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.]
COGHLAN, JEREMIAH (1776 ?-1844), captain in the navy, was in January 1796 mate of a merchant ship at Plymouth, and on the occasion of the wreck of the Button East Indiaman [see Pellew, Edward, Viscount Exmouth] displayed such energy and courage that Pellew offered to put him on the Indefatigable's quarter-deck. In the Indefatigable he continued for three years, and in March 1799 followed Pellew to the Impetueux. In June 1800 he was put by Pellew in command of the Viper cutter ; and while watching Port Louis conceived the design of cutting out a French gun-vessel lying in the entrance of the harbour. Pellew lent him a ten-oared cutter, and in this, with eighteen men and a midshipman Silas Hiscutt Paddon on the night of 29 July, he boarded and after a hard fight captured the gun-brig Cerbere, 'mounting three long 24-pounders and four 6-pounders, full of men, moored with springs on her cables, in a naval port of difficult access, within pistol-shot of three batteries, surrounded by several armed craft, and not a mile from a 74 bearing an admiral's flag, and two frigates' (Pellew, Despatch). Being repulsed in the first attempt, wounded and thrown back into the boat, Coghlan renewed the struggle. Both he and Paddon received several severe wounds, six of his men were wounded, and one was killed ; but the Cerbere was taken and towed out under a heavy fire from the batteries. The squadron, to mark their admiration of the exploit, gave up the prize to the immediate captors ; and Pellew, in his official letter to Lord St. Vincent, excused himself for dwelling on the courage and skill 'which formed, conducted, and effected so daring an enterprise.' St. Vincent, in forwarding Pellew's letter to the admiralty, spoke of the pride and admiration with which the service had filled him, rivalling, as it did, the enterprise of Sir Edward Hamilton [q. v.] and of Captain Patrick Campbell [q.v.], and in his letter to Pellew desired him to give his thanks in 'the most public manner' to acting-lieutenant Coghlan, Mr. Paddon, and the other brave fellows under his command, and privately begged him to present to Coghlan ' in the most appropriate manner' a sword of one hundred guineas' value. On St. Vincent's representation, Coghlan, though he had only served in the navy for four and a half years, was promoted to the rank of lieutenant on 22 Sept. 1800, and continued in command of the Viper till she was paid off in October 1801. In the spring of 1802 he was appointed to the Nimble cutter ; and on 1 May 1804 was promoted to the command of the Renard sloop on the Jamaica station. On 20 March 1806 he fell in with and brought to action the French privateer, General Ernouf, whose captain, it was said, hailed the Renard in English, commanding her to 'strike.' 'Strike I will,' answered Coghlan, 'and damned hard too.' After an action of thirty-five minutes the General Ernouf was set on fire and blew up with the loss of upwards of one hundred men. In August 1807 Coghlan was moved into the Elk brig on the same station, and for nearly four years was senior