[C. Dudley Langford, chemist and mathematician whose discussion of ‘Langford pairing’ (Langford sequence) is of importance in computing.] Two Autograph Letters Signed to ‘Sir Richard [Dundas Hamilton]’, one about his health, the other about a theorem

Langford trained as an industrial chemist and was a member of Royal Chemical Society. In later life he turned to mathematics, and published thirty articles in the Mathematical Gazette. One of these (‘Problem’) appeared in 1958 and concerned what came to be known as the Langford Sequence. Its significance is discussed by Martin Gardner, in his ‘Mathematical Magic Show’ (1978). Both items aged and creased, with closed tears, but with text complete and legible. Both are addressed to ‘Dear Sir Richard’ and signed ‘C Dudley Langford’. ONE: 3pp, 12mo. On two leaves. After thanking him for his ‘Letter Card’ he writes: ‘I like the proof. The thing that I think astonishes everyone is that the converse of such an early theorem should prove to be such a hard nut to crack and require such things as cyclic qudrilaterals etc!’ After a short speculation on this question he writes: ‘I’ll see what I can do - - but five or six years of pain from my wrist have reduced me to pretty poor state mentally! I don’t think I honestly could have taken even half a dozen aspirins etc in the last four years; yet I’ve taken enough to affect my head very seriously (My heart is so pharmaceutically good that it is untouched!)’ He continues discussing his incapacity, before noting: ‘One curious effect of the continuous pain is that, at times, I feel quite light headed and wonder, afterwards, what the shop assistants think! I hope, anyhow, that they realise its my wrist making me not know quite what I’m doing. Sometimes I have to ask them to pack the things in the basket for me as I just cannot manage it myself’. He ends by proposing that they both work on ‘a proof based on early work’, and let one another know about the results. TWO: 3pp, 16mo. He lays something that ‘may be well known to specialists, but if you don’t know it, it may interest you’. He explains that he ‘noticed about 10 years ago that the 9th and 5th terms of mutations ended in the same digits as the numbers themselves. One night recently I was woken by the pain in my wrist and it dawned on me that, if one substituted the original number one would get something ending in O, ie a multiple of 10.’ He gives a page and a half of mathematical calculations, including one arrived at with ‘a hint from Mr Broadbent’ (i.e. Thomas Alan Arthur Broadbent). He ends by apologising for his handwriting, with further reference to his ‘fractured wrist’: ‘There is a good chance, therefore, that I shall never again be able to write legibly, be free from pain, able to dress myself unaided or even use a walking stick!’ Accompanying the letters is a printed ‘Programme for the Annual Meeting East, 1949’ of the Mathematical Association (3pp, 16mo; bifolium).