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 In modern medicine, a surgeon is a medical professional who performs surgery. Although there are different traditions in different times and places, a modern surgeon usually is also a licensed physician or received the same medical training as ...

, 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 Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

, he entered the

Middle Temple The Honourable Society of the Middle Temple, commonly known simply as Middle Temple, is one of the four Inns of Court exclusively entitled to call their members to the English Bar as barristers, the others being the Inner Temple, Gray's I ...

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 The Supreme Court of Queensland is the highest court in the Australian State of Queensland. It was formerly the Brisbane Supreme Court, in the colony of Queensland. The original jurisdiction of the Supreme Court allows its trial division to h ...

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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

(FRS) on 1 June 1865. He received the honour of

knighthood A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the ...

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 Brisbane ( ) is the capital and most populous city of the Australian state of Queensland, and the third-most populous city in Australia and Oceania, with a population of approximately 2.6 million. Brisbane lies at the centre of the South ...

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 Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problem ...

(1821–1895) on the theory of

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrice ...

. Like many young mathematicians he attacked the problem of solving the quintic equation, notwithstanding Abel–Ruffini theorem that a solution by

radical Radical may refer to: Politics and ideology Politics * Radical politics, the political intent of fundamental societal change *Radicalism (historical), the Radical Movement that began in late 18th century Britain and spread to continental Europe an ...

s 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 equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...

s, 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 The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...

, of which he was president from 1886 to 1888, and the

Royal Astronomical Society (Whatever shines should be observed) , predecessor = , successor = , formation = , founder = , extinction = , merger = , merged = , type = NG ...

, serving as a member of the council from 1888 to 1892. He died in London on 27 January 1895. An

obituary An obituary ( obit for short) is an article about a recently deceased person. Newspapers often publish obituaries as news articles. Although obituaries tend to focus on positive aspects of the subject's life, this is not always the case. Ac ...

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 The British Museum is a public museum dedicated to human history, art and culture located in the Bloomsbury area of London. Its permanent collection of eight million works is among the largest and most comprehensive in existence. It docum ...

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 The Biodiversity Heritage Library (BHL) is the world’s largest open access digital library for biodiversity literature and archives. BHL operates as worldwide consortiumof natural history, botanical, research, and national libraries working toge ...

has London-Dublin-Edinburgh

Philosophical Magazine The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Oxford Dictionary of National Biography, Oxford Univer ...

, 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.

References

External links

* * * John J. O'Connor & Edmund F. Robertson (2006
MacTutor Biography
found on the

MacTutor History of Mathematics archive The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathem ...

.
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

Personal life

Mathematical and scientific investigations

Works

See also

References

External links