The companion of Sylvester was Arthur Cayley 1. (1) He was the son of an English merchant who had settled in Petrograd and who looked forward to his son's taking part in the business which he had established. Soon after young Cayley, at the age of fourteen, was sent to King's College School, London, it was found that he showed such ability in mat hematics that his father decided that he should proceed to Cambridge. He accordingly entered Trinity College at the age of seventeen, and his progress was such that he graduated with the highest honors, secured a fellowship, and devoted himself to the pr eparation of a number of important memoirs. Forced to find some remunerative employment, he then took up the law, and for fourteen years made a specialty of conveyancing, devoting his leisure to the preparation of further scientific memoirs. Sylvester w as at this time an actuary in London, and the two were close friends and were in frequent consultation. About 1860 the Sadlerian professorship of pure mathematics was established at Cambridge, and Cayley was the first to occupy the chair (1863) 2. Although he wrote but one extensive work, the Treatise on Elliptic Functions (Cambridge, 1876), he contributed a large number of important memoirs to various scientific public ations. In 1889 the Cambridge University Press began the publication of his papers, nearly a thousand in number, in collected form. Seven volumes appeared under his own editorship, the remaining six volumes being published under the supervision of Profe ssor Forsyth.

Cayley's papers cover a very wide range, but it may be said that his chief interest was in the fields of elliptic functions, the theory of invariants, and analytic geometry. Of these the theory of invariants was the one which he did most to advance.

America is indebted to him for his course of lectures at Johns Hopkins University in 1882 on the Abelian and theta functions, whereby he again cooperated with Sylvester, who was then helping to place mathematics in this country on a university bases. Well might Sylvester say of him that whatever he touched he embellished 3

(Smith, pp.465-467)