sacT. i.] DISSERTATION SECOND. 11 



which its utility extended. Logarithms have been ap- 

 plied to numberless purposes, which were not thought of at 

 the time of their first construction. Even the sagacity of 

 their author did not see the immense fertility of the prin- 

 ciple he had discovered ; he calculated his tables merely to 

 facilitate arithmetical, and chiefly trigonometrical computa- 

 tion, and little imagined that he was at the same time con- 

 structing a scale whereon to measure the density of the 

 strata of the atmosphere, and the heights of mountains ; that 

 he was actually computing the areas and the lengths of in- 

 numerable curves, and was preparing for a calculus which 

 was yet to be discovered, many of the most refined and most 

 valuable of its resources. Of Napier, therefore, if of any 

 man, it may safely be pronounced, that hi& name will never 

 be eclipsed by any one more conspicuous, or his invention 

 superseded by any thing more valuable. 



As a geometrician, Napier has left behind him a noble 

 monument in' the two trigonometrical theorems, which are 

 known by his name, and which appear first to have been 

 communicated in writing to Cavalleri, who has mentioned 

 them with great eulogy.' They are theorems not a little 

 difficult, and of much use, as being particularly adapted to 

 logarithmick calculation. They were published in the 

 Canon Mirificus Logarithmornm, at Edinburgh, in 1614. 2 



1 Wallis, Opera Math. Tom. II. p. 875. 



2 A reprint of the Canon Mirificus, from the original edition, 

 is given in the 6th volume ol the great Thesaurus, in which Ba- 

 ron Maseres, with his usual zeal and intelligence, has collected 

 and illustrated ever}' thing of importance that has been written on 

 the subject of logarithms. See Scriptorcs Logarithmici, 4to. vol. 

 VI. p. 475. 



