to various awkward expedients for making these forms express somewhat
higher numbers. On the other hand, the Hebrews seem to have been
provided with an alphabet as soon as they were to constitute a nation;
and they were taught to use the successive letters of that alphabet to
express the first ten numerals. In this way b and c might denote 2 and 3
just as well as those figures; and numbers might thus be expressed by
single letters to the end of the alphabet, but no further. They were
taught, however, and the Greeks learnt from them, to use the letters
which follow the ninth as indications of so many tens; and those which
follow the eighteenth as indicative of hundreds. This process was
exceedingly superior to the Roman; but at the end of the alphabet it
required supplementary signs. In this way bdecba might have expressed
245321 as concisely as our figures; but if 320 were to be taken from
this sum, the removal of the equivalent letters cb would leave bdea, or
apparently no more than 2451. The invention of a cipher at once
beautifully simplified the notation, and facilitated its indefinite
extension. It was then no longer necessary to have one character for
units and another for as many tens. The substitution of 00 for cb, so as
to write bdeooa, kept the d in its place, and therefore still indicating
40,000. It was thus that 27, 207, and 270 were made distinguishable at
once, without needing separate letters for tens and hundreds; and new
signs to express millions and their multiples became unnecessary.

I have been induced to trespass on your columns with this extended
notice of the difficulty which was never solved by either the Hebrews or
Greeks, from understanding your correspondent "T.S.D." p. 367, to say
that "the mode of obviating it would suggest itself at once." As to the
original query,--whence came the invention of the cipher, which was felt
to be so valuable as to be entitled to give its name to all the process
of arithmetic?--"T.S.D." has given the querist his best clue in sending