154 SCIENCE PROGRESS 



papers perished in a fire which broke out in the house of one 

 of his descendants ; in consequence, Mark Napier's monumental 

 life of his ancestor is largely composed, so far as the facts of 

 the life go, of conjecture. What can be rescued from the mass 

 of hypothesis may be briefly condensed as follows : Born, as 

 stated above, in 1550, he was educated at St. Salvator's College, 

 St. Andrews. It is believed that he travelled on the Con- 

 tinent during several years but he was certainly at home again 

 in 1 571. Little is known of the details of his home life, save 

 that for years his attention was drawn, like Newton's, to specu- 

 lative theology. The results of these studies are shown in 

 his treatise, A Plaine Discovery of the Whole Revelation of 

 St.fohn, published in 1593. About this time he seems to have 

 made some progress towards his great discovery, for we are 

 told, on the authority of Kepler, that about this time Tycho 

 Brahe had heard from a Scottish correspondent that a canon 

 or table of such aids to computation was in process of con- 

 struction. The canon itself was not published until 1614, when 

 it appeared under the title of Mirifici Logarithmorum Canonis 

 Descriptio. Napier died in 1617; two years afterwards the 

 posthumous work Mirifici Canonis Logarithmorum Constructio 

 was published, which explains the manner in which Napier 

 constructed his canon. 



It is a remarkable fact in the history of scientific discovery 

 that Napier's great work sprang, Minerva-like, in full per- 

 fection from the head of its discoverer. In the development 

 of the discovery of the infinitesimal calculus, we find all through 

 the seventeenth century foreshadowings in the writings of 

 Cavalieri, Roberval, Barrow and others of the comprehensive 

 calculus finally developed by Newton and Leibniz. But with 

 one solitary exception and that exception as old as the days 

 of Archimedes, we find nothing to show that Napier's dis- 

 covery was the culmination of a series of stages leading up to 

 that point. The discovery was almost perfectly self-contained. 



The exception referred to above is to be found in Archimedes' 

 treatise Arenarius, an attempt to extend the cumbrous Greek 

 numerical notation so as to include integral numbers of 

 extremely large magnitude. With the structure of this treatise 

 we need not here concern ourselves. What is important to our 

 purpose is to note that Archimedes incidentally develops 

 therein some properties of geometrical progressions, one of 



