' Memoirs of John Napier of Merclmion. 275 



to be unsparingly worked out to the close, without being ex- 

 cused a single figure in the largest numbers, — we may very well 

 understand how the universal desire of mathematicians was bent 

 upon their delivery from this grievous burden, and that the ne- 

 cessity of the case should suggest a thousand means, more or 

 less perfect, for removing it. But, for that purpose, Napier 

 alone has given us — has published the logarithms ; no one, be- 

 fore his time or since his day, has hit upon any invention equal 

 to this for the purpose ; and it alone serves us still, with- 

 out permitting us to feel a desire or necessity for any other. 

 By that charter, his right of inventor, of sole inventor, is incon- 

 testable. But that right becomes, if possible, yet clearer, when 

 we study the principle of his tables, when we analyze the idea 

 upon which they are based, when we make ourselves master of 

 its originality, and can appreciate the accuracy with which he 

 applies it, and the precision of the results he deduces. This is 

 what I mean to endeavour to make all readers sensible of, re- 

 serving the details of the calculus for a note to be placed at 

 the conclusion of this article. If it be my fortune to draw this 

 merit from the tomb to which the commentators had consigned 

 it, I will not pretend to say of him, as Cicero once said of Ar- 

 chimedes, Humilem Jiomunculum e radio et pulvere excitabo ; 

 but I shall feel confident of having communicated a subject of 

 genuine satisfaction to those enlightened philosophers who love 

 the glory of their predecessors as their own inheritance, and find 

 their own happiness in being able to render a just homage to 

 their labours. 



It was that mighty genius of Syracuse who, in his treatise 

 Arenarius, was the first to record those properties of numerical 

 progressions upon which the theory of logarithms is founded. 

 Archimedes proposed to himself, not the idle question, how many 

 grains of sand might be contained in a sphere equal in diameter 

 to a sphere of the known universe, but to demonstrate that a 

 number as great as that, or infinitely greater, could be specified, 

 and written, by means solely of the numerical characters in use 

 among the Greeks of his time. It is well known that those 

 characters were the letters of the alphabet, which they emf^oyed 

 consecutively, in their natural order, simple and accented, to 

 designate the various classes of units, lens, hundreds, thousands, 



