by W. J. Harrison, rev. I. Grattan-Guinness
© Oxford University Press 2004 All rights reserved
Donkin, William Fishburn (1814-1869), astronomer and mathematician, the first son of Thomas Donkin, was born at Bishop Burton, Yorkshire, on 15 February 1814. He early showed a marked talent for languages, mathematics, and music. He was educated at St Peter's School, York, and in 1832 entered St Edmund Hall, Oxford. In 1834 he won a classical scholarship at University College, Oxford, where in 1836 he obtained a double first class in classics and mathematics, and a year later he carried off the mathematical and Johnson mathematical scholarships. He proceeded BA on 25 May 1836, and MA in 1839. He was elected as a fellow of University College, and he continued for about six years at St Edmund Hall as mathematical lecturer. During this period he wrote an able 'Essay on the theory of the combination of observations' for the Ashmolean Society, which was also published in French; and he also contributed some excellent papers on Greek music to Dr Smith's Dictionary of Antiquities.
In 1842 Donkin was elected Savilian professor of astronomy at Oxford, a post which he held for the remainder of his life. That year he was elected a fellow of the Royal Society, and also of the Royal Astronomical Society. In 1844 he married Harriet, the third daughter of the Revd John Hawtrey of Guernsey.
Between 1850 and 1860 Donkin contributed several important papers to the Philosophical Transactions, including 'On a class of differential equations, including those which occur in dynamical problems' (PTRS, 144, 1854) and 'The equation of Laplace's functions' (PTRS, 147, 1857). In these and other papers he drew upon W. R. Hamilton's theory of quaternions. He also deployed the symbolic methods of solving differential equations widely used by English mathematicians at the time; a major figure was George Boole, who published some of Donkin's results in his Treatise on Differential Equations (1859). They included new ways of solving Laplace's equation, and also an important equation due to Laplace concerning potentials of a nearly spherical spheroid (such as the earth). He and Boole also exchanged ideas on methods of computation in probability theory. In 1861 he read an important paper to the Royal Astronomical Society entitled 'The secular acceleration of the moon's mean motion' (printed in the society's Monthly Notices for 1861). He was also a contributor to the Philosophical Magazine, his last paper in which, 'Note on certain statements in elementary works concerning the specific heat of gases', appeared in 1864.
Donkin's acquaintance with practical and theoretical music was very thorough. His work on acoustics, intended to be his opus magnum, was commenced in 1867, and the fragment of it which he completed was published, after his death, in 1870. Basing his mathematical treatment on Fourier series, he covered transverse and lateral vibrations of strings and rods, and free and forced oscillations. He also examined the composition of the musical scale, and had intended to present musical theory and practice in a third part. The second part would have treated elastic membranes, plates and solids, and the mathematical theory of sound. Although incomplete, his book was the principal work in English on this topic until Lord Rayleigh's Theory of Sound appeared in two volumes in 1877 and 1878. Among other interests, Donkin also corresponded on geometrical problems with William Spottiswoode.
Donkin's constitution was always delicate, and failing health compelled him to live much abroad during the latter part of his life. He died at his home in Broad Street, Oxford, on 15 November 1869. He was survived by his wife.
W. J. HARRISON, rev. I. GRATTAN-GUINNESS
Sources
Monthly Notices of the Royal Astronomical Society, 30 (1870-71), 84 ff.
G. Boole, Treatise on differential equations (1859)
M. Panteki, 'Relationships between algebra differential equations and logic in England, 1800-1860', CNAA PhD, Middlesex Polytechnic, 1992
d. cert.
Foster, Alum. Oxon.
Archives
MHS Oxf., corresp. with Sir B. C. Brodie
RS, Boole MSS
Wealth at death
under £5000: probate, 10 Jan 1870, CGPLA Eng. & Wales
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