uare, I chanced on a
theorem (which seems _true_, though I cannot prove it),
that if x squared + y squared be even, its half is the sum of two squares.
A kindred theorem, that 2(x squared + y squared) is always the sum of two
squares, also seems true and unprovable.

_Nov. 5th.--_I have now proved the above two theorems.
Another pretty deduction from the theory of square numbers
is, that any number whose square is the sum of two squares,
is itself the sum of two squares.

I have already mentioned Mr. Dodgson's habit of thinking out problems
at night. Often new ideas would occur to him during hours of
sleeplessness, and he had long wanted to hear of or invent some easy
method of taking notes in the dark. At first he tried writing within
oblongs cut out of cardboard, but the result was apt to be illegible.
In 1891 he conceived the device of having a series of squares cut out
in card, and inventing an alphabet, of which each letter was made of
lines, which could be written along the edges of the squares, and
dots, which could be marked at the corners. The thing worked well, and
he named it the "Typhlograph," but, at the suggestion of one of his
brother-students, this was subsequently changed into "Nyctograph."

He spent the Long Vacation at Eastbourne, attending service every
Sunday at Christ Church, according to his usual rule.

_Sept._ 6, 1891.--At the evening service at Christ
Church a curious thing happened, suggestive of telepathy.
Before giving out the second hymn the curate read out some
notices. Meanwhile I took my hymn-book, and said to myself
(I have no idea _why_), "It will be hymn 416," and I
turned to it. It was not one I recognised as having ever
heard; and, on looking at it, I said, "It is very prosaic;
it is a very unlikely one"--and it was really startling,
the next minute, to hear the curate announce "Hymn 416."

In October it became generally known that Dean Liddell was going to
resign at Christmas. This was a great blow to Mr. Dodgson, but little
mitigated by the fact that the very man whom he himself would have
chosen, Dr. Paget, was appointed to fill the vacant place. The old
Dean was very popular in College; even the undergraduates, with whom
he was seldom brought into contact, felt the magic of his commanding
personality and the charm of his gracious, old-world manner. He was a
man whom, once seen, it was almost impossible to