THE INVENTION OF LOGARITHMS 199 



is almost purely mechanical ; but here again it could be of no 

 real advantage to any one who knew the multiplication table 

 for numbers up to nine. 



To complete our conception of John Napier as a mathema- 

 tician some reference must be made to the posthumous work 

 De Arte Logistica, published in 1839 by Mark Napier. Through 

 the kindness of its present possessor, John Spencer, F.I.A., 

 London, the manuscript from which the book was printed was 

 on view at the Tercentenary Exhibition. It appears to have 

 been copied from the original by Robert Napier, John Napier's 

 son. It bears no title ; but on the outside leaf were inscribed 

 by hand across the top the words " The Baron of Merchiston 

 his booke of Arithmeticke and Algebra," and along the right- 

 hand margin and at right-angles to the first inscription the 

 words " For Mr Henrie Briggs, professor of Geometrie at 

 Oxforde." Some other words had also been written but had 

 been defaced. These hand-written inscriptions were chosen by 

 Mark Napier as a second title to the book, the Latin title, De 

 Arte Logistica, being constructed from the opening sentence. A 

 detailed account of the contents of this remarkable work is 

 given in the memorial volume by Prof. Steggall. Published as 

 it was so long after Napier's death, this book had of course no 

 direct influence on the development of algebra; but its contents 

 show that Napier was in possession of mathematical knowledge 

 and methods in advance of his time. Like all pioneers he had 

 to invent his own notation. It is conceivable that had Henrie 

 Briggs received the manuscript of De Arte Logistica (as was 

 obviously intended) some of Napier's symbolism might have 

 become the common property of the race, and the art of the 

 ready reckoner been more rapidly developed. The Baron of 

 Merchiston was undoubtedly himself a skilled arithmetician and 

 had many tricks for shortening the processes of multiplication 

 and division. His treatment of vulgar fractions and of decimal 

 fractions is indeed most masterly and lucid. In his exposure of 

 the disadvantages of the cumbrous astronomical notation of 

 hours, minutes, seconds, as compared with the simple decimal 

 system, John Napier voiced a much-needed reform which the 

 intellectual inertia of the centuries still prevents. 



Napier's treatment of powers and roots is remarkable and 

 instructive. He makes use of what is virtually the binomial 

 theorem up to the twelfth power and constructs an ingenious 



