# Joseph Proudman

### Quick Info

Born
30 December 1888
Unsworth, near Bury, Lancashire, England
Died
26 June 1975
Fordingbridge, Hampshire, England

Summary
Joseph Proudman was a mathematician who made major contributions to oceanography, particularly to the theory of tides. He was Professor of Applied Mathematics, then Professor of Oceanography at the University of Liverpool. He headed the Liverpool Tidal Institute, now called the Proudman Oceanographic Laboratory.

### Biography

Joseph Proudman was the son of John Proudman (1866-1943) and his wife Nancy Blease (1867-1942). John Proudman, the son of Ralph Proudman of "3 Acres Farm" Sevenoaks, was a farm bailiff at Thurston Fold Farm, Unsworth, when he married Nancy Blease in 1887 at Prescot, Lancashire. Nancy was the daughter of the police constable Joseph Blease. John and Nancy Proudman had two sons, Joseph Proudman, the subject of this biography, and William Proudman (1890-1959). Joseph was baptised on 24 February 1889 in the Wesleyan-Methodist Chapel in Unsworth.

In 1894, Joseph began his education at the primary school in Unsworth. In 1898, when he was nine years old, the family moved to Bold Heath, about 6 miles north of Widnes in Lancashire, when his father became a small tenant farmer at Nursery Farm. Joseph continued his primary education at the school in Bold Heath until 1902 when, at the age of thirteen, he became a pupil-teacher at Farnworth primary school between Bold Heath and Widnes [3]:-
He tells us that in 1902 his salary was £6 10s. Od. per year, and in 1907 it was £24 per year. His secondary education was begun by the headmaster, A R Smith, who gave him a lesson each morning from 8 to 8.45 before the school opened at 9. During the winters of 1902-4 he attended evening classes at the Widnes Technical School, studying art, mathematics and physiography. From 1903 to 1907 he only taught for half of each week; the other half he attended classes at the Widnes Secondary School. This was an excellent school, and it was here that the mathematical bent of his life was determined.
Proudman's home in Bold Heath was about two and a half miles from Farnworth and Farnworth was a further four miles from Widnes so, between 1903 and 1907, he was walking about thirteen miles (about 21 km) on half the school days. One of his lifetime interests arose at this time, namely reading history. This was a great benefit to writers of his obituary, for, conscious of the need to record history, he left a wealth of autobiographical notes which are still available. He won a Tate Technical Science Entrance Scholarship to study at Liverpool University in 1907, was awarded First Class in the B.Sc. examinations of 1909 and received a scholarship to continue to honours. In 1910 he was awarded First Class Honours in Mathematics and, for his outstanding performance, he received the Derby scholarship for mathematics and the Ronald Hudson prize for geometry. The Ronald Hudson prize was awarded on the results of the examination in the Honours School of Mathematics in Geometry. The Derby scholarship funded further study and Proudman went to Trinity College, Cambridge for this. In addition he was also supported by a Trinity College Entrance Exhibition.

At Cambridge Proudman matriculated at Trinity College in 1910 and studied the Mathematical Tripos taking a wide range of subjects in pure mathematics, applied mathematics and mathematical physics. He had Ernest Barnes as his tutor and he attended courses in pure mathematics given by G H Hardy and by J E Littlewood. He particularly enjoyed the lectures on hydrodynamics and on astronomy, both topics taught by Robert Alfred Herman (1861-1927). The courses on electric waves and on potential theory were delivered by Thomas J I'A Bromwich and it was from the courses by Herman and Bromwich, Proudman later wrote, that he learnt most. Made a senior scholar in 1911, he took the Tripos examinations in 1912, being awarded First Class in schedule A and a distinction in schedule B of Part Two of the Tripos.

After taking the Tripos, Proudman was keen to undertake research in hydrodynamics and approached several of the people who had taught him. None seemed particularly keen to supervise research on the aspects which interested Proudman, and so he ought advice from Ernest Barnes who suggested he contact Horace Lamb at the University of Manchester. The first two of Proudman's paper's were published in 1913. On Some Cases of Tidal Motion of Rotating Sheets of Water was communicated by Horace Lamb to the London Mathematical Society and it was received on 27 February 1913. The paper, which appeared in the Proceedings, begins:-
The following investigations arose out of an attempt to obtain an expression for the free tidal motion of a rotating flat sheet of water in the form of a circular sector. This was suggested as a subject for research by Prof Lamb. No progress, however, was made with the original problem except in the case of the semicircle, and in this case only when the angular velocity of rotation was small compared with the free periods of the relative motion of the water. Even in this restricted case the resulting expression was so complicated as to make interpretation very difficult, if not impossible, and consequently it is not given below.

After a statement of the general conditions (which were first investigated by Lord Kelvin), and their application to the case of a nearly circular sheet of water, a discussion is given of the limiting forms of forced tides as the period of the disturbing force tends to become infinite. It appears that these limiting forms are, for rotating flat sheets of water of uniform depth, always different from the forms given by the equilibrium theory. The limiting form is calculated for a rectangular sheet, and the result may, perhaps, be of interest, as the complete determination of the tides on such a sheet has not yet been obtained. Some partial solutions are then given, and, finally, the free symmetrical motion is obtained for a particular small circular sea on a sphere, as the next approximation after that which regards the sea as flat.
We see that Lamb had set Proudman on the research path on which he spent the rest of his life.

The other paper which appeared in May 1913 was Note on the pressure of rotation on a small reflecting sphere; it was published in the Monthly Notices of the Royal Astronomical Society. The paper related to ideas which Proudman had discussed with Bromwich while at Trinity College, and it was submitted to the Royal Astronomical Society by Bromwich. The paper begins:-
This problem has been discussed by Schwarzschild and Professor Nicholson, but their numerical results are not in complete agreement. The analysis of the latter is much the shorter, and it appeared likely that his results were nearer the truth. Dr Bromwich, however, was in possession of an independent treatment which showed that this was not the case as regards the magnitude of the maximum pressure. He informed me of this, and suggested that I should make a fresh calculation, very kindly showing me his results. I have worked through all the cases considered by Professor Nicholson, together with some additional and intermediate ones, and the results are substantially in agreement except as regards the maximum pressure. The present note contains the results referring to this maximum, making the determination much more precise than was done by Schwarzschild.
Frank Stanton Carey had been the Professor of Mathematics at the University of Liverpool since 1886 and he offered Proudman a lectureship soon after the results of the Tripos examinations were announced. Proudman took up the lectureship in mathematics in October 1913 [3]:-
He found that being a lecturer was much harder than being a student, either undergraduate or postgraduate. He gave twelve lectures per week, two each morning for 6 days per week. During his first year as a lecturer he had no time for research except during vacations, but he found time to direct the postgraduate work of A T Doodson for the degree of M.Sc. and thus began a collaboration which continued until Doodson's death.
Although he had to concentrate on teaching, research which Proudman had undertaken before taking up the lectureship at Liverpool led to publications in 1914. One of these was Limiting Forms of Long Period Tides. The introduction begins as follows:-
As the equations of tidal motion have been solved in only a few cases, which are very restricted when compared with the actual conditions of terrestrial tides, it is of interest to try to obtain some approximation to the long period tides by means of a discussion of the limiting forms of these tides as the period of the disturbing forces tends to become infinite.
World War I began in 1914 but Proudman was medically unfit for armed service and continued to work in Liverpool. His annual salary as a lecturer was £150 which was hardly enough to live on (perhaps the 2021 equivalent would be about £7000). This remained fixed for six years despite a quite high inflation rate. Financially, however, Trinity College came to his rescue for, in 1915, he was made a Fellow with an annual salary of £350. The Fellowship came with no duties and lasted for six years. This gave him the financial security to marry. On 10 July 1916 he married Rubina Ormrod (1891-1958) at Chorlton Upon Medlock, Lancashire. Rubina, the daughter of Thomas and Rebecca Ormrod, had been born in Salford, Lancashire. At the time of the 1911 census, Rubina was living in Manchester and her occupation is given as Ladies Companion. Joseph and Rubina Proudman had three children, two sons James Proudman (born 1918) and Ian Proudman (born 1927), and a daughter Nancy Proudman (born 1924).

In 1919 Proudman succeed in encouraging two Liverpool shipowners to fund the establishment of the Liverpool Tidal Institute for the University of Liverpool and to provide funds to run it for the first five years. Proudman was named as Honorary Director of the Tidal Institute with Arthur Doodson as its Secretary [6]:-
Although a separate body, separately governed and funded, there was a very early association with Bidston Observatory. It was intended as a research institution with both theoretical and practical aspects of tidal dynamics as topics of study.
We note that the Director of the Liverpool Bidston Observatory was William Plummer, the father of the mathematician and astronomer Henry Plummer.

The University of Liverpool established a Chair of Applied Mathematics so that they could promote Proudman to a professorship and, in 1919, he was appointed as the first Professor of Applied Mathematics at the University of Liverpool. This improved his financial position considerably for in 1918 he had an annual salary of £150 while two years later his annual salary was £1000. A significant step forward occurred in 1923 when Proudman was awarded the Adams Prize by the University of Cambridge for his Essay on the Tides. In 1924 Proudman and Doodson published the joint paper The Principal Constituent of the Tides of the North Sea, the first four sections being part of Proudman's Adams Prize Essay. The paper begins:-
This paper is concerned exclusively with the principal lunar semi-diurnal harmonic constituent of the tides which is denoted by $M_{2}$. The primary object is to show how the fundamental dynamical equations of the tides may be used to obtain a knowledge of the distribution of the surface-elevation from such observational data as are available. The dynamical equations, as formulated in §4, connect the elevation-gradients with the currents and the external forces, including those of friction. From a knowledge of the currents and a hypothesis for the frictional forces the elevation-gradients can be calculated.

When the elevation is also known the directions of the co-tidal and co-range lines, and also the distance apart of neighbouring members of these lines, can be calculated. Such conditions are fulfilled for coastal stations, and it is remarkable that, in spite of the great attention that has been paid to co-tidal charts, these simple calculations do not appear to have been previously made. But if the elevation-gradients can be calculated along a line which passes through one or more points at which the elevation is known, it is clear that methods can be devised by which the elevation can be calculated all along the line. Again, such calculations do not appear to have been previously made.
Proudman's achievement here was far-reaching, one of the many consequences being that Hydrographic Department saw that his work meant co-tidal charts could be constructed for the North Sea [6]:-
The association between the [Tidal] Institute and Bidston [Observatory] gradually strengthened, with William Plummer joining the governing board of the Institute. Significantly a tide-predicting machine was installed at Bidston at the end of 1924. Tide-predicting machines are devices that can be 'programmed' with the harmonic tidal constants for a particular port and then proceed to provide predictions or hindcasts for any desired date. As they required very high precision engineering, very few were in existence and several foreign governments asked the Institute to supervise the construction of machines for their own use.
In collaboration with Frank Stanton Carey, by this time the Emeritus Professor of Mathematics at Liverpool, Proudman published the book The Elements of Mechanics in 1925. Harry Bateman writes [1]:-
This book by a professor emeritus in the University of Liverpool and a young professor who has made notable advances in the study of the tides is a good example of what can be accomplished when the experience of a great teacher is combined with the brilliance of an ardent investigator. The subject is well presented ...
For more information about this book, including extracts from the Preface and some reviews, see THIS LINK.

Oceanographic research at Liverpool strengthened with the Liverpool Bidston Observatory and the Liverpool Tidal Institute forming a single institute in 1929 [6]:-
In 1928, William Plummer died and this may have been the catalyst for the amalgamation of the Observatory and Tidal Institute, which took place on the 1 January 1929. This was a pivotal moment as the next decade brought a considerable increase in oceanographic research to Bidston. With Joseph Proudman as Director and Arthur Doodson as Associate Director, the Liverpool Observatory and Tidal Institute developed new methods for the analysis of tides and their prediction, and a second tide-predicting machine was acquired.
In 1933 Proudman requested that he transfer from the Chair of Applied Mathematics to the Chair of Oceanography at the University of Liverpool [3]:-
... it was Proudman's idea that the department should be converted to one of physical oceanography. At that time there was much less provision for marine physics in this country than for marine biology. In addition to widening his own research interests to include oceanic circulation and the distribution of temperature and salinity in oceans and seas, Proudman initiated observational work in the Irish Sea.
To study turbulence and internal friction in a tidal current, Proudman and some colleagues purchased a fishing boat, the Zepyr which they converted into a research boat and crewed it themselves except for having one professional seaman. The advent of World War II in 1939 meant they could no longer carry out this work and they had to sell the Zepyr. Their experience, however, meant that after the war ended the University of Liverpool purchased a larger boat and employed a professional crew. They resumed their research on turbulence and internal friction and, as a result, wrote several papers such as Proudman's On the mixing of sea-water by turbulence (1948) and (with K F Bowden) Observations on the turbulent fluctuations of a tidal current (1949).

In 1953 he published the book Dynamical Oceanography. David Vaux writes in the review [17]:-
Prof Proudman's book is written from the mathematical standpoint, but its results and implications are in terms which should be understood by scientists engaged in marine, as well as in physical, oceanography. Before his appointment as Professor of Oceanography at Liverpool University twenty years ago, he had been professor in the department of Applied Mathematics for some fourteen years. His book, therefore, has a particularly sound hydrodynamical background. Results applicable to practical oceanography are deduced from the basic equations of dynamics.
For more information about this book, including extracts from the Preface and some reviews, see THIS LINK.

Proudman reached retirement age in 1954 and was made Professor Emeritus. He left Liverpool, living at first in Shropshire, then in Dorset. On 6 May 1958, his wife Rubina died. He married Beryl Gladys Waugh Barker on 29 May 1961 in Poole, Dorset. Beryl, born in Southampton on 17 July 1909, was the daughter of Walter George Barker and his wife Alice Mary Waugh. Beryl married Basil Frederick Cabourne Bassett in 1932 but, following his death in 1936, she married Donald Jack Gould in 1939. Donald Gould had died in 1958, three years before she married Proudman.

We should record a few of the many honours which Proudman received. He was elected a Fellow of the Royal Society of London in 1925. On 13 October 1944 he delivered the Royal Astronomical Society's George Darwin lecture choosing as his title The Tides of the Atlantic Ocean. He began his lecture as follows:-
It is appropriate, I think, that I should lecture on a subject connected with the tides of the ocean, for Sir George Darwin himself gave a great deal of his attention to the subject. From about 1882 until the end of his life in 1912, he was generally regarded as the greatest living authority on ocean tides.
Two years later, in 1946, he was awarded the Alexander Agassiz Medal for
his work on oceanography by the National Academy of Sciences [11]:-
The National Academy of Sciences awarded one of its highest honours, the Alexander Agassiz medal, to an English researcher on the mathematics of the oceans' tides, Prof Joseph Proudman, F.R.S., director of the Liverpool Observatory and Tidal Institute. Since Prof Proudman was unable to be present in person, the medal was accepted in his behalf by Sir Alfred Egerton, secretary of the Royal Society of London.
He was elected to the Norwegian Academy of Science and Letters in 1946, was elected Vice-President of the International Association of Physical Oceanography in 1948 and its President in 1951. He was honoured with a C.B.E. in 1952. He was awarded an honorary degree by the University of Liverpool in 1956 and, in 1957, he was awarded the Hughes Medal by the Royal Society.

His final home was in Dorset, where he lived in Dewlands Way, Verwood, but he died in a nursing home in Fordingbridge, Hampshire, quite near his home.

### References (show)

1. H Bateman, Review: The elements of mechanics, by F S Carey and J Poudman, Amer. Math. Monthly 33 (4) (1926), 224.
2. D E Cartwright, Tides. A scientific history (Cambridge University Press, Cambridge, 2000).
3. D E Cartwright and F Ursell, Biographical Memoirs of the Royal Society 22 (1976), 319-333.
4. Celebrating 100 years of Oceanography, University of Liverpool (21 October 2019).
https://alumni.liv.ac.uk/news/stories/title,1172325,en.html
5. G E R D, Review: Dynamical Oceanography, by J Proudman, The Geographical Journal 120 (1) (1954), 105-106.
6. J E Jones, Astronomy to Oceanography - a brief story of Bidston Observatory, Ocean Challenge 9 (1) (1999), 29-35.
7. Joseph Proudman 1889-1975, Bulletin of the American Meteorological Society 56 (10) (1975), 1116.
8. Local heroes - Joseph Proudman, 1888-1975, Time & Tide, National Oceanography Centre.
https://www.tide-and-time.uk/local-heroes-joseph-proudman
9. C R MacInnes, Review: The elements of mechanics, by F S Carey and J Poudman, Bull. Amer. Math. Soc. 32 (2) (1926), 172.
10. Professor Joseph Proudman, Insight into marine science, Proudman Oceanographic Laboratory (13 June 2014).
http://resources.schoolscience.co.uk/POL/insight/proudman.html
11. Prof Joseph Proudman Wins Alexander Agassiz Medal, The Science News-Letter 50 (18) (1946), 279.
12. J Proudman, Dynamical Oceanography (Methuen, 1953).
13. M Sears and D Merriman, Oceanography, the past (Springer, 1980).
14. D E Smith, Review: The elements of mechanics, by F S Carey and J Poudman, The Mathematics Teacher 18 (7) (1925), 438-439.
15. H Stommel, Review: Dynamical Oceanography, by J Proudman, Science, New Series 118 (3065) (1953), 365.
16. F Ursell, Proudman, Joseph (1888-1975), mathematician and oceanographer, Oxford Dictionary of National Biography (Oxford University Press, Oxford, 2004).
17. D Vaux, Review: Dynamical Oceanography, by J Proudman, Science Progress (1933-) 42 (165) (1954), 129-130.

### Additional Resources (show)

Other pages about Joseph Proudman:

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### Honours (show)

Honours awarded to Joseph Proudman

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