**Tom Cowling**'s mother, Edith Eliza Nicholls, had trained as a teacher. His father, George Cowling [1]:-

... was a highly intelligent person. His own father died young, and he had to start work at the age of14as an office boy at five shillings a week. He worked his way up, studying for examinations in the evening: After some years as a telegraph operator, he at age30won his way into the Post Office engineering staff, where he finally reached the grade of executive engineer.

George and Edith Cowling had four sons, Thomas being the second. They were members of the Baptist Church [1]:-

With this background, we four naturally adopted what is often called the Puritan work ethic.

Thomas attended Sir George Monoux Grammar School at Walthamstow from 1917 to 1923. His studies there were supported by a county scholarship. He writes in [1]:-

The Grammar school was strong on mathematics. This suited me, because I was fond of the subject ...; however, I was a slow and untidy writer, losing no opportunity of making blots and smudges. ... I was fascinated by chemistry but too clumsy to have made a success of experimental work.

In his sixth year at school he studied double mathematics, a little physics and (non-examinable) French. He sat the mathematics scholarship examinations for Cambridge in December 1923 but just missed out on an award. After working hard for the scholarship examination to Brasenose College, Oxford, he sat this in March 1924 and won a scholarship which was augmented by Essex County and the UK Education Department (on the expectation that he would become a school teacher). He entered Brasenose College in October 1924, won a University Junior Mathematical Exhibition in 1925 and a Scholarship in 1926. He graduated with First Class honours in 1927 after a course which [1]:-

... was old-fashioned and run inadequately by tutors who had other responsibilities too.

He did find Hardy's lectures inspiring, but was attracted towards applied mathematics. The award of a three year postgraduate scholarship was a slight embarrassment given that the UK Education Department had funded him to become a school teacher. He therefore took a teaching diploma before undertaking research and although this did nothing for his subsequent career, it meant that by the time he was ready to undertake research E A Milne was in post. He had approached Milne while in the middle of his diploma year, knowing he would arrive to take up his duties at Oxford in January 1929, asking if he would supervise his research. Milne agreed on condition that Cowling work on an astronomical topic. It was, therefore, totally by chance that he began to undertake research in mathematical astronomy.

Milne did not have a problem in mind for Cowling to work on, so he asked Chapman at Imperial College, London. Cowling found difficulties at first because of Chapman's suggested approach, but soon adopted a different approach solving the problem. The result of this was that after Cowling completed his doctorate in 1930, Chapman offered him a position as a demonstrator in the Mathematics Department at Imperial College where he worked for three years before being appointed as an assistant lecturer in mathematics at Swansea University. While at Swansea he married Doris Marjorie Moffatt on 24 August 1935; they had two daughters (Margaret Ann and Elizabeth Mary) and one son (Michael John). After three years at Swansea, he was appointed as a lecturer in mathematics at Dundee (1937-38), and then at the University of Manchester (1938-45). Of course his time at Manchester pretty much coincided with World War II but he was not involved in technical war work [1]:-

According to what I later heard, I was regarded as one who should not be entrusted with state secrets because I had unreliable associates. Thus I was left undisturbed to teach Applied Mathematics at Manchester University.

He did, however, have duties as an Air Raid Warden during the war.

In 1945 Cowling was appointed Professor of Mathematics at University College Bangor, moving to a similar post in Leeds in 1948. He remained at Leeds for the rest of his career, retiring from his duties in 1970 when he became Professor Emeritus. However he did suffer health problems long before he retired [2]:-

During his time at Leeds the heavy load on a conscientious university professor with both departmental responsibilities and a commitment to scholarship took its toll; a series of health problems - a duodenal ulcer operation in1954, a slipped disk in1957and a mild heart attack in1960- caused a slowing down of his activities well before his retirement.

Cowling's main contributions were in the areas of stellar structure, cosmical magnetism, kinetic theory and plasma-physics. His first paper *On the radial limitation of the Sun's magnetic field* (1929) actually criticised Chapman's theory that the magnetic field of the sun had radial limitations. He showed in the paper that Chapman's theory was inconsistent and showed that the field must have open field lines. Cowling's second paper *On a point-source model of a star* (1930) began his publications on stellar structure. Certainly showing inconsistencies in Chapman's theory of the sun's magnetic field did not hinder collaboration between the two men, and they published a major classic text *The Mathematical Theory of Non-uniform Gases* in 1939. Bateman reviewed the book, indicating its contents and importance. After an introductory chapter the next:-

... deals with the properties of a gas and some basic definitions and theorems. The equations of Boltzmann and Maxwell are then developed, Enskog's generalization of Maxwell's equation of transfer being given. The theory of molecular encounters is then presented. The next three chapters are concerned with Boltzmann's H-theorem, the Maxwellian velocity distribution, the free path, persistence of velocities and the elementary theory of the transport phenomena. In the important chapter on the non-uniform state for a simple gas, use is made of Enskog's method of solving the integral equation and of Burnett's calculation of certain quantities A and B with the aid of Sonine's polynomials. The non-uniform state for a mixture of gases is discussed in the next chapter. General expressions are first found and then formulae are obtained for special molecular models. The results of the analysis are of much physical interest and a large part of the book is devoted to the comparison of theory and experiment for viscosity, thermal conduction and diffusion. The appearance of the book is timely on account of the interest which is now being taken in thermal diffusion...

The importance of the work is illustrated by the fact that a second edition appeared in 1952 (reprinted in 1960) and a third edition in 1970 which was revised and reprinted in 1990. Few books have such a long life!

To give an indication of the topics of Cowling papers we list a few from the first part of his career: *On certain expansions involving products of Legendre functions* (1940); *The non-radial oscillations of polytropic stars* (1942); *The electrical conductivity of an ionized gas in a magnetic field, with applications to the solar atmosphere and the ionosphere* (1945); *The oscillations of a rotating star* (1949); *The condition for turbulence in rotating stars* (1951); *Magneto-hydrodynamic oscillations of a rotating fluid globe* (1955). In 1957 he published another major text *Magnetohydrodynamics* which gave a concise account of the subject, making particular reference to applications in astronomy and geophysics.

Cowling received many honours throughout his career. He was awarded the Johnson Memorial Prize by Oxford University in 1935 for original work in astronomy. Elected to the Royal Society in 1947 he was awarded their Hughes Medal in 1990. Although the award was made two days before his death, sadly he did not learn about this prestigious honour. He was awarded the Gold Medal of the Royal Astronomical Society in 1956. He received this Medal from Harold Jeffreys. He was elected President of the Society for the years 1965-67. In 1985 he received the Bruce medal from the Astronomical Society of the Pacific.

Mestel writes in [2]:-

Everyone knew Tom by sight; his red hair and his great height made him conspicuous. ... Most of us looked up to him also metaphorically because of his jestified reputation for kindliness combined with high critical standards, which he applied as strictly to his own works as that of others.

**Article by:** *J J O'Connor* and *E F Robertson*