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'Theory of Numbers', 1946-47.

Davenport was approached, initially by E.A. Milne, to write a book on this subject as one of a series of mathematical works for the interested layman. The book was published in 1952 as 'The higher arithmetic'.

4 letters from E. A. Milne, 1946, outlining the proposed series, the level of mathematics to be aimed for and the publishers' terms.

Letter from Hutchinson & Co., publishers, 1947, enquiring re Davenport's progress, with his reply apologising for the delay, due to pressure of work.

'The Natural Numbers'.

5pp. typescript draft, probably of introduction to the book.

6pp. untitled typescript draft, paginated 15-20.

Two examination scripts written by Davenport for the Honours School of Mathematics, Part III, May 1927, set, marked and preserved by L.J. Mordell, who sent them to Mrs. Davenport in 1971.

Covering note (A.30), gives names of other examiners, Bailey, Milne and Chapman, which papers they set and Davenport's marks for each.

Milne was Davenport's tutor in applied mathematics at Manchester, 1924-27. Letters of 1926-27 are re Davenport's Scholarship at Trinity (Milne's own college, to which he was devoted), with advice on directions of study. Letter of 1945 is on current leaders in mathematics.

The list gives the name of each recipient, and a brief note of what they were sent of Cayley's papers by Rouse Ball. The copies of letters sent to recipients are in most case form letters, explaining that on the death of Cayley's widow his papers were put into Rouse Ball's hands with a request that he should destroy or dispose of them as he saw fit; 'all involving matter which might be published was dealt with years ago, and what was preserved has no interest beyond the fact that it is a specimen of his work'. Longer letters were sent to G. T. Bennett, also asking whether he would like to see the models of Archimedean and other solids made by W. W. Taylor, and to D. E. Smith, also taking the opportunity to send a paper on Euler which might be of interest to the American Mathematical Monthly. A long second letter to E. H. Neville gives details of the nature of Cayley's papers, and the principles by which Rouse Ball decided what should be destroyed: 'As for letters to him, of which many hundreds were put in my hands, I laid down the rule that in general such letters should be destroyed or sent back to the writers if they were alive'; lists the few exceptions; the letter also suggests that Neville take a look at Monge's Card-Shuffling Problem.