ing the "hand-cursive" of the Jews and
Saracens, than into one respecting the constitution of the languages. Of
the Jewish we know nothing, or next to nothing, at the period in
question; whilst the Arabic is as well known as even our own present
style of calligraphy. It deserves to be more carefully inquired into
than has yet been done, whether the invention of contracting the written
compound symbols of the digital numbers into single symbols did not
really originate amongst the Jews rather than the Saracens; and even
whether the Arabs themselves did not obtain them from the "Jew
merchants" of the earlier ages of our era. One thing is tolerably
certain:--that the Jew merchant would, as a matter of precaution, keep
all his accounts in some secret notation, or in cipher. Whether this
should be a modified form of the Hebrew notation, or of the Latin, must
in a great degree depend upon the amount of literary acquirement common
amongst that people at the time.

Assuming that the Jews, as a literate people, were upon a par with their
Christian contemporaries, and that their knowledge was mainly confined
to mere commercial notation, an anonymous writer has shown how the
modifications of form could be naturally made, in vol. ii. of the _Bath
and Bristol Magazine_, pp. 393-412.; the motto being _valent quanti
valet_, as well as the title professing it to be wholly "conjectural."
Some of the speculations in it may, however, deserve further
considerations than they have yet received.[1]

The contraction of the compound symbols for the first nine digits into
single "figures," enabled the computer to dispense with the manual
labour of the _abacus_, whilst in his graphic notation he retained its
essential principle of _place_. It seems to be almost invariably
forgotten by writers on {280} the subject, what, without _this
principle_, no improvement in mere notation would have been of material
use in arithmetic; and on the other hand that the main difference
between the arithmetic of the _abacus_ and the arithmetic of the
_slate_, consists in the inevitable consequences of the denotation of
the single digits by single symbols.

The _abacus_, however, in its ordinary form, is essentially a decimal
instrument: but its form was also varied for commercial purposes,
perhaps in different ways. I never heard of the existence of one in any
collection: but there is preserved in the British Museum a picture of
one. This was printed by Mr. Ha