_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 forget.
[Illustration: The Dean of Christ Church. _From a photograph by Hill & Saunders._]