# Dictionary of National Biography, 1901 supplement/Cockle, James

​COCKLE, Sir JAMES (1819–1895), chief justice of Queensland and mathematician, born on 14 Jan. 1819, was the second son of James Cockle, a surgeon of Great Oakley in Essex. He was educated at Stormond House, Kensington, from 1825 to 1829, and at Charterhouse from 1829 to 1831, and afterwards under the tuition of Christian Lenny. He left England on 29 Nov. 1835, and, after a year's sojourn in the West Indies and the United States of America, entered into residence at Trinity College, Cambridge, on 18 Oct. 1837, graduating B.A. in 1842 and M.A. in 1845. On 12 April 1838 he entered the Middle Temple as a student. He began to practise as a special pleader in 1845, and on 6 Nov. 1846 was called to the bar. In the spring of 1848 he joined the midland circuit. His ability attracted the attention of Sir William Erie [q. v.], then chief justice of the court of common pleas. At his instance he was appointed the first chief justice of Queensland in 1863. In this post his services were of a high order. His judgments were marked by laborious and conscientious preparation, and in only two instances were they reversed on appeal. He was knighted on 29 July 1869, and retired from office in 1879. When the consolidation of the state law of Queensland was effected in 1867 he was senior commissioner.
Cockle, however, was still more eminent as a mathematician than as a judge. He was elected a fellow of the Royal Astronomical Society on 10 March 1854, a fellow of the Royal Society on 1 June 1865, and a fellow of the London Mathematical Society on 9 June 1870. He wrote on the Indian astronomical literature, on the Indian cycles and lunar calendar, on the date of the Vedas and Jyotish Sastra, and on the ages of Garga and Parasara. He also published four elaborate memoirs on the motion of fluids, and some notes on light under the action of magnetism. His chief interest, however, was centred in problems in pure mathematics. His analytical researches were confined for the most part to common algebra and the theory of differential equations. For many years he laboured among the higher algebraic equations with the hope of being able to solve the general equation of the fifth degree. He failed to obtain a general solution, and indeed in 1862 reproduced Abel's attempt to demonstrate its impossibility with Sir William Rowan Hamilton's modifications, in the 'Quarterly Journal of Mathematics' (v. 130-43), but he determined the explicit form of a sextic equation, on the solution of which he showed that that of the general quintic depended. This result was independently confirmed by the Rev. Robert Harley in a paper published in the 'Memoirs of the Manchester Literary and Philosophical Society' (1860, xv. 172-219), to which Cockle had also contributed his result. Mr. Harley pursued the subject, in two papers on the 'Theory of Quintics' in the 'Quarterly Journal of Mathematics' (1860-2, iii. 343- ​359, v. 248–60), and also in an exposition of Cockle's method of symmetric products in 'Philosophical Transactions' in 1860. These papers attracted the attention of Arthur Cayley [q. v. Suppl.], who carried the investigation further.
Cockle's contributions to the theory of differential equations were also noteworthy. He found that from any rational and entire algebraic equation of the degree n, whereof the coefficients are functions of a single parameter, it is possible to derive a linear differential equation of the order n–1, which is satisfied by any one of the roots of the algebraic equation. From this discovery the theory of differential resolvents was evolved. He was also the first to discover and develop the properties of those functions called criticoids or differential invariants. He contributed numerous papers on mathematical and philosophical subjects to the journals already mentioned, as well as to the 'Philosophical Magazine' and the 'Proceedings 'of the Royal Societies of New South Wales and Victoria.
Cockle returned to England in 1879. He was president of the Queensland Philosophical Society (now incorporated into the Royal Society of Queensland) from 1863 to 1879. From 1886 to 1888 he was president of the London Mathematical Society, and from 1888 to 1892 he served on the council of the Royal Astronomical Society. He died at his residence in Bayswater on 27 Jan. 1895, and was buried at Paddington cemetery on 2 Feb. On 22 Aug. 1855 he was married at St. John's, Oxford Square, Paddington, to Adelaide Catherine, eldest surviving daughter of Henry Wilkin, formerly of Walton, Suffolk. His wife and eight children survived him. A volume entitled 'Mathematical Researches,' consisting of Cockle's contributions to scientific journals between 1864 and 1877, was presented to the British Museum by Lady Cockle in 1897.
[Memoir by the Rev. Robert Harley, F.R.S., in the Proc. of the Royal Soc. vol. lix. (with portrait); Men and Women of the Time, 1891.]
E. I. C.