THE INVENTION OF LOGARITHMS 191 



those which treat directly of Napier himself or of his work, and 

 those which have regard to mathematical developments and 

 applications more or less closely associated with the loga- 

 rithmic idea connected with the name of Napier. 



When the Royal Society of Edinburgh announced the 

 intention of holding a Tercentenary Celebration, a widespread 

 interest was aroused all over the civilised globe. A few 

 biographical sketches of real value were prepared by mathe- 

 maticians of reputation ; and in many journals and newspapers 

 there appeared articles on the life, character, and deeds 

 of the ingenious Baron of Merchiston. These but served to 

 increase the interest in the coming celebration, in spite of the 

 general feeling that all that was worth saying had been said long 

 ago concerning Napier and logarithms. It was difficult to 

 imagine that after three hundred years there could be anything 

 to add to our knowledge of what Napier did and how he did it. 



Nevertheless in his opening address Lord Moulton showed 

 that there was still a problem to solve in regard to the genesis 

 and growth of the conception of the logarithm. In other words, 

 how are we to connect the very remarkable manner in which 

 Napier presented his definition of the logarithm with the mathe- 

 matical conceptions of his time ? This was Lord Moulton's 

 theme, and his treatment of it forms the first contribution to the 

 Memorial Volume. Other papers, notably those by Dr. Glaisher, 

 Prof. Eugene Smith, Prof. G. A. Gibson, and Prof. Florian Cajori, 

 take up other historic aspects of the evolution of the logarithm. 

 Though not intended by their authors to be in any strict sense 

 novel, these are all fresh discussions by master hands ; and we 

 may safely regard this group of historical essays as containing 

 the most accurate account yet presented of Napier's great work. 



There had crept into the popular accounts of Napier and his 

 work certain inaccuracies which it is hoped will be once and for 

 ever disposed of. Such inaccuracies, copied slavishly by one 

 " authority " after another, die hard ; and it is only by going back 

 to the originals that the real facts can be established. 



Now there are three aspects in which Napier's invention 

 should be considered, if a true idea of the greatness of his work 

 is to be gained. First, there is the general conception, which 

 Napier shared with others of his time, that arithmetical opera- 

 tions might be simplified by suitable tabulations. Secondly 

 there is the particular method by which Napier realised the first 



