high reputation and a large connection. Routh was elected fellow of Peterhouse next year, and was appointed college lecturer in mathematics, a post which he retained till 1904. He was also assistant tutor from 1856 to 1868 and was at various times junior dean, junior bursar, and praelector of his college.
In 1857 he was invited to the Royal Observatory, Greenwich, with a view to a vacant post there as a first assistant. He did not take the appointment, but at Greenwich he met Hilda, eldest daughter of Sir George Biddell Airy [q. v. Suppl. I], the astronomer-royal, whom he married on 31 Aug. 1864.
For more than thirty years Routh's chief energies were spent at Cambridge in preparing private pupils for the mathematical tripos. On Steele's early death he became the chief mathematical coach in the university, and the successes of his pupils were unprecedented. In the tripos of 1856 Charles Baron Clarke, his first pupil [q. v. Suppl. II], was third wrangler. In 1858 two pupils, Slesser (Queens') and (Sir) Charles Abercrombie Smith, were respectively first and second wrangler and first and second Smith's prizemen. In the following years, pupils of his were senior wranglers twenty-seven times and Smith's prizemen forty-one times. In the tripos of 1862 fifteen of his nineteen pupils were in the list of thirty-two wranglers, seven among the first ten. From 1862 to 1882 inclusive he had an unbroken succession of twenty-two senior wranglers (two in 1882, one in January and one in June under new regulations), and he had four more in 1884, in 1885, in 1887 (when four seniors were bracketed), and in 1888, when he retired. His senior wranglers included Lord Justice Stirling (1861), Lord Justice Romer (1863), Lord Rayleigh (1865, chancellor of Cambridge University), Lord Moulton (1868), John Hopkinson (1871), (Sir) Donal McAlister (1877, principal of Glasgow University), (Sir) Joseph Larmor (1880, M.P. for Cambridge University); and of other wranglers may be mentioned (Sir) J. J. Thomson, O.M., (Sir) C. A. Parsons, Lord Justice Buckley, and (Sir) Richard Solomon. Of the 990 wranglers between 1862 and 1888, 480 were Routh's pupils. On Routh's retirement from his work as private coach in 1888 his old pupils presented Mrs. Routh with her husband's portrait by (Sir) Hubert von Herkomer (The Times, 6 Nov. 1888).
Apart from his personality, which inspired his pupils with implicit confidence in his powers, and his lucidity of exposition, Routh owed his success as a teacher to his perception of the relative proportions in which the many subjects of the tripos should be studied; to his capacity for showing his pupils how to learn and how to use their knowledge, and to his practice of continually testing their work by causing them to reproduce what they had been learning. Despite his absorption in teaching Routh kept fully abreast of current advances in mathematical knowledge and made many original investigations. Elected fellow of the Cambridge Philosophical Society in 1854, an original member of the London Mathematical Society in 1865, a fellow of the Royal Astronomical Society in 1866, and of the Royal Society in 1872, he contributed to the 'Proceedings' of these societies as well as to the 'Mathematical Messenger' and the 'Quarterly Journal of Mathematics' numerous papers on varied topics in geometry, dynamics, physical astronomy, wave motion, 'vibrations, and harmonic analysis. As early as 1855 he had joined Lord Brougham in preparing a separate volume, 'All Analytical View of Newton's Principia,' and in 1860 he supplied an urgent want by issuing a masterly elementary treatise on 'Rigid Dynamics' (7th enlarged edit. 2 vols. 1905; German transl., Leipzig, 1898, with pref. by Prof. Klein of Gottingen). Other important contributions by Routh to mathematical literature were a treatise on 'Statics' (1891, 2 vols.; revised edit. 1896; enlarged edit. 1902) and 'Dynamics of a Particle' (1898). These three dynamical treatises constitute an encyclopaedia and bibliography on the subject which have no equal either here or abroad. In 1877 Routh won the Adams prize with his 'Treatise on the Stability of a Given State of Motion, particularly Steady Motion,' which he wrote in a Christmas vacation. Since the publication of Hamilton's equations of motion and Sir William Thomson's (Lord Kelvin) theory of the 'ignoration of co-ordinates 'no greater advance has probably been made in dynamics than by Routh's theorem of the 'Modified Lagrangian Function,' first given in this essay. A large part of the work on equations of motion in Thomson and Tait's 'Natural Philosophy' was rewritten for the second edition in the light of Routh's developments of the theme.
Routh took little part in academic business, but he served for four years (1888-92) on the council of the senate of Cambridge University, and also on the Board of Mathematical Studies. He examined in the
