William Fishburn Donkin (15 February 1814 – 15 November 1869) was an astronomer and mathematician, and Savilian Professor of Astronomy at the University of Oxford.
He was born at Bishop Burton, Yorkshire, the son of Thomas Donkin, Land Agent, and was educated at St Peter's School, York and (from 1832) St Edmund Hall, Oxford He was a nephew of Bryan Donkin.
In 1844 he married Harriet, the third daughter of the Revd John Hawtrey of Guernsey. They had six children: William Frederick (an explorer and mountaineer), Arthur (assistant master, Rugby School), Alice Emily (a painter), Alfred, Edward and Reginald.
He was a contemporary of Charles Dodgson (Lewis Carroll).
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.
From an early age Donkin showed talent for languages, mathematics, and music. In 1834 he won a classical scholarship at University College, Oxford, where in 1836 he obtained a double first class in classics and mathematics (BA 1836, MA 1839). In 1837 he won the mathematical and Johnson mathematical scholarships.
He was a fellow of University College, and for about six years was a mathematical lecturer at St Edmund Hall. During this period he wrote an early statistical essay for the Ashmolean Society, the ‘Essay on the theory of the combination of observations’. He also contributed some papers on Greek music to Dr Smith's Dictionary of Antiquities.
In 1842 Donkin was elected Savilian Professor of Astronomy, a post which he held for the remainder of his life. That year he was elected a Fellow of the Royal Society and the Royal Astronomical Society.
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.