In 1954, I was appointed Lecturer in applied Mathematics at University College, Cardiff. The Head of the Mathematics department was Professor Lionel Cooper, and the senior applied mathematician was Dr Rosa Morris. There were no other particle theorists at Cardiff, but I kept in touch with the subject by attending conferences and visiting the Harwell (later, the Rutherford Laboratory) Theory Group most summers. 
 
I continued work started in Glasgow, and showed that the field theory based on neutral pseudoscalar mesons with pseudovector interactions was equivalent, after renormalisation, to the theory with exponential interactions (ref 5). With my research student Milo Dixon, I extended these ideas to the more realistic charge-symmetric PS-PV theory, but this paper (ref 6) was a great deal more complicated. Milo Dixon also carried out a very beautiful piece of work, examining in detail how Feynman graphs in neutral PS- PV theory combined to become Feynman graphs in exponential theory. His report on this work earned him a valuable Studentship at Cambridge. However, he felt that this work was incomplete, and should be extended to symmetric theory before publication. I urged him repeatedly to complete his doctoral thesis and to publish his very significant analysis of the neutral theory, but I was not able to persuade him to do this. I have known other occasions, sadly, when a student, ambitious to complete a very difficult task, has not realised that some limited results are extremely valuable and interesting. 
 
In a more general study of equivalent field theories (ref 8), I showed that almost local changes of variable in renormalised field theories left the physical content unchanged, provided that the free-particle Lagrangian was unchanged. This work was related to Haag's theorem, and I benefited from discussions on the Reimann-Lebesgue theorem with Lionel Cooper and Milo Dixon. 
 
At Cardiff, I lectured on a wide variety of topics to mathematics, science and engineering students. Around 1958, Dr Roger Blin-Stoyle, acting for North-Holland Press, asked me whether I would write a textbook on mathematical methods for scientists and engineers. This seemed to be a huge task for one person. I knew Rosa Morris to be a very clear, careful and experienced expositor, and she agreed to share the task. This was acceptable to Blin-Stoyle, so we divided the writing of chapters between us. Some material was new to both of us, and we each tackled some of these areas of ignorance; my study of the basics of statistics and probability came in useful later. We continually discussed details of the work, and checked each other's material carefully. Writing and production took us several years, and the book (booklist2) was well over 700 pages long. The effort was worth it: in the late 1960's, North-Holland told us that we had broken their publication record for technical books. We even made a little money. Around 1984, we were asked whether we would update the book, but neither of us felt that we could undertake what would be a very substantial re-write, including new material on computation and numerical analysis. 
 
One apparently small piece of work I did was to review a book (ref 9) on the foundations of statistical mechanics. In fact, the job took five months, and I learnt a great deal from the study. My thoughts turned to the definition of entropy, and I realised, as others have done, that entropy is a relative concept. I invented the parable of a 19th and a 20th century physicist each observing a simple experiment: 
 
A box is partitioned into two equal halves, and the two halves contain two isotopes of a gas at STP, indistinguishable except that one isotope is radioactive and the other is not. The partition is raised, mixing the gases, and each physicist is asked whether the entropy has changed. The 19th century physicist detects no change in entropy; but the 20th century physicist, possessing a Geiger counter, can detect the radioactivity of one isotope, and so knows that the entropy gain is R ln2. 
 
When I related this parable to Professor Rudolph Peierls in 1964, he immediately added, 'Yes, and he can get work out of it'