# John Ronald Womersley

### Quick Info

Morley, Yorkshire, England

Columbus, Ohio, USA

**John Womersley**was an applied mathematician who became involved in the early development of computers. Perhaps his most significant work, however, was in essentially creating the mathematical theory of blood flow.

### Biography

**John Womersley**was the son of the grocer George William Womersley and his wife Ruth Gledhill. George Womersley had married Ruth at St Paul's Church in King Street, Morley, on 7 July 1904. The marriage record gives George Womersley as 26 years old, living at Bridge Street, Morley, the son of James Womersley who was a mill-hand. It also gives Ruth Gledhill as 27 years old, living at 47 King Street, Morley, the daughter of David Gledhill (deceased), who had been a mill-manager. Ruth, who was the youngest of a family of at least eight children, was living with her sister Alice Mary Pettler's family at 47 King Street. Alice, who was 17 years older than Ruth, had married John Pettler who was a newspaper reporter. The 1911 Census lists John Ronald Womersley as 3 years old, living with his parents at 3 Stanhope Road, Thorpe, Wakefield, about 4 km from Morley. His father is recorded as a Cooperative grocery store manager. John was his parents' only child.

John Womersley attended primary school in Morley, then in 1917 he entered Morley grammar school and, in 1922, he was awarded a Northern Universities School Certificate. He graduated from the school in 1925 and his outstanding performance meant that several possibilities opened up or him with the award of an Open Scholarship to the University of Cambridge and the Royal Scholarship in Physics to study physics at the Imperial College of Science and Technology in London [16]:-

John turned down a prestigious Cambridge University admission to enrol at London's Imperial College of Science and Technology.Despite these tempting awards, in fact he chose to specialise in mathematics at the Imperial College of Science and Technology. He took a wide variety of courses in pure mathematics, applied mathematics and physics, in particular hydrodynamics and the kinetic theory of gasses. He graduated with a First Class honours degree in mathematics in 1928 and received the honorary distinction of being made an associate of the Royal College of Science. He remained at the Imperial College for a further two years undertaking research in hydrodynamics. He was awarded the Diploma of Imperial College in 1930. While he was studying at Imperial College, Womersley got to know Jean Isobel Jordan (1907-1995). Jean, born in Deal, near Dover, was working in commercial design and art.

While in London, Womersley had decided that he would try to return to the north of England and get a position involving applications of mathematics. In 1930 he was appointed as a junior research officer in the Shirley Institute in Manchester. The Shirley Institute for Fabric Research [2]:-

... 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.Let us note that the donor was William Greenwood, M.P. for Stockport, and also that the Shirley Institute, after mergers, became the Cotton, Silk, and Man-Made Fibres Research Association in 1961, then the British Textile Technology Group in 1989.

On 18 April 1931 Womersley married Jean Isobel Jordan in St Catherine Coleman alias St Katherine's Church, North Hammersmith. The marriage certificate gives Womersley's address as 45 Whitby Road, Fallowfield, Manchester while Jean Jordan's address is given as 58 Braybrook Street, London W12. The witnesses included Womersley's father, George William Womersley, and his Jean Jordan's father, Alfred George Jordan, a publisher's agent. John and Jean Womersley had three daughters: Barbara Jean Womersley, Ruth Womersley, and Marion Womersley.

Two papers which Womersley published on the work he was undertaking at the Shirley Institute are

*Two nomograms for calculating the fluidity of cellulose solutions*(1934) and

*The application of differential geometry to the study of the deformation of cloth under stress*(1937). In this last mentioned paper [18]:-

... 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.While at the Shirley Institute, he met Leslie John Comrie (1893-1950) who had been promoted to Superintendent of the Nautical Almanac Office in 1930. Comrie was an expert on numerical analysis and had developed punched card computing equipment to construct interpolating tables. At Comrie's suggestion, Womersley spent a month at the Nautical Almanac Office learning Comrie's computational techniques.

Another of Womersley's friends was Douglas Hartree, the Professor of Applied Mathematics at the University of Manchester. They co-authored the paper

*A Method for the Numerical or Mechanical Solution of Certain Types of Partial Differential Equations*(1937), published by the Royal Society, which has the following introduction:-

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.Two further multi-author papers relating to Womersley's work at the Shirley Institute were put on hold and only published after the war ended.

The British government was well aware that the world was moving towards military conflict as Nazi Germany moved rapidly to build its military capabilities. Womersley's reputation was by this time high and, in February 1937, he joined the Civil Service when he was recruited as a scientific officer in the Ballistics Branch of the Research Department. This move meant that the family were now based in Woolwich in East London, which brought Womersley's wife back to her home territory. At first they lived in Bexleyheath, but then moved to Charlton which meant he was nearer to his work at Woolwich [2]:-

Womersley's work at Woolwich had two aspects, general computation, and mathematics and statistics applied to ammunition proofing.On 1 September 1939 German armies invaded Poland and, following the British Prime Minister Chamberlain's ultimatum to Hitler, which was ignored, Britain declared war on Germany on 3 September. At first, for those living in London, there was little evidence that Britain was at war but this changed rapidly with bombing raids in 1940. Although Womersley's family survived, their house in Charlton was destroyed by a bomb and the family were evacuated to Cambridge. After a month living on Cherry Hinton Road to the south east of Cambridge, they found a house in the village of Great Shelford about 6 km due south of Cambridge. By 1942 London was considered safe enough for them to return.

Womersley had been building a differential analyser at Woolwich, but before the work was finished, it was destroyed in a bombing raid in September 1940. His work on computation was, therefore, not carried out by a mechanical computer but rather by a room full of girls operating desk calculators [2]:-

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."By 1942 he was in charge of a department with 40 staff, but also contracted out some of the computational work to supplement that being done by his staff. In May of that year he was promoted to assistant director of scientific research at the Ministry of Supply. This position put him in charge of research in statistics, mathematics and computing. His department, based at Berkeley Court in London, was staffed by many young mathematicians who had studied at Cambridge.

His successful work led to him becoming the Superintendent of the Mathematics Division at the National Physical Laboratory in 1944. The reason for setting up the Mathematics Division is given in [10]:-

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.Donald Sadler was also in the running for the post of Superintendent and writes in [17]:-

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.To prepare Womersley for one of his main tasks at the Mathematics Division, namely to build an electronic stored program computer, he was given clearance to visit the ENIAC (Electronic Numerical Integrator and Computer) project at the University of Pennsylvania's Moore School of Electrical Engineering. During his time as Superintendent of the Mathematics Division, Womersley published one paper

*Scientific Computing in Great Britain*. We quote from this paper [19]:-

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.After returning from the United States, Womersley took up his role as Superintendent of the Mathematics Division in 1945 [6]:-

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.He was denied permission to advertise for staff by the Ministry of Labour in March 1945 but allowed to appoint six senior staff and six assistants with personal recommendations. Having been advised by Hartree that Alan Turing would be a good man to employ, he invited Turing to his home in June 1945. After giving Turing a copy of von Neumann's report on EDVAC (John Mauchly and J Presper Eckert's Electronic Discrete Variable Automatic Computer) to read, he offered him the position of running the project to develop the ACE (Automatic Computing Engine) computer. Turing drew up proposals for ACE and, with supporting documents from Womersley, they were submitted to Executive Committee which approved the project by the summer of 1946. There does seem, however, to have been an unfortunate disagreement between Turing and Womersley about the project. Turing had brilliant ideas of his own, but Womersley wanted to follow the general principles of the ENIAC project. Although Womersley was a good mathematician, he was not in Turing's class, and it appears that Turing had little respect for him [4]:-

Turing's lack of respect for Womersley rubbed off on some of the other Mathematics Division staff.We should note that, of course, Turing was fully aware of the developments in building computers he had been closely connected with at Bletchley Park. Womersley was not aware of these and could not be told because of the Official Secrets Act. This must have resulted in unavoidable tension between the two men when they discussed the ACE project. Turing knew that ACE was based on the pioneering work done at Bletchley Park while Womersley believed it was based on pioneering work done in the United States.

The ACE project was delayed and Turing left the project in 1947, returning to Cambridge. Womersley's Mathematics Division continued to work on a prototype machine, the Pilot ACE, but in September 1950 Womersley left his role as Superintendent of the Mathematics Division at the National Physical Laboratory to take up the post of Director of Research at the British Tabulating Machine Company (B.T.M.C.). There he tried to move the development of computers to try to produce smaller less expensive machines which would be suitable for businesses to use. He read the paper

*High Speed Computers: Their Logical Design, Programming and Other Problems*at the Annual Conference of the Royal Statistical Society at Oxford on 20 July 1952. He began his talk as follows [20]:-

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.He advocated building a library of computer programs [20]:-

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.Donald Sadler writes [17]:-

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.Let us note that Womersley was actually about four years at B.T.M.C. and we should understand that Donald Sadler, having lost out in the appointment to Superintendent of the Mathematics Division at the National Physical Laboratory, may have been harder on Womersley then he deserves.

Leaving B.T.M.C. in 1954, Womersley undertook research at St Bartholomew's Hospital, London, on the mathematical theory of blood flow. This highly productive year led to four single-author papers:

*Flow in the larger arteries and its relation to the oscillating pressure*(1954);

*Oscillatory flow in arteries: effect of radial variation of viscosity on rate of flow*(1955);

*Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known*(1955); and

*Oscillatory motion of a viscous fluid in a thin-walled elastic tube: I: the linear approximation for long waves*(1955). He was also an author on two multi-author papers:

*Velocity profiles of oscillating arterial flow, with some calculations of viscous drag and the Reynolds number*(1955); and

*The Counter Chronometer Method for Recording Pulse-Wave Velocity*(1955).

Womersley continued this line of research when appointed to a mathematical post with the United States Air Force at Wright Field, Dayton, Ohio in 1955. He published

*Oscillatory flow in arteries: I. the constrained elastic tube as a model of arterial flow and pulse transmission*(1957) and wrote the Wright Air Development Center Technical Report

*An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries*(1957) [3]:-

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.After he was diagnosed with cancer, he returned to England in 1957, undergoing several cancer operations in London. Although he returned to Dayton, Ohio before the end of 1957 his treatment had not been successful and he died aged 50 at Columbus, Franklin County, Ohio, USA in March 1958. He was buried at Woodland Cemetery and Arboretum in Dayton, Montgomery County, Ohio.

Donald Sadler writes (somewhat inaccurately) in [17]:-

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.Jean Womersley remained in the United States and died on 28 February 1995 in Montgomery County, Ohio.

Let us end this biography by quoting from Frank Smithies about Womersley's character [18]:-

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.

### References (show)

- M Campbell-Kelly,
*ICL: A business and technical history*(Clarenden Press, Oxford, 1990). - B E Carpenter and R W Doran, John Womersley: Applied Mathematician and Pioneer of Modern Computing,
*IEEE Annals of the History of Computing***36**(2) (2014), 60-70. - B E Carpenter and R W Doran,
*Bibliography of Publications by John R Womersley: Pioneer of Modern Computing and Applied Mathematician*(Centre for Discrete Mathematics and Theoretical Computer Science, October 2015). - B J Copeland,
*Turing. Pioneer of the Information Age*(Oxford University Press, Oxford, 2012). - M Croarken, Womersley, John Ronald (1907-1958), mathematician,
*Oxford Dictionary of National Biography*(2004). - M G Croarken,
*Early scientific computing in Britain*(Oxford University Press, Oxford, 1990) - C G Darwin, Mr J R Womersley,
*Nature***181**(1958), 1240 - C F Fischer,
*Douglas Rayner Hartree His Life in Science and Computing*(World Scientific, 2003). - H H Goldstine,
*The computer from Pascal to von Neumann*(Princeton University Press, 1972). - Government as Producers,
*Electrical Review***87**(3550) (1945), 807-808. - D R Hartree and J R Womersley, A Method for the Numerical or Mechanical Solution of Certain Types of Partial Differential Equations,
*Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences***161**(906) (1937), 353-366. - John Ronald Womersley,
*The Times*(19 March 1958), 13. - John Ronald Womersley,
*Grace's Guide to British Industrial History*.

https://www.gracesguide.co.uk/John_Ronald_Womersley - John Ronald Womersley,
*findagrave.com*.

https://www.findagrave.com/memorial/195190861/john-ronald-womersley - John R Womersley,
*Project Gutenberg*.

http://self.gutenberg.org/articles/John_R._Womersley - M Olinick,
*Simply Turing*(Simply Charly, 2021).

https://www.google.co.uk/books/edition/Simply_Turing/z3ESEAAAQBAJ?hl=en&gbpv=0 - D H Sadler,
*A Personal History of H M Nautical Almanac Office: 30 October 1930 - 18 February 1972*(United Kingdom Hydrographic Office, 2008).

https://astro.ukho.gov.uk/nao/history/dhs_gaw/nao_perhist_0802_dhs.pdf - F Smithies, John Ronald Womersley,
*Journal of the London Mathematical Society***34**(1959), 370-372. - J R Womersley, Scientific Computing in Great Britain,
*Mathematical Tables and Other Aids to Computation***2**(15) (1946), 110-117. - J R Womersley, High Speed Computers: Their Logical Design, Programming and Other Problems,
*The Incorporated Statistician***3**(4) (1952), 3-14.

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Written by J J O'Connor and E F Robertson

Last Update September 2021

Last Update September 2021