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Sir James Cockle FRS FRAS FCPS (14 January 1819 – 27 January 1895) was an English lawyer and mathematician. Cockle was born on 14 January 1819. He was the second son of
James Cockle Sir James Cockle FRS FRAS FCPS (14 January 1819 – 27 January 1895) was an English lawyer and mathematician. Cockle was born on 14 January 1819. He was the second son of James Cockle, a surgeon, of Great Oakley, Essex. Educated at Charterh ...
, a surgeon, of Great Oakley, Essex. Educated at Charterhouse and
Trinity College Trinity College may refer to: Australia * Trinity Anglican College, an Anglican coeducational primary and secondary school in , New South Wales * Trinity Catholic College, Auburn, a coeducational school in the inner-western suburbs of Sydney, New ...
, 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 William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of Eng ...
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.


Personal life

Sir James married Adelaide, who became Lady Cockle when he was knighted in 1869. His residence
Oakwal Oakwal is a heritage-listed villa at 50 Bush Street, Windsor, City of Brisbane, Queensland, Australia. It was designed by architect James Cowlishaw and built in 1864 by John Petrie with subsequent modifications to . It was added to the Queens ...
in Windsor, Queensland, Brisbane is listed on the
Queensland Heritage Register The Queensland Heritage Register is a heritage register, a statutory list of places in Queensland, Australia that are protected by Queensland legislation, the Queensland Heritage Act 1992. It is maintained by the Queensland Heritage Council. ...
. 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
tessarine In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^* = (w, -z), and the product of two bicomplex numbers as :(u,v)(w,z) = (u w - v z, u z ...
s and
coquaternion In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers. After introduction i ...
s, 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 The Royal Society of Queensland was formed in Queensland ) , nickname = Sunshine State , image_map = Queensland in Australia.svg , map_caption = Location of Queensland in Australia , subdivision_type = Country , subdivision_name = Austr ...
(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, Cockle became wealthy during his lifetime, leaving an estate of £32,169, which is approximately £2.7 million if adjusted for inflation as of 2008.UK Inflation (CPI) calculator
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Works

Biodiversity Heritage Library has London-Dublin-Edinburgh Philosophical Magazine, series 3 and 4, where articles by James Cockle were published: * 1848
On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra
33:435–9. * 1849
On a New Imaginary in Algebra
34:37–47. * 1849
On the Symbols of Algebra and on the Theory of Tessarines
34:406–10. * 1849
On Systems of Algebra involving more than one Imaginary, and on Equations of the Fifth Degree
35: 434 to 7 * 1850
On the True Amplitude of a Tessarine, on the Origin of the word Theodolite, and on Light under the action of Magnetism
36:290-2. * 1850
On Impossible Equations, on Impossible Quantities and on Tessarines
37:281–3. * 1851
On the Solution of Certain Systems of Equations
series 4, 2: 289 to 93 * 1852
On Algebraic Transformation, on Quadruple Algebra and on the Theory of Equations
series 4, 3 : 436 to 39 * 1852
On the Method of Symmetric Products
4: 492 to 96 * 185
Method of Symmetric Products, continued
5: 170 to 74 * 1853
Fragment on Multiple Values
6: 444 to 48 * 1854
On Method of Symmetric Products, concluded
7: 130 to 38 Cockle also wrote a series "Method of Vanishing Groups" for the Cambridge and Dublin Mathematical Journal, volumes and pages 2: 267 to 73, 3: 179 to 81, and 4: 174 to 78.


See also

* Judiciary of Australia * List of judges of the Supreme Court of Queensland


References


External links

* * * 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, . {{DEFAULTSORT:Cockle, James 1819 births 1895 deaths People educated at Charterhouse School 19th-century English mathematicians Chief Justices of Queensland Judges of the Supreme Court of Queensland Fellows of the Royal Society Knights Bachelor Colony of Queensland judges 19th-century Australian judges