JEANS returned to Cambridge in 1903, completely cured, and settled down to the tenure of his fellowship at Trinity. His earliest research, as we have seen, was concerned with the distribution of velocity amongst the molecules of a gas. Whilst still convalescent, he had engaged in researches, inspired by the work of Sir George Darwin, on the stability of a spiral nebula, and the problem of the forms of equilibrium of rotating and gravitating fluid masses. Jeans had indeed always two strands of interest in mathematical physics, the analysis of the very small (molecular physics) and the analysis of the very large (cosmogony). His actual results in these fields will be described later. Here we note that, though on his return from convalescence he devoted himself principally to molecular physics in the form of statistical mechanics, his work in the two distinct fields had made him known to the leading English and Continental mathematicians of the day. Consequently when, in the autumn of 1904, he was a candidate for the vacant chair of mathematics in the University of Aberdeen, he was able to support his application by testimonials from men of world-wide reputation.

‘Ever since we elected him to an open Major Scholarship here,’ wrote the Master of Trinity (H. M. Butler), ‘his career has been one of exceptional distinction, and he is regarded as one of the most brilliant and original of our younger mathematicians. His character is of the highest, his manners are most agreeable, and he has won the warm regard of us all.’

G. H. (later Sir George) Darwin wrote:

I did not see anything of Mr Jeans during his career as an undergraduate at Trinity College, but a very remarkable essay by him was submitted to me as one of the examiners for the Fellowship at Trinity College. The paper showed much originality and a very unusual power of dealing with a mathematical problem of great difficulty. The subject was especially interesting to me, and we had several long discussions of it after the fellowship examination. I ultimately had the pleasure of presenting the paper to the Royal Society for publication in the Philosophical Transactions.