_Sept. 27th.--Dies notandus._ Discovered rule for
dividing a number by 9, by mere addition and subtraction. I
felt sure there must be an analogous one for 11, and found
it, and proved first rule by algebra, after working about
nine hours!

_Sept. 28th.--Dies cretâ notandus._ I have actually
_superseded_ the rules discovered yesterday! My new
rules require to ascertain the 9-remainder, and the
11-remainder, which the others did _not_ require; but
the new ones are much the quickest. I shall send them to
_The Educational Times_, with date of discovery.

On November 4th he wrote:--

Completed a rule for dividing a given number by any divisor
that is within 10 of a power of 10, either way. The
_principle_ of it is not my discovery, but was sent me
by Bertram Collingwood--a rule for dividing by a divisor
which is within 10 of a power of 10, _below_ it.

My readers will not be surprised to learn that only eight days after
this he had superseded his rule:--

An inventive morning! After waking, and before I had
finished dressing, I had devised a new and much neater form
in which to work my Rules for Long Division, and also
decided to bring out my "Games and Puzzles," and Part iii.
of "Curiosa Mathematica," in _Numbers_, in paper covers,
paged consecutively, to be ultimately issued in boards.