Raphael did receive some tutoring from a local clergyman before he was thirteen years old then, in 1873, he entered Mr Watson's boarding school at Caversham near Reading. After three years at the school, followed by several months of private study, he entered University College, London, in 1876. There he studied a wide range of subjects which he took in preparation for studying medicine. He was taught mathematics by Henrici who impressed Weldon more than any of his other lecturers; he later wrote that Henrici was the first naturally gifted teacher he had studied under.
In 1877 Weldon went to King's College, London, his aim still being to enter the medical profession. He moved to St John's College in Cambridge, matriculating on 6 April 1878, and, influenced by Francis Maitland Balfour, his interests turned towards zoology. He won scholarships and produced outstanding results despite periods of ill health. Before he sat the Natural Science Tripos in 1881 he suffered a tragedy when his brother Dante died suddenly. Despite the exceptionally difficult circumstances under which he took the examinations, he gained a First Class degree that year.
After graduating he began research, going to Naples where he worked at the Zoological Station. He was appointed a demonstrator in zoology at Cambridge in 1882, becoming a fellow of St John's College and a university lecturer in invertebrate morphology in 1884. His teaching was described in these glowing terms:-
Seldom is it given to a man to teach as Weldon taught. He lectured almost as one inspired. His extreme earnestness was only equalled by his lucidity. He awoke enthusiasm even in the dullest, and had the divine gift of compelling interest.Weldon married Florence Tebb, from Burstow in Surrey, on 13 March 1883. She played a large role in Weldon's scientific work, assisting him on many of his projects. After he was married Weldon took all his holidays with his wife in places where they could study marine biology. In particular they visited the Bahamas in 1886 for a visit which was scientifically very profitable. The Marine Biological Association set up a laboratory in Plymouth and Weldon and his wife began spending all their vacations there undertaking research. By 1888 they were spending as much time there as Weldon's duties at Cambridge would allow, and he only went to the university to give his lectures. He undertook research June to January, teaching at Cambridge for two terms each year.
Why is this zoologist in our History of Mathematics Archive? His work soon began to involve statistical analysis. He was led in this direction by work of Galton on natural inheritance. He extended the statistical analysis that Galton and Quetelet had applied to humans to other zoological species. Realising that his mathematical skills were somewhat less than he wished, Weldon read widely studying, in particular, the leading works by the French mathematicians on the calculus of probability. His work involved studying correlation coefficients for the relation between measurements of organs in animals and is important for the beginnings of biometry.
He studied shrimps making measurements of different features on shrimps from different locations. He soon found that the measurements he took lay on a normal distribution. He published two papers on this topic, the second investigating correlations between measurements of certain organs in the shrimps. Many consider that these two papers lay the foundations of "biometrics".
Weldon was elected a fellow of the Royal Society in May 1890 and later that year he was appointed Jodrell professor at University College, London, taking up his duties in 1891. This was a fortunate appointment, for it brought him in close contact with Pearson who had been appointed there five years earlier. Walker writes (see Pearson's biography):-
The importance for science of the intense personal friendship which soon sprang up between Pearson and Weldon, then both in their early thirties, can scarcely be exaggerated. Weldon asked the questions that drove Pearson to some of his most significant contributions.What were the questions which Weldon asked Pearson? How does one describe asymmetrical, double-humped, and other non-Gaussian frequency distributions? How does one derive best values for the parameters of such distributions? What are the probable errors of such estimates? What is the effect of selection on one or more of the correlated variables?
By 1893 Weldon was serving on a Royal Society Committee along with Galton and Pearson 'For the Purpose of conducting Statistical Enquiry into the Variability of Organisms'. In a paper which he published in 1894 Some remarks on variation in plants and animals which arose from the work of the Royal Society Committee, Weldon wrote:-
... the questions raised by the Darwinian hypothesis are purely statistical, and the statistical method is the only one at present obvious by which that hypothesis can be experimentally checked.Weldon proposed a journal for biometrics in a letter written to Pearson dated 16 November 1899. It was written after William Bateson, a pioneer in genetics, had been highly critical of one of Pearson's papers submitted to the Royal Society. Weldon wrote:-
The contention 'that numbers mean nothing and do not exist in Nature' is a very serious thing, which will have to be fought. Most other people have got beyond it, but most biologists have not. Do you think it would be too hopelessly expensive to start a journal of some kind? ...The journal Biometrika was named within weeks and Weldon and Pearson became joint editors. They were remarkably quick in getting the journal up and running, for the first issue appeared in October 1901. The editorial, written by Weldon and Pearson, set out the scope:-
Biometrika will include (a) memoirs on variation, inheritance, and selection in animals and plants, based upon the examination of statistically large numbers of specimens (this will of course include statistical investigations of anthropometry); (b) those developments of statistical theory which are applicable to biological problems; (c) numerical tables and graphical solutions tending to reduce the labour of statistical arithmetic; (d) abstracts of memoirs, dealing with these subjects, which are published elsewhere; and (e) notes on current biometric work and unsolved problems.Weldon was appointed to a chair in Oxford in 1900 and he held this post until his death in 1906. In 1898 he had given the presidential address to Section D, the zoology section, of the British Association, and during the 1904 meeting in Cambridge he became involved in an argument over Mendel's work on plant hybridisation :-
Mr William Bateson, as president of Section D for that year, had devoted his address to a vindication of Mendelian principles in regard to heredity and variation, and subsequent discussion on the same subject provoked from professor Weldon and Professor Karl Pearson some rather severe criticism, to which Mr Bateson replied. The debate, which was conducted before a large and somewhat agitated audience, resolved itself into a dialectical duel between the president of the section and professor Weldon, and developed quite a considerable amount of heat.In the Easter vacation of 1906 Weldon was staying with his wife in an inn at Woolstone when he contracted pneumonia. It is likely that the illness became serious due to overwork and Weldon's refusal to stop work when he became ill. Refusing to give up work, he returned to London by which time the pneumonia had become acute. He was admitted to a nursing home but died there. He was buried at Holywell in Oxford.
In  Pearson gives this rather touching description of Weldon:-
He was by nature a poet, and these give the best to science, for they give ideas.
Article by: J J O'Connor and E F Robertson