John turned down a prestigious Cambridge University admission to enrol at London's Imperial College of Science and Technology.

... was based on the outskirts of Manchester in an elegant Victorian building, "The Towers," described as the "grandest of all Manchester mansions." Originally a private residence, it accommodated the newly founded British Cotton Industry Research Association, named the Shirley Institute after the daughter of a major donor in 1920.

... he set up the equations of equilibrium for a piece of cloth under tension and normal pressure and examined the appropriateness of various types of boundary condition; in particular, he calculated the form assumed by a circular cylinder of cloth subjected to tension at both ends.

The development of mechanical means of evaluating solutions of ordinary differential equations, in the form of the differential analyser of Dr Bush, has made it feasible to undertake the investigation of many problems of scientific and technical interest leading to differential equations which have no convenient formal solution, and which are too elaborate, or for which the range of solutions required is too extensive, for calculation of the solutions by numerical methods to be practicable. The practical success of this machine, and the wide range of equations to which it can be applied, have led to the hope that it may be found possible to apply it to partial differential equations, which are usually regarded as less amenable to numerical methods than ordinary equations. The present paper gives one way of applying it to such equations in two independent variables with certain types of boundary conditions. As will appear, the possibility of applying this method depends more on the form of the boundary conditions than on the exact form of the equations. The method is particularly suited to the differential analyser, though it is also practicable for numerical work.

Womersley's work at Woolwich had two aspects, general computation, and mathematics and statistics applied to ammunition proofing.

He specialised in work on mathematical statistics between 1940 and 1942, publishing an interesting report, "The Statistical Analysis of Variations in Muzzle-Velocity at Cordite Proof and Gun Proof."

Much time may be spent in working out formulae involving a number of variables by research workers who may not have the special aptitude required or are out of practice. Often the effort involved would be better transferred to calculating machines, which have been developed considerably in recent years but are not generally ready to hand. The setting up by the Department of Scientific and Industrial Research of a Mathematics Division, equipped with mechanical computing devices, under Mr J R Womersley, in the National Physical Laboratory should meet a real need. The Division is in three sections, dealing with computing, statistics and the development of calculating machines, and it is also available for consultation in regard to applied mathematics, with particular reference to industrial research.

I was invited by Sir Charles Darwin to apply for the post of Superintendent of the new Division. ... There was, I think, only one other applicant, J R Womersley, who entered this story in 1936 when he was in charge of the Army statistical research unit. He had the ability to speak well and he made a powerful speech at the meeting, on behalf of a statistical organisation (mainly on quality control). I did not have such powerful advocacy and he got the job.

1. Introduction: Commercial Machines In Scientific Computing. The commercial calculating machine has been used in scientific work, after a fashion, for many years. Twenty years ago one or two hand-operated machines were to be found in the mathematics departments of British universities, used by graduate students. But a great stimulus to their better and wider use was given by L J Comrie in lectures given at the London School of Economics in 1926 and 1927, in which he stressed the importance of the intelligent and resourceful use of commercial machines.

About the same time Comrie described the "end-figure" method of constructing mathematical tables by subtabulation, and a means of using this method on Hollerith punched-card equipment. Four years later came his description of the Burroughs Class 11 machine and its use for integration from second differences. About the same time he described his application of the Hollerith tabulator to Ernest W Brown, 'Tables of the Moon', which still stands as a remarkable achievement.

His next great advance was the use of the six-register National Accounting machine as a "difference-engine" to handle problems in finite differences. As a result there are now fifteen National machines in use in research establishments in Great Britain, several times as many as there are in similar use in the United States, where the machine originated!

The story of the adaptation of commercial machines to uses in the scientific field in Great Britain is almost wholly the story of Comrie's life and work. ...

5. Conclusion. There is a great need, with the recent growth of the use of numerical methods, for a critical and exhaustive survey of computing methods, with a study of their field of usefulness in connection with present-day equipment. The examples given are only "small samples" from a vast mass of published material. Before undertaking the design of special machines performing single calculations, the methods and equipment already available should be carefully studied. It is also worth stressing that the great new machines now under development should be provided with "instructions" based on methods suited to their capabilities. Aitken's method of interpolation is a particularly good example of the kind of method that should be looked for, and in the future it will be worth while to think in terms of processes of this kind, rather than formulae in the conventional sense.

Once Womersley had established broad long term plans for the NPL Mathematics Division, he gave the executive committee a brief outline of how he intended to put these plans into operation during 1945. He stated that much time during 1945 would be devoted to recruitment and training of staff and to performing computations for other NPL divisions. He anticipated that very little work would be done towards the construction of the new differential analyser. In the event recruitment to the Mathematics Division was delayed because of restrictions imposed by the Ministry of Labour and National Insurance governing the appointment of staff before the end of the war had been officially declared.

Turing's lack of respect for Womersley rubbed off on some of the other Mathematics Division staff.

Since the second world war we have seen brought to fruition a remarkable series of developments in the means of calculation, envisaged 100 years ago by Charles Babbage, the significance of which is realised at present by only a few people. A number of these machines have been described in lectures and in scientific papers and there is already a considerable literature on the subject. Now it is clear to the professional statistician, whose work involves good deal of computing and the handling of numerical information in various ways, that the advent of equipment of this kind must have a powerful effect on his work.

My own feeling is that programming makes great demands, not on intellectual ability as such, but on powers of concentration, and experience both at the National Physical Laboratory and at Cambridge has shown that the work is tedious and exhausting in a most unexpected way which it is difficult to appreciate unless one has had the actual experience. Moreover, the checking of programmes and the weeding out of mistakes can be quite a difficult business. For these reasons one cannot claim that a computer is complete until it has had built for it a permanent library of useful programmes which have been checked and used in practice.

Womersley had little more than a year with B.T.M.C.. Some said that the comparative failure of all earlier B.T.M.C. computers was due to his leadership. I was told by [Cedric Charles] Dickens of B.T.M.C. that its slow start in computer design and production was, partially at least, attributed to Womersley's appointment.

This report contains a compilation of Womersley's writings and results on blood flow, amounting to a book of 254 typed pages, including hundreds of equations, the results of calculations from "the 1103 computer" (presumably WADC's UNIVAC 1103), and more than 100 pages tabulating numerical results from 40 hours work by "the [Harvard] Mark IV Calculator". It neatly illustrates the arc of Womersley's life from applied mathematics to numerical analysis and electronic computers.

Womersley was later (I think) attached to the British Scientific Staff in Washington, but died suddenly leaving his widow in straitened circumstances in Washington as he had left her nothing! I was asked by the British scientific representative in Washington to suggest possible sources of help for Mrs Womersley. She asked me to seek government aid; I did what I could, but the case was poor. The government did, however, make an 'ex gratia' payment.

John Womersley was tall and heavily built; his favourite exercise was walking, and he once walked with a newly purchased perambulator from Golders green to his home in Wimbledon. He was proud of his Yorkshire origin and never completely lost his accent; he was always very good company, and had a fund of entertaining stories, in dialect and otherwise. he had a restless nature, and was often captured by some new enthusiasm; in consequence, he was always at his best when he was starting a new job or setting up a new organisation. Once the show was in running order, however, he tended to lose patience with administrative detail and routine; he had many ideas about new uses for mathematical techniques, and he would soon be looking round for a new field in which his particular talents could be employed. Although not himself a brilliant mathematician, he was often the first to perceive the existence of a problem and to translate it into mathematical language; in this way he stimulated many others to do important work.