CannuTHERS.—AÀ 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 instead 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. Thirty-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 desirable, and 16 would be an 
improvement from every point of view. 
