66 



cess a little heavier than they remain under the adoption of 

 the radix 10. And in yet another point of view, although 

 the number 3 comes before 5 in frequency, its loss as a 

 factor of the. radix is well nigh compensated by the cir- 

 cumstance that it enters compounded into the radix dimi- 

 nished by unity (3 2 =9=10—1), which circumstance of 

 itself offers several precious advantages in analysis, that 

 could not appear under the radix 12, where 12—1=11 is an 

 infrequently occurring prime, too high to possess any 

 facility whatever. 



Since we have seen that it is not possible to retain all 

 the first three prime numbers 2, 3, 5, as factors of our 

 arithmetical radix, so as to ensure a scale perfect in its 

 constitution, because it is unmanageable in practice, would 

 it be wise to replace 5 by 2, merely for the sake of preserv- 

 ing inviolate the number (three) of the factors in the radix, 

 although one of them is a mere duplicate ? Or rather shall 

 we not reject one of them, either 3 or 5, and let convenience 

 decide which it shall be, if indeed any great difference 

 between the two shall be found to attach to this considera- 

 tion ? Now any difference of convenience between oper- 

 tions performed under the radix 10, and under the more 

 simple radix 6, is so slight as not to be worth taking into 

 the account ; while a very perceptible difference in favor 

 of the former radix would accrue in expressing the results 

 of operations in very large numbers, a difference much 

 more than counterbalancing any fancied advantage of the 

 smaller radix. But, in addition to these motives, the 

 inconvenience of changing a radix founded upon considera- 

 tions so familiar and elementary as the number of fingers 

 of the individual man, and fortified by immemorial and 

 universal custom, for advantages so slight as would accrue 

 from the interchange of the factors 5 and 3, would be alto- 

 gether insurmountable : therefore, convenience alone being 

 thrown into the scale, will never allow the beam to alter its 

 present inclination ; and, finally, it is hoped that the reasons 



