SCALES OF NOTATION 67

wardly in this notation. The only fractions represented
simply, besides 1/2, are 1/5 and 1/°f and their multiples.

In the duodecimal scale the fifths and tenths are repre-
sented by non-terminating series and the others by terminating
series, the fractions 1/2, 1/4, 1/3, 1/6, 1/8 and their multiples
very simply, the others awkwardly.

In the scales whose bases are 2, 4, 8, [0 the fractions 1/2,
1/4, 1/8, 1/I0 and their multiples are represented by termi-
nating series, the others by non-terminating series. In the
quaternary notation 1/2, 1/4, 3/4 are represented very simply,
but 1/8, 1/10 and their odd multiples not very simply. In the
octimal notation 1/2, 1/4, 3/4, 1/8, 3/8, 5/8, 7/8 are represented
very simply, but 1/I0 and its odd multiples not so simply.
In the sexidenal scale all these fractions are represented very
simply.

137. Which is the best radix? The answer to this question
depends on the use to be made of the notation.

For some purposes it is convenient to have a number repre-
sented as a sum of powers of 2 (including the zeroth power,
which is 1). : § 103.

For instance, in applied electricity resistance boxes contain
spools of wire whose resistances are represented by 1, 2, 22,
23 24 ... In order to pick out the resistance represented by
a certain number it is therfor useful to have this number
represented in the binary scale.

Thus 14(°?) = 1110(2) = 23 4 22 4 2

47(¢) = 101111(2) = 25+ 28 + 22+ 2 + 1

Resistance boxes are made up in this way, it is said, because
it takes on the average less spools to make up a given resistance
with this kind of a box, a binary box, than with a box built
up according to any other scale.

A decimal box would contain 9 spools each with the unit
resistance, 9 spools each with a resistance of ten units, 9 with
a resistance each of one hundred units, and so on.

A resistance of 47 units would be represented in the decimal
box by 4 spools of 10 units each and 7 unit spools, 11 spools