72 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

bility of dividing twelv into thirds and quarters, as well as
into halves. On this account, apparently, altho they counted
by tens, they divided the foot into twelv inches. Carrying
out the same idea they divided the inch into twelv parts called
lines and the line into twelv parts called points(!).

But the advantages of twelv as a measuring number seem
not to have been very great. We have given up the division
of the inch into lines and points. We now divide it into
half-inches, and each half-inch into halves, and so on. Or,
sometimes, for the sake of saving time in computation, we
divide the inch into tenths and hundredths, because we com-
pute in the decimal system. Similarly we sometimes even
divide the foot into tenths and hundredths, giving up its
division into twelv inches.

A similar phenomenon has happend in the dry goods trade.
A clerk never sells goods by the third of a yard, the foot, but
by the half, quarter, and eighth of a yard.

Now why do we divide the inch and other units into halves
rather than into thirds or fifths? Simply because it is easier
for us to compare two things than to compare three or five
things. Therfor we do not naturally divide things into either
thirds or fiftths. We divide them into halves, quarters, eighths,
sixteenths, and so on.

This natural tendency keeps cropping up in all sorts of
places, even where we might think decimal division would be
more natural. Thus the dollar is divided into halves and
quarters as well as into dimes. We do not coin the eighth of
a dollar, but we use it in prices. We even give a name to the
eighth of a dollar, we call it a shilling or a bit. The French
divide the liter into quarters(?).

141. For these reasons eight and sixteen seem to me to be
much the best bases. We can use either just as well as ten
or twelv for counting and much better for measurement. The
most useful fractions 1/2, 1/4, 1/8, 1/I0 and their multiples are

() See D. E. Smith, l. c., p. 11; Vera Sanford, 1. c., p. 78.
() W. Woolsey Johnson, L. c., p. 1.