1887.] ^1^ [Taylor. 



Had any intelligent forethought ever presided over the inception of a 

 numerical scale — had any comprehensive conception of the uses aud pur- 

 poses of figures, in any single instance guided the selection of a ratio 

 for their multiplication — that ratio must inevitably have been something 

 else than ten; the duplication of an odd number — incapable of any other 

 division — neither a square, a cube, nor other power of any integer — and in 

 its successions among the most inefficient for the expression of fractional 

 values, or for the extraction of roots. And if among the patriarchs of 

 the human family, a rational scale had ever been so devised, some traces 

 of this wiser S3'stem must have been found, to give a "sign" and me- 

 mento of man's pristine elevation. 



"The number ten," remarks Mr. Anderson, in his treatise on Arith- 

 metic, "has been adopted by every civilized nation for the radix of the 

 numerical scale. It has no peculiar advantages to recommend it, and 

 seems to have been selected for that important function, merely because 

 it expresses the number of the human fingers. We must regret that a 

 circumstance so totally unconnected with every scientific consideration, 

 should have determined an elemental principle, of the last importance 

 to one of the most abstract, as well as one of the most useful of all the 

 sciences ; and that the decimal notation should still be retained, not- 

 withstanding its evident imperfections, and the superior claims of other 

 scales" {Edinburgh EncydoiJedia ; edited by Sir David Brewster, art. 

 "Arithmetic," Vol. ii, page 411). 



An able and philosophical writer in the Edinburgh Meview holds very 

 similar language. "Ten has indeed," he observes, "no advantage as the 

 radix of numerical computation ; and has been raised to the dignity 

 which it now holds, merely by the circumstance of its expressing the 

 number of a man's fingers. They who regard science as the creature 

 of pure reason, must feel somewhat indignant that a consideration so 

 foreign and mechanical, should have determined the form and order of 

 one of the most intellectual and abstract of all the sciences" {FJdin- 

 burgh Review, for January, 1807, Vol. ix, page 376). 



A large number (perhaps even a large majority) of the well-educated 

 have been accustomed to regard the decimal system as possessing a 

 peculiar beauty and expressiveness, from the great facility with which the 

 ordinary operations of arithmetic are performed by it. Indeed, after 

 laboring at the tedious aud troublesome reductions of compound num- 



other ; although the scuealogy (as in English) was probably more ancient than the lou- 

 giiages tliemselves. So uniform are the laws of mind and matter, tliat we have only to 

 select some rude and Isolated tribe of modern savages to discover witli a naturalist's 

 confidence, the exact process of development in numeration, with tlie aborigines of our 

 race, milleniums on milleniiuns ago. Klaproth, in speaking of tlie inhabitants of the 

 peninsula of Kamtschatka, says; "It is very amusing to see them attempt to reckon 

 above ten ; for having reckoned the fingers of both hands, they clasp tliera togetlier, 

 whieli signifies ten ; they tlien liegin at tlieir toes and count to twenty ; after whicli they 

 are (piitc confounded, and cry '• Matcha,' ' that is, where shall 1 take more ?" {Sprachat- 

 las, page 16.) 



