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.

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).

... 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 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 ...

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'.

... 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"

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."

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.

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.

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.