John T. Graves
Encyclopedia
John Thomas Graves was an Irish
jurist
and mathematician
. He was a friend of William Rowan Hamilton
, and is credited both with inspiring Hamilton to discover the quaternion
s and with personally discovering the octonion
s, which he called the octaves. He was the brother of the mathematician Charles Graves.
, D.D., and cousin of Robert James Graves
, M.D. He was an undergraduate at Trinity College, Dublin
, where he distinguished himself in both science and classics, and was a class-fellow and friend of William Rowan Hamilton
, graduating B.A. in 1827. He then moved to Oxford, where he became an incorporated member of Oriel College
, 11 November 1830. Graves proceeded M.A. at Oxford in 1831, and at Dublin in 1832.
He was called to the English bar in 1831 as a member of the Inner Temple
, having previously (1830) entered the King's Inns, Dublin. For a short time he went the western circuit, and in 1839 he was appointed professor of jurisprudence in London University College in succession to John Austin
, who finally retired in 1835. Not long after Graves was elected an examiner in laws in the University of London
.
Graves was one of the committee of the Society for the Diffusion of Useful Knowledge
. In 1839 he was elected a member of the Royal Society
, and he subsequently sat upon its council. He was also a member of the Philological Society
and of the Royal Society of Literature
. In 1846 Graves was appointed an assistant poor-law commissioner, and in the next year, under the new Poor Law Act, one of the poor-law inspectors of England and Wales.
He married in 1846 a daughter of William Tooke, and died without issue on 29 March 1870 at Cheltenham.
and the complex logarithm
; they were printed in the Philosophical Transactions for 1829 under the title ‘An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ.’ M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock
, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, ‘On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm.’ It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy
on 24 November 1833, ‘On Conjugate Functions or Algebraic Couples,’ and subsequently published in the seventeenth volume of the ‘Transactions’ of the Royal Irish Academy. To this memoir were prefixed ‘A Preliminary and Elementary Essay on Algebra as the Science of Pure Time,’ and some ‘General Introductory Remarks.’ In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was ‘in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms,’ that he was conducted to ‘the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers.’ Hamilton's work culminated in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine
for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions Graves employed himself in extending to eight squares Euler's theorem that the sum of four squares multiplied by the sum of four squares gives a product which is also the sum of four squares, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i j k, and conforming to ‘the law of the modulus.’
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus
.
Graves contributed also to the Philosophical Magazine for April 1836 a paper ‘On the lately proposed Logarithms of Unity in reply to Professor De Morgan,’ and in the London and Edinburgh Philosophical Magazine for the same year a ‘postscript’ entitled ‘Explanation of a Remarkable Paradox in the Calculus of Functions, noticed by Mr. Babbage.’ To the same periodical he contributed in September 1838 A New and General Solution of Cubic Equations; in 1839 a paper On the Functional Symmetry exhibited in the Notation of certain Geometrical Porisms, when they are stated merely with reference to the arrangement of points; and in April 1845 a paper on the ‘Connection between the General Theory of Normal Couples and the Theory of Complete Quadratic Functions of Two Variables.’ A subsequent number contains a contribution ‘On the Rev. J. G. MacVicar's Experiment on Vision,’ and the ‘Report’ of the Cheltenham meeting in 1856 of the British Association contains abstracts of papers communicated by him ‘On the Polyhedron of Forces’ and ‘On the Congruence nx ≡ n + 1 (mod. p.).’
and canon law
. He was also a contributor to William Smith
's Dictionary of Greek and Roman Biography, with lives of the jurists Cato, Crassus, Drusus, Gaius, and an article on the legislation of Justinian.
Attribution
Ireland
Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...
jurist
Jurist
A jurist or jurisconsult is a professional who studies, develops, applies, or otherwise deals with the law. The term is widely used in American English, but in the United Kingdom and many Commonwealth countries it has only historical and specialist usage...
and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was a friend of William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
, and is credited both with inspiring Hamilton to discover the quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s and with personally discovering the octonion
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H...
s, which he called the octaves. He was the brother of the mathematician Charles Graves.
Life
Born in Dublin 4 December 1806, he was son of John Crosbie Graves, barrister, grandnephew of Richard GravesRichard Graves
Richard Graves was an English minister, poet, and novelist.Born at Mickleton Manor, Mickleton, Gloucestershire, to Richard Graves, gentleman, and his wife, Elizabeth, Graves was a student at Abingdon School and Pembroke College, Oxford...
, D.D., and cousin of Robert James Graves
Robert James Graves
Robert James Graves, M.D., F.R.C.S. was an eminent Irish surgeon after whom Graves' disease takes its name. He was President of the Royal College of Physicians of Ireland, Fellow of the Royal Society of London and the founder of the Dublin Journal of Medical Science...
, M.D. He was an undergraduate at Trinity College, Dublin
Trinity College, Dublin
Trinity College, Dublin , formally known as the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by letters patent from Queen Elizabeth I as the "mother of a university", Extracts from Letters Patent of Elizabeth I, 1592: "...we...found and...
, where he distinguished himself in both science and classics, and was a class-fellow and friend of William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
, graduating B.A. in 1827. He then moved to Oxford, where he became an incorporated member of Oriel College
Oriel College
Oriel College is a constituent college of the University of Oxford in Oxford, England. Located in Oriel Square, the college has the distinction of being the oldest royal foundation in Oxford...
, 11 November 1830. Graves proceeded M.A. at Oxford in 1831, and at Dublin in 1832.
He was called to the English bar in 1831 as a member of the Inner Temple
Inner Temple
The Honourable Society of the Inner Temple, commonly known as Inner Temple, is one of the four Inns of Court in London. To be called to the Bar and practise as a barrister in England and Wales, an individual must belong to one of these Inns...
, having previously (1830) entered the King's Inns, Dublin. For a short time he went the western circuit, and in 1839 he was appointed professor of jurisprudence in London University College in succession to John Austin
John Austin
John Austin may refer to:* John Austin , English Catholic writer* John Austin , noted for having been the last person hanged on the famous gallows at Tyburn, London*John Austin...
, who finally retired in 1835. Not long after Graves was elected an examiner in laws in the University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
.
Graves was one of the committee of the Society for the Diffusion of Useful Knowledge
Society for the Diffusion of Useful Knowledge
The Society for the Diffusion of Useful Knowledge , founded in 1826, and wound up in 1848, was a Whiggish London organisation that published inexpensive texts intended to adapt scientific and similarly high-minded material for the rapidly expanding reading public...
. In 1839 he was elected a member of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, and he subsequently sat upon its council. He was also a member of the Philological Society
Philological Society
The Philological Society, or London Philological Society, is the oldest learned society in Great Britain dedicated to the study of language. The society was established in 1842 to "investigate and promote the study and knowledge of the structure, the affinities, and the history of languages"...
and of the Royal Society of Literature
Royal Society of Literature
The Royal Society of Literature is the "senior literary organisation in Britain". It was founded in 1820 by George IV, in order to "reward literary merit and excite literary talent". The Society's first president was Thomas Burgess, who later became the Bishop of Salisbury...
. In 1846 Graves was appointed an assistant poor-law commissioner, and in the next year, under the new Poor Law Act, one of the poor-law inspectors of England and Wales.
He married in 1846 a daughter of William Tooke, and died without issue on 29 March 1870 at Cheltenham.
Mathematical work
In his twentieth year (1826) he engaged in researches on the exponential functionExponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
and the complex logarithm
Complex logarithm
In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the natural logarithm ln x is the inverse of the real exponential function ex. Thus, a logarithm of z is a complex number w such that ew = z. The notation for such a w is log z...
; they were printed in the Philosophical Transactions for 1829 under the title ‘An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ.’ M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock
George Peacock
George Peacock was an English mathematician.-Life:Peacock was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, County Durham. His father, the Rev. Thomas Peacock, was a clergyman of the Church of England, incumbent and for 50 years curate of the parish of Denton, where he also kept...
, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, ‘On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm.’ It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy
Royal Irish Academy
The Royal Irish Academy , based in Dublin, is an all-Ireland, independent, academic body that promotes study and excellence in the sciences, humanities and social sciences. It is one of Ireland's premier learned societies and cultural institutions and currently has around 420 Members, elected in...
on 24 November 1833, ‘On Conjugate Functions or Algebraic Couples,’ and subsequently published in the seventeenth volume of the ‘Transactions’ of the Royal Irish Academy. To this memoir were prefixed ‘A Preliminary and Elementary Essay on Algebra as the Science of Pure Time,’ and some ‘General Introductory Remarks.’ In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was ‘in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms,’ that he was conducted to ‘the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers.’ Hamilton's work culminated in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine
Philosophical Magazine
The Philosophical Magazine is one of the oldest scientific journals published in English. Initiated by Alexander Tilloch in 1798, in 1822 Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since; it was the journal of choice for such luminaries as...
for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions Graves employed himself in extending to eight squares Euler's theorem that the sum of four squares multiplied by the sum of four squares gives a product which is also the sum of four squares, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i j k, and conforming to ‘the law of the modulus.’
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus
Icosian Calculus
The Icosian Calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations....
.
Graves contributed also to the Philosophical Magazine for April 1836 a paper ‘On the lately proposed Logarithms of Unity in reply to Professor De Morgan,’ and in the London and Edinburgh Philosophical Magazine for the same year a ‘postscript’ entitled ‘Explanation of a Remarkable Paradox in the Calculus of Functions, noticed by Mr. Babbage.’ To the same periodical he contributed in September 1838 A New and General Solution of Cubic Equations; in 1839 a paper On the Functional Symmetry exhibited in the Notation of certain Geometrical Porisms, when they are stated merely with reference to the arrangement of points; and in April 1845 a paper on the ‘Connection between the General Theory of Normal Couples and the Theory of Complete Quadratic Functions of Two Variables.’ A subsequent number contains a contribution ‘On the Rev. J. G. MacVicar's Experiment on Vision,’ and the ‘Report’ of the Cheltenham meeting in 1856 of the British Association contains abstracts of papers communicated by him ‘On the Polyhedron of Forces’ and ‘On the Congruence nx ≡ n + 1 (mod. p.).’
Academic lawyer
The records of Graves's work as a jurist are twelve lectures on the law of nations, reported in the Law Times, commencing 25 April 1845, and two elaborate articles contributed to the Encyclopædia Metropolitana on Roman lawRoman law
Roman law is the legal system of ancient Rome, and the legal developments which occurred before the 7th century AD — when the Roman–Byzantine state adopted Greek as the language of government. The development of Roman law comprises more than a thousand years of jurisprudence — from the Twelve...
and canon law
Canon law
Canon law is the body of laws & regulations made or adopted by ecclesiastical authority, for the government of the Christian organization and its members. It is the internal ecclesiastical law governing the Catholic Church , the Eastern and Oriental Orthodox churches, and the Anglican Communion of...
. He was also a contributor to William Smith
William Smith (lexicographer)
Sir William Smith Kt. was a noted English lexicographer.-Early life:Born at Enfield in 1813 of Nonconformist parents, he was originally destined for a theological career, but instead was articled to a solicitor. In his spare time he taught himself classics, and when he entered University College...
's Dictionary of Greek and Roman Biography, with lives of the jurists Cato, Crassus, Drusus, Gaius, and an article on the legislation of Justinian.
Legacy
For many years he collected mathematical works. This portion of his library, more than ten thousand books and about five thousand pamphlets he bequeathed to University College, London.External links
- Graves Scientific Papers at University College LondonUniversity College LondonUniversity College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
Attribution