1 98 SCIENCE PROGRESS 



of a spherical triangle are connected by formulae suitable for 

 logarithmic treatment. These trigonometrical theorems by 

 themselves are sufficient to place Napier in the front rank of 

 mathematicians. In this connection Prof. Sommerville con- 

 tributes to the Memorial Volume a short paper in which he 

 extends Napier's Rules and trigonometrically equivalent 

 polygons to non-Euclidean geometry. 



In still another direction the far-reaching influence of 

 Napier's discoveries is clearly demonstrable. In an article on 

 the Graphical Treatment of some crystallographical problems 

 Dr. A. Hutchinson points out that, once the simple geo- 

 metrical laws governing crystalline structure were recognised, 

 " crystallographers found in the inventions and discoveries 

 of Napier powerful tools ready forged to their hands." Dr. 

 Hutchinson then proceeds to describe a form of logarithmic 

 slide rule specially suitable for crystallographic investigations. 



In everything mathematical which Napier himself placed 

 before the world his great aim was to facilitate calculation. 

 In the popular mind Napier is known chiefly for his logarithms 

 and for his calculating rods, which were in great vogue during 

 the seventeenth and part of the eighteenth century. These rods, 

 or " Neper's Bones," as they were frequently called, were simply 

 rods of wood or ivory inscribed with the multiples of the 

 natural numbers. A complete set of rods was in fact a multipli- 

 cation table, mechanically adjustable so as to reduce multiplica- 

 tion to simple addition. The Rabdologia, the small Latin treatise 

 in which Napier describes the use of his rods, was translated 

 into Italian in 1623, a fact which testifies to the early recognition 

 of its practical value. As the memorising of the multiplication 

 table became an essential part of education, Napier's Bones 

 gradually fell into disuse. 



In the Rabdologia other and more complicated methods of 

 calculation by rods are described ; but it is doubtful if these 

 ever came into general use. The last section of the book is 

 devoted to what Napier calls Local Arithmetic, in which the 

 multiplication of two numbers is effected (first) by expressing 

 each number in the scale of 2, (second) by representing them by 

 means of counters on the spaces of an enlarged chess-board, 

 (third) by manipulating them in a simple way so as to produce 

 the product in the binary scale, (fourth) by re-translating the 

 result finally in the ordinary denary scale. The whole process 



