SCALES OF NOTATION : 69

which they could easily be transformd to the binary scale, as
the quaternary, octimal, or sexidenal (§§ 125-127, 129).

138. For the purpose of ordinary counting a radix should
be neither very large nor very small. A large radix would
have the advantage of representing large numbers with few
figures, but the disadvantage of requiring the memorizing of
a long list of symbols. A small base has the advantage of
requiring the memorizing of only a short list of symbols, but
the disadvantage of representing small numbers with many
figures.

It is very possible that where small numbers only are in-
volved the base 4 would be ideal for counting.

And where large numbers are concernd, as in numbering
bank notes and automobiles, the advantage of being able to
represent very large numbers with only a few figures is so
great (') that it would seem advisable to adopt some large
base for such counting.

The difficulty of memorizing a long list of symbols can be
minimized by using letters for digits.

Thus, with 25 for base, using the notation of § 116,

1000(*?) = Y8
10000(‘'*) = 9RG
100000(*?) = 31NO

With 26 for base 100000(*f) would be represented by three
digits(?).
139. For the purpose of computation a large base has the

disadvantage of requiring the memorizing of large addition
and multiplication tables, unless the work is done by machine,

(1) See an editorial in American Medicine, New York, for June 1913,
quoted in The Literary Digest, New York, of Aug. 9, 1913.

(?) King Charles XII of Sweden is reported by Swedenborg to have
invented an easily rememberd set of symbols for the base sixty-four.
Swedenborg, however, never publisht the set of symbols.

See S. White, Emmanuel Swedenborg, his life and writings, Vol. I,
p. 51, London, 1867; also the one volume edition, pp. 35-38, 1868.