of the Proceedings of the King's Council in Ireland for a portion of the Sixteenth Year of the Reign of Richard II, A.D. 1392–3’ (London, 1877). A government pension of 100l. was awarded him. He died at Inisnag on 20 March 1886.
[Unpublished letters and papers of Rev. James Graves; Transactions of the Kilkenny Archæological Society; Journals of the Royal Historical and Archæological Association of Ireland.]
GRAVES, JOHN THOMAS (1806–1870), jurist and mathematician, born in Dublin 4 Dec. 1806, was son of John Crosbie Graves, barrister, grandnephew of Richard Graves, D.D. [q. v.], and cousin of Robert James Graves, M.D. [q. v.] After an undergraduate career in Trinity College, Dublin, where he distinguished himself in both science and classics, was a class-fellow and friend of Sir William Rowan Hamilton [q. v.], and graduated B.A. in 1827, he removed to Oxford, where he became an incorporated member of Oriel College, 11 Nov. 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 [q. v.], who finally retired in 1835. Not long after Graves was elected an examiner in laws in the university of London.
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 law and canon law. He was also a contributor to Smith's ‘Dictionary of Greek and Roman Biography,’ in which, among other articles from his pen, are very full lives of the jurists Cato, Crassus, Drusus, Gaius, and one on the legislation of Justinian. Graves held a high place among the mathematicians of his day in England. In his twentieth year (1826) he engaged in researches respecting exponential functions, which conducted him to important results. They were printed in the ‘Philosophical Transactions’ for 1829 under the title ‘An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ.’ Of these results one of the principal is the discovery of the existence of two arbitrary and independent integers in the complete expression of an imaginary logarithm. He considered that thus a solution was afforded for various difficulties that had formerly perplexed mathematicians, and that he had elucidated the subject of the logarithms of negative and imaginary quantities, which at different periods had occasioned controversies between Leibnitz and John Bernoulli, Euler, and D'Alembert. His claim to independent discovery and priority of printed publication was undisputed, though 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 Peacock, who referred to them in his well-known ‘Report on Algebra,’ nor by Sir John Herschel. Graves accordingly communicated to the British Association in 1834 (see the Report for that year) a defence and explanation of his discovery, and in the same report is contained a paper by Sir W. Rowan Hamilton, in which he comes to the support of his friend, giving the conclusions Graves had arrived at the fullest confirmation. This paper bears as its title ‘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 Nov. 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 carefully 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,’ became the foundation of his future remarkable contributions to algebraical science, culminating in the discovery of quaternions. For many years Graves and Hamilton maintained an active correspondence, in which they vied with each other in endeavours to carry into space a full and coherent interpretation of imaginaries. Graves worked as having for his aim the perfecting of algebraic language; Hamilton had persistently in view the higher object of arriving at the meaning of the science and its operations. These con-
