in his head, and
consequently we have the solutions exactly as he worked them out
before setting them down on paper. Of the Problems themselves there is
not much to be said here; they are original, and some of them (e.g.,
No. 52) expressed in a style peculiarly the author's own. The subjects
included in their range are Arithmetic, Algebra, Pure Geometry
(Plane), Trigonometry, Algebraic Geometry, and Differential Calculus;
and there is one Problem to which Mr. Dodgson says he "can proudly
point," in "Transcendental Probabilities," which is here given: "A bag
contains two counters, as to which nothing is known except that each
is either black or white. Ascertain their colour without taking them
out of the bag." The answer is, "One is black and the other white."
For the solution the reader is referred to the book itself, a study of
which will well repay him, apart from the chance he may have of
discovering some mistake, and the consequent joy thereat!

A few extracts from the Diary follow, written during the early part of
1894:--

_Feb._ 1_st.--Dies notandus._ As Ragg was reading
Prayers, and Bayne and I were the only M.A.'s in the stalls,
I tried the experiment of going to the lectern and reading
the lesson. I did not hesitate much, but feel it too great a
strain on the nerves to be tried often. Then I went to the
Latin Chapel for Holy Communion. Only Paget (Dean) and Dr.
Huntley came: so, for the first time in my recollection, it
had to be given up. Then I returned to my rooms, and found
in _The Standard_ the very important communication from
Gladstone denying the rumour that he has decided upon
resigning the Premiership, but admitting that, owing to
failing powers, it may come at any moment. It will make a
complete change in the position of politics! Then I got,
from Cook Wilson, what I have been so long trying for--an
accepted transcript of the fallacious argument over which we
have had an (apparently) endless fight. I think the end is
near, _now_.

_Feb._ 4_th._--The idea occurred to me that it
might be a pleasant variation in Backgammon to throw
_three_ dice, and choose any two of the three numbers.
The average quality of the throws would be much raised. I
reckon that the chance of "6, 6" would be about two and a
half what it now is. It would also furnish a means, similar
to giving points in billiards, for equalisin