joint labours bore their great fruit in 1843, when Hamilton discovered quaternions, and it was to Graves that he made on 17 Oct. 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 will be found ample acknowledgments of his indebtedness to his friend for stimulus and suggestion. Graves modestly disclaimed the credit of suggestion, and continued to be a sympathetic companion of the great mathematician in all his future work. Soon after the communication to him of 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 analogous to Hamilton's theory of quarternions, introducing four imaginaries, additional to Hamilton's i j k, and conforming to ‘the law of the modulus.’ This he imparted to Hamilton, in whom it excited great interest, but on account of its imperfection in the combination of factors it had to resign competition with quaternions as a working calculus. The same is to be said of a pure-triplet system founded on the roots of positive unity, which about this time Graves devised in remarkable coincidence with his brother, Professor Charles Graves, now bishop of Limerick. He afterwards stimulated Sir W. Rowan Hamilton in the study of polyhedra, and received in consequence from him the first intimation of the discovery of the icosian calculus, to which Hamilton was conducted by that study. In addition to the publications already mentioned Graves contributed 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.).’
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. For many years he occupied himself in forming a collection of mathematical works of all ages and countries. This portion of his library he bequeathed to University College, London, in remembrance of his former connection as professor with that institution. From the preface to the catalogue of the library of University College the following extract is taken as showing the extent and value of this bequest: ‘The Graves Library is a most valuable collection of more than ten thousand books and about half as many pamphlets. … Perhaps no private scholar has ever formed a mathematical library so nearly complete. Many of the books are very rare, some probably unique, and about one half of the whole collection is in handsome bindings.’ 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, F.R.S., and died without issue on 29 March 1870 at Cheltenham, soon after his resignation of his office.
[An obituary notice of Graves is prefixed to the Proceedings of the Royal Society, vol. xix., and the University College (London) Gazette, vol. i. No. 12, contains a memoir, which concludes with a sketch of his personal character. For additional particulars reference may be made to the Life of Sir William Rowan Hamilton, 3 vols. Dublin, 1882, 1885, 1888.]
GRAVES, RICHARD, the elder (1677–1729), antiquary, born at Mickleton, Gloucestershire, on 22 April 1677, was the eldest son of Samuel Graves of Mickleton Manor, by his wife Susanna, daughter of Captain Richard Swann of the royal navy. After some schooling at Campden, Gloucestershire, under Robert Morse, and at Stratford-on-Avon, he was sent to Pembroke College, Oxford, but left without taking a degree. A devoted student of antiquities and genealogy, he lived a retired life at Mickleton. Besides amassing materials for an elaborate historical pedigree of his own family, he made large collections in illustration of the history and antiquities of the hundred of Kiftsgate, Gloucestershire, and of the several places where his estate
