JohrrNapier 7 



of logarithms, and gave to the world a method by means 

 of which multiplication is converted into addition, division 

 into subtraction, and the extraction of square or cube root 

 into a division by two or three respectively. The scientific 

 merit of introducing logarithmic functions into the domain 

 of mathematics is surpassed by the incalculable importance 

 of assisting the complicated numerical calculations which 

 were vital to the progress of astronomy and of other branches 

 of science. Without explaining the objects which Napier 

 primarily had in view, or the steps by which he arrived at 

 his final results, we may justify the prominent position 

 here given to him in the history of science by quoting a 

 few passages from an article contributed by Dr. J. W. L. 

 Glaisher to the " Napier Tercentenary Memorial Volume " : 

 " The process of multiplication is so fundamental 

 and direct that, from an arithmetical point of view, 

 it might well be thought to be incapable of simplifica- 

 tion or transformation into an easier process, so that 

 there would seem to be no hope of help except from 

 an apparatus. But Napier, not contented with such 

 aids, discovered by a most remarkable and memorable 

 effort of genius that such a transformation of multipli- 

 cation was possible, and he not only showed how the 

 necessary table could be calculated, but he actually 

 constructed it himself. That Napier at a time when 

 algebra scarcely existed should have done this is most 

 wonderful; he gave us the principle, the method of 

 calculation, and the finished table. 



" The ' Canon Mirificus ' is the first British contribution 

 to the mathematical sciences, and next to Newton's ' Prin- 

 cipia ' it is the most important work in the history of the 

 exact sciences that has been published in Great Britain, 

 at aJl events until within the memory of living persons. 



" In whatever country the * Canon Mirificus ' had 

 been produced, it would have occupied the same com- 

 manding position, for it announced one of the greatest 

 scientific discoveries ever made." 



Independently of his work on logarithms, Napier's con- 

 tributions to spherical trigonometry would alone have 

 secured him a high position among mathematicians. 



