have referred "E.V." to
several other authorities which he will do well to consult.

9. Wallis's _Algebra_, p. 9. and p. 153. of the additions.

10. _Phil. Trans._, Nos. 439. and 475.

11. Montucla, _Histoire des Mathematiques_, tom. i. chap. 2.

12. Baillie, _Histoire de l'Astronomie_.

13. Delambre[1], _Hist. de l'Astr. du moyen age_.

14. Hutton's _Tracts_ (8vo. ed. 1812.), vol. ii. (subject "History of
Algebra")

15. Huet, _Demonstratio Evangelica_.

16. Dr. John Taylor's Translation of the _Lilawati_. (Bombay, 1816.)

17. Strachey's Translation of the _Bija Ganita_[2].

18. Colebrooke's _Algebra of the Hindus_.

Would it not be worth while to give a _facsimile_ of the "Tabel for
all manere of merchauntes," in the "Notes and Queries"? It is not only
a curiosity, but an important element (and unique as far as is known)
in the philosophic history of our arithmetic. It was, no doubt, an
actual instrument in constant use in the merchant's office, as much so
as an almanac, interest-tables, a "cambist" and a copying-press, are
now.

As regards the cipher, the difficulty only commenced with _writing
numbers_ in the new symbology. With persons accustomed to the use
of this instrument, there is no doubt that the mode of obviating the
difficulty of "keeping the place," would suggest itself at once. In
this instrument an empty hole (without its peg) _signified_ "none of
this denomination." What then more simple than to make the outline
of the empty hole which occupied the "local position" of any
denomination, when none of that precise denomination occurred in the
number itself? Under this view the process at least becomes simple
and natural; and as the early merchants contributed so largely to the
improvement of our arithmetical processes, such a conclusion is wholly
divested of improbability on any other ground. The circle would then
naturally become, as it certainly has practically become, the most
appropriate symbol of _nothingness_.

As regards the term _cipher_ or _zero_ (which are so obviously the
same as to need no remark), it is admitted on all hands to be derived
from one or other of the Semitic languages, the Hebrew or the Arabic.
It is customery with the mathematical historians to refer it to the
Arabic, they being in general more conversant with it than with the
Hebrew. The Arabic being a smaller hand than the Hebrew, a dot was
used instead of the circle for marking the "place" at which the hiatus