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Seventy-seven volumes of handwritten quarterly report forms from branches of the Amalgamated Society of Engineers, Machinists, Millwrights, Smiths and Pattern Makers all over the country, including notes and figures on income and expenditure, membership numbers, excluded members, quarterly admissions, superannuated members, members gone abroad and the death of members or the wives (1853-1879).

The Brain archive comprises his personal and professional papers together with sampled case notes from his private practice, 1865-1977. As well as medical papers, there is a significant amount of material relating to Brain's philosophical and literary interests, and some papers of Brain's family and of his wife Stella (nee Langdon-Down).

Letter from Matthew Collins of 40 Upper Pitt Street, Liverpool to Augustus De Morgan, 8 Apr 1853. Covering note, enclosing a pamphlet, On Clairaut's theorem ... (1853).

Autograph, with signature. A note in De Morgan's hand states that the content of the pamphlet, published in the Cambridge and Dublin Mathematical Journal, new series vol IX (1854), were plagiarized from a lecture given by Mr James MacCullagh in 1846.

3 letters from John Thomas Graves of 29 Grosvenor Place, Cheltenham to Augustus De Morgan, 28 Jan, 4 Feb and 4 Jun 1853. Relating to the works of Simon Stevin and other mathematical literature.

Autograph, with signature.

Letter from John Taylor of London to Richard Taylor, Esq [probably the writer's son or brother], 5 Jul 1837. 'The bearers Messrs. [Gabriel] Daubrée and Sentis have studied at the Ecole des Mines at Paris and are strongly recommended by Messrs. [François] Arago and Combes. I have furnished them with introductions to some of our agents, but if you will give them further advice and assistance in Cornwall I shall be obliged to you.'

Autograph, with signature.

Letter from Wililam Wallace to Rev George Peacock, Dean of Ely, [1833]. Describing Wallace's part in the introduction of foreign mathematical notation to England and 'the Reformation .... the the Mathematical science in Britain'.

Autograph, with signature. Headed 'First Copy'. Inscribed in another hand: 'Found among Mr Thomas Galloway's papers'.