William Fishburn Donkin

Quick Info

15 February 1814
Bishop Burton, Yorkshire, England
15 November 1869
Oxford, England

William Donkin was a mathematician who became Savilian Professor of Astronomy at the University of Oxford. He had broad interests writing on least squares, Laplace's functions, attraction of solids, and music.


William Donkin was the son of Thomas Donkin (1776-1856) and Alice Bateman (1785-1860). Thomas Donkin, baptised 8 July 1776 at St John Lee, Sandhoe, Northumberland, was a land agent who married Alice Bateman on 6 June 1809 in Whitby, Yorkshire. Thomas and Alice Donkin had eleven children: William Bateman Donkin (born 1810), Sarah Donkin (born 1811), Alice Donkin (born 1812), William Fishburn Donkin (born 1814), Mary Donkin (born 1815), Thomas Bateman Donkin (born 1818), Henry Donkin (born 1820), James Rumsey Donkin (born 1822), Henry Donkin (born 1823), Edward Donkin (born 1825), and Frederick Donkin (born 1828). William Fishburn Donkin was, therefore, the second son, but William Bateman Donkin did not survive and so William became the eldest surviving son. He had two elder sisters, one younger sister and seven younger brothers but several of his younger siblings died as babies.

William Donkin had two uncles who were men of considerable importance. Bryan Donkin (1768-1855), a brother of William's father, was both a fellow of the Royal Society and a fellow of the Royal Astronomical Society. A leading engineer, he developed a paper making machine, set up perhaps the first canning factory, assisted Thomas Telford in canal construction, assisted Isambard Kingdom Brunel in tunnel building and helped Charles Babbage in constructing his computers. Thomas Bateman (1778-1821), a brother of William's mother, studied medicine in Edinburgh and became a leading expert on dermatological diseases.

It was while still a young child that Donkin showed his wide range of interests [6]:-
Very early in life his taste for languages, mathematics, and music, became apparent, and, in addition, he possessed perseverance and love of acquiring knowledge, that almost before he left the nursery he was known to cry when help was forced upon him which he felt he did not need, and which deprived him of the discovery he wanted to make for himself. The education he received from his father also developed a love for physics and chemistry.
Donkin's family wanted him to have a top quality education but they did not want to see him lose the influence that his family were able to provide. To achieve this the family moved to York in 1829 so that William Donkin could be educated at the famous St Peter's School, York. This school, which claims to be the third oldest school in the world which is still operating, was founded in 627 and Alcuin was one of the early headmasters around 750. At St Peter's School, Donkin was taught classics by Stephen Creyke (1796-1883). Creyke had been appointed headmaster of the school in 1827 and he was very successful both as headmaster and as teacher. We note that Creyke went on to become Archdeacon of York from 1845 to 1866. Donkin spent three years at St Peter's School and always emphasised what a huge debt he owed to Creyke who he considered to be a truly outstanding teacher.

Donkin left St Peter's School in 1832 and matriculated at St Edmund's Hall, University of Oxford, on 10 October 1832. In 1834 he won a classical scholarship at University College, Oxford, and he graduated with a B.A. on 25 May 1836 being awarded first class honours in both classics and in mathematics. He was elected a fellow of University College in 1836, defeating the well-known hymn writer and theologian Frederick William Faber. Donkin continued to hold the fellowship until 1843. He was awarded the Senior Mathematical Scholarship and the Johnson Mathematical Scholarship, both in 1837. The Johnson Mathematical Scholarship was named for John Johnson (1776-1831) who had been a fellow of Magdalen College 1800-1827. After inheriting a considerable amount of property from his mother in 1827 Johnson resigned his fellowship and after he died in 1831 he left money to fund a Mathematical Scholarship and a Theology Scholarship, both open to the whole University. From 1836 to 1842, Donkin was a mathematics lecturer at St Edmund's Hall; he became bursar in 1840.

One of Donkin's early publications was not on mathematics but on ancient music. This article appeared in William Smith's "A Dictionary of Greek and Roman Antiquities" published in 1842. In this year he was appointed as Savilian professor of astronomy at Oxford and shortly after this he was elected a fellow of the Royal Society and also a fellow of the Royal Astronomical Society. His first mathematical publication was An Essay on the Theory of the Combination of Observations (1844) which he presented to the Ashmolean Society on 26 February 1844. W Leon Harter writes [5]:-
William Fishburn Donkin (1844) starts from the assumption that the weight of an observation is proportional to the square of its precision (inversely proportional to its variance) and, as one would expect, he reaches the same conclusion as the one Gauss (1823) reached by assuming a squared error loss function, namely that the method of least squares should be used, independently of the law of facility of error.
Donkin (1851) offers some critical remarks on the theory of least squares, and especially on the remarks of Ellis. Donkin says that Herschel's proof "should be treated with respect" and that the method of least squares may be used, if for no other reason, because "it is a very good method", as shown by Gauss (1823).
We have collected information on Donkin's publications which you can read at THIS LINK.

On 25 June 1844, Donkin married Harriet Hawtrey (1816-1876) in St Peter's Church, Oxford. Harriet had been born in Exeter, Devon, on 6 March 1816, the daughter of the Rev John Hawtrey, at that time Rector of St James' Church, Guernsey and later Rector of Kingston Seymour, Somerset, and his wife Anne Watson who had been born in Quebec, Canada. William and Harriet Donkin had six children, one of whom died as a child: William Frederick Donkin (1845-1888); Arthur Edward Donkin (1848-1937); Alice Emily Donkin (1850-1929); Alfred Henry Donkin (1850-1855); Edward Hawtrey Donkin (1853-1927); and Reginald Donkin (1855-1937). Let us record a little about some of these children at this point.

William Frederick Donkin [7]:-
... was the son of the late Savilian Professor of Astronomy at Oxford, and inherited from his father scientific tastes, and a rare musical talent. The father was brilliant as a scholar as well as profound as a mathematician, and the son combined the fine taste of an artist with the patience and accuracy of a scientific worker. Indefatigable and successful as lecturer on chemistry at St George's Hospital, and in pursuing the practical developments of electric lighting, Mr Donkin had made his leisure a source of pleasure and instruction to a large public.
He was a member of the Alpine Club and the Photographic Society, and he died on a mountaineering trip in the Bezingi district of the Central Caucasus mountains. We note that both father and son, William Fishburn Donkin and William Frederick Donkin, wrote papers under the name "W F Donkin", a complication for historians!

Arthur Edward Donkin became a mathematics lecturer. He was a fellow of Exeter College 1874-75 and a tutor at Keble College. He has a portrait in the National Portrait Gallery. Edward Hawtrey Donkin studied at Lincoln College, Oxford and became Professor of Classics at Royal Holloway College in 1890. He wrote articles for A Dictionary of Music and Musicians.

Let us return to our description of Donkin's life. Even at the time of his marriage [6]:-
... he was beginning to suffer from a delicacy of constitution, which became a cause of great anxiety to his family; and in the midst of the most hopeful anticipations for science, when his rare abilities seemed to promise some of the discoveries which only fall to the lot of such men as he, - even then he was obliged from time to time to relinquish the duties and occupations in which he delighted, in order to try and preserve in other climates the health which was gradually leaving him. In the intervals of improvement he continued with untiring energy to attend to the duties of his Professorship, and to the advance of science in its various branches in Oxford ...
His most productive period for mathematical research was between 1850 and 1860. For information about the papers he wrote during this period, see THIS LINK.

At the time of the 1851 Census the family, consisting of Donkin, his wife and five children, were living in New College Lane, Oxford. They had six servants: a nurse, a cook, a housemaid, a nursemaid and two house servants. He also owned a house in the High Street, Moreton-in-Marsh, Stow on the Wold, Gloucestershire which was let out to Charles Phipps.

Let us look briefly at Donkin's involvement in refereeing papers by Arthur Cayley as described by Sloan Evans Despeaux in [1]:-
Boole's pioneering work on invariant theory of 1841 had inspired Cayley to further the subject, thereby producing 'the most important idea of his mathematical life'. ... Boole was saddled with the task of evaluating Cayley's submission 'On certain formulae of differentiation' for publication in 'Philosophical Transactions'.
Boole was doubtful whether the paper should be published and suggested a second referee be sought: Donkin was asked and [1]:-
... he applauded Cayley's effort, but was unsure of the value of his conclusions: "The cases here examined lead to very complicated calculations, which to ordinary mathematicians would most likely have seemed inextricable, and I believe few besides Mr Cayley would have arrived at any available result. I do not know what may be the value of the conclusions actually obtained at all events the processes might probably to some extent serve as a guide or pattern for similar investigations. Considered in this light, and as a specimen of unusually complex analysis conducted with great skill, I think [the] paper deserves a place in the Transactions; though I should regret its omission less than that of either of the two former memoirs"
Donkin had always been interested in music and so when the University of Oxford was asked about their attitude to music as an academic subject, they asked him to reply. John Donaldson (1789-1865) was professor of music at the University of Edinburgh. Realising that both Oxford and Cambridge had inactive music professors he wanted their opinion whether they considered music as an academic subject [3]:-
William Fishburn Donkin (1814-69), Savilian Professor of Astronomy, wrote on behalf of the University of Oxford. Donkin's interest in acoustics might explain why he was thought a suitable respondent; his 'Acoustics, Theoretical: Part 1' was published after his death. He noted that the current professor neither resided in Oxford nor gave lectures, although William Crotch, professor from 1799 to 1847, had given lectures at the start of the nineteenth century. The only duty performed by the music professor in 1851 (none other than Edinburgh's former professor, Henry Bishop) was "examination of the exercises written by Candidates for Musical Degrees." The case at Oxford was complicated by the presence of a "Choragus," appointed to teach, organise, and oversee practical music within the university. Nevertheless, according to Donkin, "I never heard of any other instrument or apparatus provided either for Choragus or Professor." With regard to the Edinburgh Trustees' particular interests, Donkin had an interesting further observation: "I may add that the subject of Harmonics is assigned to the Savilian Professor of Geometry ... . But that Professor has no apparatus provided for him and has never lectured on harmonics within my recollection."
Now in the last years of his life, Donkin was combining his interest in music and in mathematics by writing a book on acoustics. He never finished this work but the first part which he had completed was published in 1870 as Acoustics. Theoretical. Bartholomew Price wrote a Preface explaining that the book was only the first part of what Donkin had intended. Price wrote:-
The Author, the late Professor Donkin, has passed away prematurely from the work. It was a work he was peculiarly qualified to undertake, being a mathematician of great attainments and rare taste, and taking an especial interest in the investigation and application of the higher theorems of analysis which are necessary for these subjects. He was, moreover, an accomplished musician, and had a profound theoretical knowledge of the Science of Music.

He began this work early in the year 1867; but he was continually interrupted by severe illness, and was much hindered by the difficulty, and in many instances the impossibility, of obtaining accurate experimental results at the places wherein his delicate health compelled him to spend the winter months of that and the following years. He took, however, so great an interest in the subject, that he continued working at it to within two or three days of his death.
For the whole of Bartholomew Price's Preface, see THIS LINK.

We end by quoting again from [6]:-
Beyond this there is little to say of those long years during which a life that might have been one of the highest distinction was kept in check by illness and consequent inability to work. Those who knew him best, know how brightly the intellect, which otherwise might have enlightened the world, shone in the narrower sphere to which it was now confined; how his failing strength seemed only to enhance the energy that never stopped short of the limits which his state of health set to its achievements, because unable to pass beyond them; the patience that never once complained through all the weariness and comparative obscurity of his life; and the cheerfulness of character and brilliant cleverness which made a centre of happiness to his home and to his friends.
On 10 January 1870:-
The Will of William Fishburn Donkin late of the City of Oxford Savilian Professor of Astronomy in the University of Oxford deceased who died 15 November 1869 at the City aforesaid was proved at Oxford by the oath of Harriet Donkin of the City aforesaid Widow the Relict the sole Executrix.

References (show)

  1. S E Despeaux, Fit to print? Referee reports on mathematics for the nineteenth-century journals of the Royal Society of London, Notes and Records of the Royal Society of London 65 (3) (2011), 233-252.
  2. Donkin, William Fishburn, Alumni Oxonienses: the Members of the University of Oxford, 1715-1886.
  3. R Golding, Seeking a Philosophy of Music in Higher Education: The Case of Mid-nineteenth Century Edinburgh, Philosophy of Music Education Review 24 (2) (2016), 191-212.
  4. W J Harrison (rev. I Grattan-Guinness), Donkin, William Fishburn (1814-1869), astronomer and mathematician, Oxford Dictionary of National Biography (Oxford University Press, Oxford, 2004).
  5. W Leon Harter, The Method of Least Squares and Some Alternatives: Part I, International Statistical Review 42 (2) (1974), 147-174.
  6. Obituary: William Fishburn Donkin, Monthly Notices of the Royal Astronomical Society 30 (1870-71), 84-86.
  7. Obituary: Mr W F Donkin, and Mr H Fox, Proceedings of the Royal Geographical Society and Monthly Record of Geography 10 (11) (1888), 715-717.

Additional Resources (show)

Other pages about William Donkin:

  1. William Fishburn Donkin's publications

Other websites about William Donkin:

  1. Dictionary of National Biography

Honours (show)

Honours awarded to William Donkin

  1. Fellow of the Royal Society 1842

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update June 2021