Cockle was born on 14 January 1819. He was the second son of James Cockle, a surgeon, of Great Oakley, Essex. Educated at Charterhouse and Trinity College, Cambridge, he entered the Middle Temple in 1838, practising as a special pleader in 1845 and being called in 1846. Joining the midland circuit, he acquired a good practice, and on the recommendation of Chief Justice Sir William Erle he was appointed as the first Chief Justice of the Supreme Court of Queensland in Queensland, Australia on 21 February 1863; he served until his retirement on 24 June 1879. Cockle was made a Fellow of the Royal Society (FRS) on 1 June 1865. He received the honour of knighthood on 29 July 1869. He returned to England in 1878. 
Sir James married Adelaide, who became Lady Cockle when he was knighted in 1869.
His residence Oakwal in Windsor, Queensland, Brisbane is listed on the Queensland Heritage Register. It is believed they derived the name Oakwal from Cockle's birthplace at Great Oakley in Essex and his wife's birthplace of Walton in Suffolk.
Mathematical and scientific investigations
Cockle is also remembered for his mathematical and scientific investigations. For instance he invented the number systems of tessarines and coquaternions, and worked with Arthur Cayley (1821–1895) on the theory of linear algebra. Like many young mathematicians he attacked the problem of solving the quintic equation, notwithstanding Abel–Ruffini theorem that a solution by radicals was impossible. In this field Cockle achieved some notable results, amongst which is his reproduction of Sir William R. Hamilton's modification of Abel's theorem. Algebraic forms were a favourite object of his studies. He also made contributions to the theory of differential equations, in particular the development of the theory of differential invariants or criticoids.
He displayed a keen interest in scientific societies. From 1863 to 1879 he was president of the Queensland Philosophical Society (now incorporated in the Royal Society of Queensland); on his return to England he became associated with the London Mathematical Society, of which he was president from 1886 to 1888, and the Royal Astronomical Society, serving as a member of the council from 1888 to 1892. He died in London on 27 January 1895. 
An obituary notice by the Revd. Robert Harley was published in 1895 in Proc. Roy. Soc. vol. 59. A volume containing his scientific and mathematical researches made during the years 1864–1877 was presented to the British Museum in 1897 by his widow. Like his father, Sir James became extremely wealthy during his lifetime, leaving an estate of £32,169, which is approximately £2.7 million if adjusted for inflation as of 2008.
- Marks, E. N. (1969). "Cockle, Sir James (1819–1895)". Australian Dictionary of Biography. Canberra: Australian National University. Retrieved 9 March 2008.
- "Cockle, James (CKL837J)". A Cambridge Alumni Database. University of Cambridge.
- James Cockle at Dictionary of National Biography
- "Oakwal (entry 600345)". Queensland Heritage Register. Queensland Heritage Council. Retrieved 1 August 2014.
- Carlyle 1901.
- UK Inflation (CPI) calculator
- This article incorporates text from a publication now in the public domain: Carlyle, Edward Irving (1901). "Cockle, James". In Lee, Sidney. Dictionary of National Biography, 1901 supplement. London: Smith, Elder & Co.
- This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Cockle, Sir James". Encyclopædia Britannica. 6 (11th ed.). Cambridge University Press. p. 627.
- John J. O'Connor & Edmund F. Robertson (2006) MacTutor Biography found on the MacTutor History of Mathematics archive.
- Bright Sparcs biography from the Australian Science and Technology Heritage Centre.
- Robert de Boer (2009) Mathematical Biography of James Cockle from WebCite.
- J. M. Bennett (2003) Sir James Cockle, First Chief Justice of Queensland, Federation Press, ISBN 1-86287-485-9 .
|New office|| Chief Justice of Queensland
1863 – 1879