the Development of his Theory. 481 



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 accom- 

 plish 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 

 so to do. But he conceived that the change ought to be 

 effected in this manner, that should become the logarithm 

 of unity, and 10,000,000,000 that uf the whole sine ; which 

 I could not but admit was by far the most convenient of all. 

 So, rejecting those which I had already prepared, I com- 

 menced, under his encouraging counsel, to ponder seriously 

 about the calculation of these tables." 



Napier also mentions his discovery of the new system in 

 the dedication of his Rahdologia (1617) in a passage quoted 

 in my previous paper *. 



It will be seen from Briggs's own words that the modi- 

 fication which he suggested to Napier was to keep the 

 logarithm of the radius as zero, but to take the logarithm of 

 one-tenth of the radius as 10,000,000,000. His reference 

 to the Canon is sufficient to show that he does not look upon 

 the radius as unity. In the construction of the Tables of 

 Logarithms, after Napier's death, he takes it as 10 10 , and it 



* See also Macdonald's English translation of the Construetio, p. 88. 

 This paper may be regarded as a supplement to a paper entitled " The 

 Discovery of Logarithms by Napier of Merchiston," Journ. of Proc. Kov. 

 Soc. N.S.W. vol. xlviii. p. 43 (1914), which deals chiefly with the 

 construction of Napier's Canon. I take this opportunity of amplifying-, 

 and to some extent correcting, the references in that paper to Briggs's 

 share in the discovery of the " better kind of logarithms." A paper 

 covering much the same ground as the above will 'be found in 'The 

 Mathematical Gazette,' vol. viii. (1915). 



