reference to the question in the preface to the 

 Arithmetica Logarithmica (1624) is familiar, I reproduce 

 it again here: — 



"I myself, when expounding publicly in London their doctrine 

 to my auditors in Gresham College, remarked that it would be 

 much more convenient that should stand for the logarithm of 

 the whole sine, as in the Canon Mirificus, but that the logarithm 

 of the tenth part of the whole sine, that is to say, 5 degrees 44 

 minutes 21 seconds, should be 10,000,000,000. Concerning that 

 matter I wrote immediately to the author himself; and as soon as 

 the season of the year and the vacation time of my public duties 

 of instruction permitted, I took journey to Edinburgh, where, 

 being most hospitably received by him, I lingered for a whole 

 month. But as we held discourse concerning this change in the 

 system of logarithms, he said that for a long time he had been 

 sensible of the same thing, and had been anxious to accomplish 

 it, but that he had published those he had already prepared, until 

 he could construct tables more convenient, if other weighty 

 matters and his frail health would permit him to do. But he 

 conceived that the change ought to be affected in this manner, 

 that should become the logarithm of unity, and 10,000,000,000 

 that of the whole sine; which I could not but admit was by far the 

 most convenient of all. So, rejecting those which I had already 



1 Hutton's Tracts on Mathematical and Philosophical Subjects, Vol. I, 

 Tract 20. 



