**Bertha Swirles**'s father, William Alexander Swirles (born 1878 at Stoke Newington, London), was a Northampton leather salesman, which certainly fits with the fact that Northampton is best known for its shoe and leather industry. Sadly he died in 1905 when Bertha was only two years old leaving her mother, Harriett Swirles (born Northampton about 1873) the task of supporting her family. She had trained as a teacher at Stockwell College so, on the death of her husband, she opened a small private school. When Bertha was nine years old her mother left her private school to become a teacher at Stimpson Avenue Elementary School. This school had strong family connections since her sister, Mercy Blaxley, was the headmistress and her late husband's sister also taught at the school. In fact [2]:-

Stimpson Avenue Elementary School was a natural place for Bertha to attend for her primary education which she did for three years until Northampton School for Girls opened in 1915. Winning a scholarship to this school she proved to be an exceptional pupil [2]:-Bertha's educational background was strong with seven of her nine aunts being teachers and her father's mother was on the staff of the Model School at Enniskillen when it was opened in1867.

However, taught mathematics by three Cambridge mathematics graduates, it was soon clear that this was the subject for her to study at university. A distinction she achieved at Northampton School was being Head Girl in her final year at school. She entered Girton College, Cambridge, in 1921 having won a Clothworkers' Scholarship. She joined ten other girls at Girton who had also entered to study mathematics [2]:-She was a talented young lady excelling in many areas: science, languages and music, playing both the piano and cello to a high standard.

Bertha Swirles had studied both mathematics and physics as an undergraduate, having attended physics courses by Joseph John Thomson and Ernest Rutherford. She then remained at Cambridge in 1925 to undertake research in mathematical astronomy under the supervision of Ralph Fowler, supported by a Yarrow Fellowship. Coming out of her research at this time was the paperUntil coming to Cambridge Bertha had been taught by women in the company of other girls and so the Cambridge lectures, in which women were very much in the minority, must have been a great change for her. However, she was not daunted and obtained first class honours in both Parts I and II of the Mathematical Tripos, but, in common with all women students prior to1948, she was not awarded her degree by the University of Cambridge.

*The internal conversion of Gamma-rays*published in the

*Proceedings*of the Royal Society of London in 1927. Another of Fowler's research students, Paul Dirac, was a couple of years ahead of Swirles. But the person who had the most influence on Swirles's research was another research student Douglas Hartree who suggested the first research problem she attacked, studying the polarizability of atomic cores.

The Yarrow Fellowship supported Swirles for the two sessions 1925-27, following which her next year was financed by a Hertha Ayrton Research Fellowship which allowed her to spent the year at Göttingen in Germany. There she studied quantum theory and other topics under Max Born and Werner Heisenberg at a really exciting time with Heisenberg's theory of quantum mechanics published in 1925 and Schrodinger's wave mechanics in 1926. Her research during this year led to her publishing a second part of *The internal conversion of Gamma-rays* again in the *Proceedings* of the Royal Society. Returning to England in 1928, Swirles was appointed as a assistant lecturer at the University of Manchester. She was awarded her doctorate from Cambridge in the following year. At Manchester she renewed her friendship with Douglas Hartree who was appointed as a professor there in 1929. Also at Manchester was Arthur Milne who had been appointed to succeed Sydney Chapman as Beyer professor of applied mathematics in 1925. Milne had collaborated with Fowler while at Cambridge and he was in a good position to provide Swirles with guidance in her research. With Milne's advice she tackled the problem of absorption of radiation by a gas, a topic which was highly relevant to the study of stellar structure.

Swirles left Manchester in 1931, working as an assistant lecturer in Bristol during 1931-32, then as an assistant lecturer at Imperial College, London, in 1932-33. In 1933 she returned to Manchester where she was appointed as a Lecturer in Applied Mathematics. She spent five years at Manchester during this second period there. During these five years she published papers such as: *The coefficients of absorption and opacity of a partially degenerate gas* (1933), *The relativistic self-consistent field* (1935), and *The relativistic interaction of two electrons in the self-consistent field method* (1936). She also collaborated with Douglas Hartree and they were assisted in their work by Hartree's father who did the numerical calculations using a Brunsviga hand calculating machine. The result was a publication of D R Hartree, W Hartree and B Swirles, *Self-consistent field, including exchange and superposition of configurations, with some results for oxygen* published in the *Philosophical Transactions* of the Royal Society of London in 1939.

By the time this paper was in print, Swirles was back at Girton College, Cambridge, where she took up a Fellowship and a Lectureship in Mathematics. She remained at Girton for the rest of her career. In 1940 she married Harold Jeffreys who at that time was teaching geophysics at Cambridge. He had taught mathematics at Cambridge from 1922 to 1932 then, after fourteen years teaching geophysics, he was appointed as Plumian Professor of Astronomy in 1946. It was in this year of 1946 that Bertha Swirles Jeffreys, in collaboration with her husband Harold Jeffreys, published the classic text *Methods of Mathematical Physics*. They wrote in the Preface:-

After her husband was knighted in 1953, she became Lady Jeffreys, better known to some as 'Lady J'. At Girton, Bertha Jeffreys continued to undertake research on quantum theory publishing papers such asThis book is intended to provide an account of those parts of pure mathematics that are most frequently needed in physics. ... We do not accept the common view that any argument is good enough if it is intended to be used by scientists. We hold that it is as necessary to science as to pure mathematics that the fundamental principles should be clearly stated and that the conclusions shall follow from them. But in science it is also necessary that the principles taken as fundamental shall be as closely related to observation as possible. ... We maintain therefore that careful analysis is more important in science than in pure mathematics, not less. We have also found repeatedly that the easiest way to make a statement reasonably plausible is to give a rigorous proof.... We consider it especially important that scientists should have reasonably accessible statements of conditions for the truth of the theorems that they use. ... We have ... often given proofs under more general conditions than are usually taught to scientists, where the usual sufficient conditions are often not satisfied in practice but less stringent ones are satisfied. ...

*The classification of multipole radiation*(1952),

*The use of the Airy functions in a potential barrier problem*(1956), and

*The asymptotic approximation*(

*AA*)

*method*(1961). She also published joint papers with her husband on seismology. She played a major role at Girton sharing the teaching of mathematics with Mary Cartwright from 1938 to 1949. Mary Cartwright became Mistress of Girton in 1949, and Bertha Jeffreys took over her previous role of Director of Studies in Mathematics and Mechanical Sciences. She held this position from 1949 until her retirement in 1969. Other roles she filled at Girton included Director of Studies in Music from 1939 to 1947 and Vice-Mistress from 1966 to 1969.

R M Williams writes [3]:-

Let us note that she was an editor for four of the volumes of theHer supervisions were informative, stimulating and enjoyable(even when the students was referred firmly to Fowler's 'Use of English')and she had an intuitive sense of the particular difficulties each individual faced. She took a personal and warm interest in all her students and there was often "open house" for them on Sunday evenings at the Jeffreys residence halfway between Girton and the centre of Cambridge. Her interest did not cease when students left Cambridge; she and Harold had no children, but there was an enormous extended family based on her former pupils. She had an amazing memory for the details of their lives. When their children and grandchildren arrived in Cambridge as students themselves, they would be invited to tea. This used to involve sampling Bertha's homemade flapjack whilst Sir Harold sat on the floor doing the Times crossword. Many a younger child received an imaginatively chosen birthday gift from Auntie Bertha.

*Collected Papers of Sir Harold Jeffreys on Geophysics and other Sciences*(1971-77). Also after her husband's death in 1989 at the age of 97, Bertha Jeffreys spent long hours sorting and cataloguing his papers so that they might provide a useful resource for future researchers.

Throughout much of her life, Bertha Jeffreys was actively involved with the Mathematical Association. She joined in January 1931, and later served on the Council. She was elected President of the Association for the year 1969-70 and continued her involvement with the Mathematical Association after she retired. Her presidential address to the Association was *An easy commerce of the old and the new* in which she reflected on how important it is for mathematicians at all stages of their careers to keep in mind that mathematics is a combination of both old and new ideas.

She received several honours for her contributions. For example, she was elected a Fellow of the Institute of Mathematics and its Applications in 1968. She was appointed Life Fellow of Girton on her retirement in 1969. She also received honorary doctorates from the University of Saskatchewan (1995) and the Open University (1996).

We have indicated her love of music by noting that she was Director of Studies in Music at Girton for eight years [3]:-

Music was an important part of her life. She was an accomplished pianist and cellist, and still played piano duets with a friend in her nineties, when she also still regularly attended concerts in college and at Kettle's Yard.

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