He clearly benefited by and often commented with satisfaction upon the breadth of his Edinburgh studies, and these were attended by marked success; he was elected both Arnott Scholar in Experimental Physics, and Maclaren and Ferguson Scholar in Mathematics, and he was a medallist in Mathematics and Natural Philosophy.

... combination of mathematical expertise and physical insight, ... the meticulous patience and persistence shown in his work, and ... his choice of problems which showed a bold and adventurous mind ...

He led bathing expeditions to almost inaccessible pools on the rugged Pembrokeshire coast (one of these could only be reached by descending the cliff-face on a chain, no doubt long since rusted away); he played an active role in a Christian study group sparked off by the publication of [C S Lewis's] 'The Screwtape Letters'; most importantly he won the hearts of many of the inhabitants of a small Welsh borough by entering to the full into their musical life, and is still warmly remembered there for his playing of the piano accompaniment in an amateur performance of Handel's 'Messiah'. ... He once got into trouble at a Welsh pub because he insisted on playing his kind of music, which was not the kind the hearty drinkers at the bar wanted to hear. He refused to stop, and was asked not to come again.

This work was carried out by Slater almost single-handedly over a number of years. It represented a new outlook on certain types of chemical reaction; it fell short of reality because, although the model was on the right lines, it involved neglecting certain features that are important.

When Mark Kac first went from Poland to the United States he was interested, as a (then) pure mathematician, in some problems related to the theory of almost-periodic functions, and one such was the distribution of the values of a superposition of vibrations with linearly independent frequencies. This is obviously closely linked to Slater's problem, but in fact it arose in an astronomical context, namely the "mean motion problem" of celestial mechanics. In 1943 Kac published two papers giving a formula for the frequency (in the probability sense) with which such a superposition of vibrations with linearly independent frequencies would cross a prescribed level "from below". To his surprise and pleasure he received a letter from Slater telling him that his formula, which Kac thought was "entirely useless", had opened the door to a new attack on an important chemical problem. This was the commencement of a long friendship.

Steady state results are presented for a multi-server queueing system with several types of customers. Each customer type has its own Poisson arrival rate and exponential service rate not dependent on the particular desk (server) providing the service. First, formulas for the mean desk occupation and the mean number waiting are presented, valid for general service time distributions. A general technique based on probability generating functions and an associated eigenvalue problem is outlined to determine all state probabilities of less than $N$ (the number of desks in the system) customers. From that all probabilities of more than $N$ customers may be shown to be the sum of geometric probabilities. The case of two desks is treated in detail.

Slater realised the importance of urgent action, and took steps to ensure that a veritable mountain of manuscript in Eddington's study should not be disturbed or so much as dusted until he had had time to go to Cambridge and sort it. When he got there he found odd bundles of sheets from numerous different drafts heaped up in a towering pile, sometimes one way up and sometimes the other, and with little to indicate their interrelationship. After the war Slater devoted himself to the separation of these into variant versions of sections of the book, representing different and competing strands in Eddington's thought, and finally, in his own book [The development and meaning of Eddington's 'Fundamental Theory'], Slater published a sort of variorum edition modelled quite consciously on the similar activities of New Testament scholars. No one was sure about the scientific status of 'Fundamental Theory' at that time, and one is even less sure now. What is important in the long term about Slater's own achievement is that it provides us with an authentic snapshot of the competing concepts simultaneously present and wrestling for expression in the mind of a great creative genius.

Many have tried to read [Eddington's] book; but all have found it difficult.

... all passages which (a) contribute materially to the understanding of the final version or (b) contain developments which were later discarded but are of intrinsic interest.