Cakeuthers. — A System of Weights and Measures. 157 



other than 10 is adopted, as in some of the more trifling affairs of business 

 the dozen has actually supplanted the ten. For instance, eggs are sold by 

 the dozen, and 12 has become the counting radix as far as eggs are 

 concerned. Everyone feels at once the number represented by six dozen 

 eggs ; but if 72 eggs are mentioned, the number is instinctively turned into 

 dozens before a clear perception of its value is obtained. If, now, everything 

 were sold by the dozen, and the pound contained a dozen shillings, and all 

 other weights and measures were reckoned in dozens, it would become a 

 very simple thing to count by the gross and dozen histead of by the hundred 

 and the ten. Twelve fails in the necessary requirement that it shall be 

 continually divisible by two without a remainder, and is not therefore 

 suitable for the radix ; but, if 16 or 8 were used as a radix of measures, 

 it would after a few months, or at most a few years, be so easy to reckon in 

 sixteens or eights, instead of in tens, and at the same time so convenient, 

 that legislation would not be required to effect the change ; it would come 

 of itself by use and habit, just as it has come about that eggs are now 

 reckoned in dozens. Some slight inconvenience might be felt at first, such 

 as is felt in going to a foreign country, where new measures are met with ; 

 but everyone who has lived abroad knows how slight this inconvenience is. 

 After a few months the new measures quite supplant the old; and it 

 becomes convenient, in thinking of English measures, to translate them 

 into those which even so short an experience has rendered familiar. It is, 

 in fact, only through pure cowardice to meet a difficulty that the scientific 

 world is taking up the imperfect French system. A far better system, 

 which would never require alteration, might be adopted, if we would only 

 fairly look in the face the difficulty of changing the counting radix ; and, 

 like most difficulties, this seems the less the more it is looked at. 



Assuming then that the radix must be changed the question arises what 

 number is to supplant ten. It must be a power of two. Two itself and four 

 are too small. Eight has some claims but is also too small. School-boys 

 would all vote for it as they would have to learn the multiplication table 

 only up to 8 times 8 instead of to 10 times 10 as at present, but the 

 inconveniences of having so small a radix are too great and a larger must 

 be sought. Thu'ty-two on the other hand is too large. The average 

 mathematical mind would not be able to work a multiplication table 

 extending to 32 times 32, and a loss of convenience would accrue. Half-way 

 between these two would be about right, that is 16 should be the radix. 

 The multiplication table would not be unwieldily large and the figures 

 required to express a large number would not be too numerous. The 

 present radix 10 is certainly smaller than is deskable, and 16 would be an 

 improvement from every point of view. 



