In the previous December he had been elected at Trinity College, Cambridge, to a Sizarship, which was exchanged for a Major Scholarship not long after he came into residence in October 1902. He was Seventh Wrangler in the Mathematical Tripos of 1904 (the Senior Wrangler being the late Sir Arthur Eddington, O.M., F.R.S.), and obtained a First Class in Part II of the Tripos in 1906. In the following October he was appointed Assistant to Professor Karl Pearson at University College, London. He had, however, always been deeply interested in the work of the Presbyterian Church, especially in its Foreign Missions, and when in December of the same year a vacancy occurred in the Chair of Mathematics in the Madras Christian College, he offered himself and was appointed, arriving in India early in 1907. Here he spent the next twenty-five years, giving himself with single-minded devotion to the interests of the College, contributing by his reputation to its scholarly prestige, and holding its religious aims close to his heart.
When home on furlough he used to work in the research school of the Mathematical Institute of Edinburgh University, and in 1921 he and a fellow-worker, Bevan Baker (afterwards Professor of Mathematics in the University of London at the Royal Holloway College), collaborated in producing a substantial paper "On the Vibrations of a Particle about a Position of Equilibrium" (Proc. Edin. Math. Soc., XXXIX (1921), 34-57). It will be remembered that the great inequality of Jupiter and Saturn, which for eighty-six years defied all attempts to account for it by the Newtonian law of gravitation, was eventually found by Laplace to be due to the fact that five times the mean motion n of Saturn is very nearly equal to twice the mean motion n' of Jupiter, and that consequently the trigonometric term whose argument is (5n - 2n')t, when it is divided by the small quantity (5n - 2n')2 in the course of the integration, gives rise to a large inequality in the motion of the planets, although it has only a very small coefficient in the perturbing function. Similarly in the case of the motion of a particle in the neighbourhood of a position of stable equilibrium, if there is approximate commensurability between the frequencies corresponding to the small oscillations about the point of equilibrium, it is possible that certain vibrations of higher order, which are normally of small amplitude compared with the principal vibrations, may acquire an abnormally large intensity. Baker and Ross elucidated this phenomenon by studying a particular problem which had the advantage of being soluble not only in periodic series but also in terms of elliptic functions: they showed that this second form of solution gives results where the series solution breaks down, and thus throws light on the cause of the divergence of the series solution.
Professor Ross was elected a Fellow of the Society in 1921.
In 1932 his health failed, and he was compelled to resign the Chair at Madras. Thereafter he lived in Edinburgh under the care of his sisters, becoming progressively more infirm until his death on January 11, 1947.