MacTutor
Ida Winifred Busbridge MA, DPhil, DSC, FRAS died on 1988 December 27. She was elected a Fellow of the RAS in 1948 and became a leading authority on the theory of Radiative Transfer, frequently serving the Society as a referee of papers on the subject. Although she contributed so much Ida was a somewhat diffident member of an astronomical body because her approach to the subject was entirely mathematical and her training was not in Physics or Astronomy. I remember well Saturday evenings spent together using the 12-inch refractor at the University Observatory in the Parks, both seeking to improve our general acquaintance with the stars! She no doubt felt much more at home in the London Mathematical Society and the Mathematical Association of which she was President 1964-65.
Ida Busbridge was born in Woolwich on 1908 February 10, the youngest member of an exceptionally talented and close-knit family. Her father died in 1909 and her mother brought up her four children while herself teaching in London. Both Ida and her brother Percy in their turn headed their respective degree lists in London University. Ida was educated at Christ's Hospital and she always took the greatest interest in its doings. From there she was elected to a scholarship at Royal Holloway College to read Mathematics and in 1929 was awarded the Lubbock Prize for the best First Class Honours degree in the subject. In 1933 she gained an MSc degree with distinction and became a Demonstrator in Mathematics at University College London.
Her association with Oxford began in 1935 when she came to help Dr Dorothy Wrinch, the brilliant Cambridge mathematician, with the teaching of women undergraduates. To quote the College Principal "St Hugh's was lucky enough to adopt Ida at this juncture, to present her for Matriculation and in 1938 to appoint her Lecturer in Mathematics. When Dr Wrinch left England for America in 1938 Ida inherited her responsibility for the teaching of women mathematicians and in 1945 was appointed Fellow and Tutor at St Hugh's". The total number of mathematicians in all five women's colleges was small in 1938; by the time Ida retired there were four times as many and each college had, for many years, had its own mathematics tutor. Ida took a close personal interest in her students, many of whom became life-long friends. Indeed she was concerned for the welfare of all with whom she came in contact and showed imaginative generosity to a great many people and to her college. After her retirement in 1970, to live in Kent with her beloved sister, she continued her teaching for a time in the Open University. She was elected an Emeritus Fellow of St Hugh's in 1970 and in 1984 an anonymous donor endowed the Ida Busbridge Fellowship in Mathematics.
Ida played a very important part in college life generally. She was a committed Christian and a pillar of the college chapel. On the Governing Body her informed judgement and robust realism were invaluable. The gardens of St Hugh's College have always been a special feature: she was Custos Hortulorum for many years and was in her element in that role. In retirement she and her sister Evelyn continued to maintain their large garden at home. St Hugh's College has had a long-standing association with the St Margaret's House Settlement, Bethnal Green and after Miss Gwyer (College Principal 1924-46) retired Ida took over the responsibility for that connection. She was a most useful member of the House Committee and this included generous personal donations when funds were low!
Notwithstanding her dedication to her work as College Fellow and Tutor, which she felt to have the first claim on her time and energy, Ida produced an impressive amount of original work as the accompanying account of it shows. This will stand to her memory as a research worker: by many she will be remembered also as an inspired teacher and a dear friend.
M.G.ADAM
___________________________________________________________
Miss Busbridge was elected Fellow of the Society in 1948 and willingly served with diligence and professional skill as a referee of mathematical papers, particularly in the theory of radiative transfer in which she became a leading authority. Originally, she worked on the Theory of Fourier Integrals and related topics, and later applied this work to problems in radiative transfer. Her friendship with Dr M.G.Adam at St Hugh's College, Oxford, was no doubt responsible for the interest that Miss Busbridge began to show in some of the problems in solar work in progress at the University Observatory under the direction of Professor H.H.Plaskett. It was in 1936 that he published his well-known paper on Solar Granulation in which he solved the integral equation of radiative transfer numerically, using a modification of a method due to Eddington, and found an isothermal region in the solar photosphere near the top of the zone in which granular convection streams were believed to occur. This result was challenged by several people on general physical grounds although Plaskett had produced a specific physical argument in support of the inferred temperature distribution. The onset of the Second World War only created a momentary truce in the controversy.
Miss Busbridge declined an invitation to work during the War in the Board of Trade because she felt very strongly that it was more important as a contribution to the war effort to provide physicists and engineers with the basic tools of mathematics. However, in spite of her heavy teaching load at St Hugh's College, she managed to make time for research and turned her attention to the problem of the inversion of the Laplace transform of the source function, which was at the root of the problem tackled numerically by Plaskett. Using the limb-darkening data of Moll, Burger and van der Bilt, meticulously prepared for her by Miss Adam, she found an ingenious representation of the data for different wavelengths which satisfied strictly the mathematical conditions required for the inversion. This led to her first paper in Monthly Notices for 1941, 'On the Solution of the Equation of Radiative Transfer', which soon became well known, and a detailed account of it appeared in Chapter XII of Waldmeier's book Einführung in die Astrophysik, published in 1948 by Birkhäuser of Basel. In that paper, she found no evidence for Plaskett's isothermal layer, and suggested that his result might have been due to the mesh size used in the numerical inversion.
However, he demonstrated forthwith that the isothermal layer persisted in the same region of the photosphere in calculations with a different division of the atmosphere into layers, and he suggested that its absence in her analysis might have arisen from the circumstance that the mathematical method required her empirical representation of the limb-darkening ratio to hold not only over the observable range of emergent angles but also in an observationally inaccessible range. It appears that the controversy was resolved a decade later by J.B.Sykes who showed that the empirical representation used by Miss Busbridge was physically unsound, as it involved an implicit assumption that the Sun was completely darkened at the limb, and that as a consequence the source function would be zero at the surface of the photosphere. However, the source function calculated by Miss Busbridge was found to agree with the detailed calculations of Sykes for optical depths greater than 0.3, thereby disproving the existence of the isothermal layer. It is interesting that Miss Busbridge had produced results that were mathematically correct although the function used for the empirical fit to the limb-darkening data was physically unsound. In another paper, published in the Astrophysical Journal for 1950, which also aroused some controversy, Miss Busbridge proved by rigorous use of Laplace transform methods that some useful results in radiative transfer, deduced by Menzel and Sen by operational methods, were only correct in form although some aspects of the mathematical treatment were shown by her to be unsound. Menzel took strong exception to some remarks in her paper until the present writer suggested to him that the role of their physical intuition, which led to correct results, might not have been fully appreciated and that a salutary reminder to authors of the need for rigour in the use of operational methods was not out of place, and also drew his attention to the role that Miss Busbridge had played in the limb-darkening controversy almost a decade earlier. Apart from these two isolated but important instances, the research contributions of Miss Busbridge were entirely devoid of controversy. She was not in any sense a controversial person: she stated clearly any assumptions that she made, stood firm on the rigour of her mathematics, and encouraged others to do the same. She was, in fact, always a kindly, courteous and stimulating colleague.
There is no doubt that her interest in the theory of radiative transfer was stimulated by her association with Professor V.Kourganoff of the University of Paris in the collaborative work that she did on his book Basic Methods in Transfer Problems published at the Clarendon Press in 1952. The first draft of Kourganoff's General Introduction, as well as the list of contents of his proposed book, was translated by Plaskett and submitted to the Delegates of the Oxford University Press who agreed to publish the work in their International Series of Monographs in Physics, edited by N.F.Mott. Miss Busbridge was introduced to Kourganoff by Plaskett and she consented to translate the manuscript into English. However, in the course of her work on the book, she became much more than a translator, and her substantial contributions can be summarized most appropriately by quoting Kourganoff who wrote in his Preface as follows: "I found in Dr Busbridge not only an excellent translator but also a most stimulating collaborator. She suggested new developments, rectified several mistakes, wrote some sections of the book, helped with the correction of the proofs, and provided general assistance of inestimable value." There is no doubt whatever that the mathematical rigour and clarity of exposition in much of the book owes a great deal to Miss Busbridge. There is also no doubt that her work with him was a great stimulus for her further work, as is evident from the fact that, setting aside the span of time, she had only written three papers on radiative transfer before working on the Monograph but had fifteen more publications in that field to her credit before retirement, including her own book entitled The Mathematics of Radiative Transfer, published in 1960 by Cambridge University Press as No. 50 in their series Cambridge Tracts in Mathematics and Mathematical Physics. She submitted this work, together with other work, to Oxford University for the DSc Degree. The submission was examined by Titchmarsh and Stibbs, and the Degree was awarded in 1961.
Detailed study of her Tract is a rewarding experience not only in the elegant use of rigorous mathematics, which she appears to have found easy, but also as a revelation of what she appears to have found difficult. It is evident from the Tract, as well as from some of her publications, that physical intuition was all right for those gifted with it, but that it was necessary to verify mathematically many of the things that those so gifted took for granted. A case in point is the development of Principles of Invariance by Chandrasekhar on the basis of the early work by Ambartsu-mian who had used a physical approach to problems in diffuse reflection. At the beginning of Chapter 6 of her Tract, Miss Busbridge makes the following assertion: "The application of these principles is not easy, and until a precise statement is given of the physical conditions which are sufficient to ensure their truth, any solution based on them ought to be verified in another way. In one of her publications, in Monthly Notices for 1955, Miss Busbridge carefully verifies mathematically the principle of invariance as applied to the case of completely non-coherent scattering and interlocked multiplet lines in the theory of line formation. Again, in the case of anisotropic scattering, which is treated in Chapter 10 of her Tract, she comments: "Chandrasekhar's method employs 'principles of invariance'. The equations for anisotropic scattering are derived and these are then reduced to H equations (if the atmosphere is semi-infinite) by an inspired insight denied to the reader." Towards the end of the same Chapter, she derives the law of diffuse reflection from the mathematical foundations of the subject in preference to it being regarded as a physical law to be called upon when required and, finally, she gives a mathematical derivation of one of the invariance equations, for an atmosphere with a constant net flux, otherwise known as an invariance arising from the asymptotic solution at infinity, which is perhaps one of the most difficult of the invariance equations to grasp. This leaves the reader with the impression that whereas Miss Busbridge might have been to some extent envious of those who had inspired physical insight, she nevertheless felt it to be in some sense suspect and, in any case, unnecessary to use it when techniques are available to deduce the results with mathematical rigour from the fundamental equations of the problem.
Some of the more formal aspects of the research that Miss Busbridge did in radiative transfer theory appeared in the Oxford Quarterly Journal of Mathematics for 1950, 1955 and 1957, in some of which the departure from physical applicability appears to be substantial and some of the notation is definitely unusual. For example, in her 1950 paper the integro-exponential function with a complex index is an interesting but curious generalization; and in her 1955 paper χ is used for the albedo instead of the standard symbol and the physical relevance of some expansions is difficult to appreciate. In her Cambridge Tract, the appearance of the notation ω instead of ω(bar) for albedo was as surprising to herself as to her readers. Unfortunately, her manuscript notation was misread by the Press and with great toleration she accepted the proofs, probably without demur. Of her seven papers published in Monthly Notices of the Society, the one in 1941 is the limb-darkening paper already referred to; her 1953, 1954 and 1955 papers are concerned with line formation in semi-infinite stellar atmospheres with coherent and non-coherent scattering, the 1954 paper being written jointly with Stibbs; and there is a fine series of three papers on finite atmospheres with isotropic scattering in 1955, 1956 and 1957. The Astrophysical Journal published six of her papers, the last two, written in collaboration with E.C.Orchard and published in 1967 and 1968, on the reflection and transmission of light by thick atmospheres, being of relevance to geometrically thin but optically thick layers of paint! Her published work on radiative transfer theory in solar, stellar and other contexts is an enduring testimonial to her uncompromisingly high standards and enviable versatility as a mathematician.
D.W.N.STIBBS
Ida Busbridge was born in Woolwich on 1908 February 10, the youngest member of an exceptionally talented and close-knit family. Her father died in 1909 and her mother brought up her four children while herself teaching in London. Both Ida and her brother Percy in their turn headed their respective degree lists in London University. Ida was educated at Christ's Hospital and she always took the greatest interest in its doings. From there she was elected to a scholarship at Royal Holloway College to read Mathematics and in 1929 was awarded the Lubbock Prize for the best First Class Honours degree in the subject. In 1933 she gained an MSc degree with distinction and became a Demonstrator in Mathematics at University College London.
Her association with Oxford began in 1935 when she came to help Dr Dorothy Wrinch, the brilliant Cambridge mathematician, with the teaching of women undergraduates. To quote the College Principal "St Hugh's was lucky enough to adopt Ida at this juncture, to present her for Matriculation and in 1938 to appoint her Lecturer in Mathematics. When Dr Wrinch left England for America in 1938 Ida inherited her responsibility for the teaching of women mathematicians and in 1945 was appointed Fellow and Tutor at St Hugh's". The total number of mathematicians in all five women's colleges was small in 1938; by the time Ida retired there were four times as many and each college had, for many years, had its own mathematics tutor. Ida took a close personal interest in her students, many of whom became life-long friends. Indeed she was concerned for the welfare of all with whom she came in contact and showed imaginative generosity to a great many people and to her college. After her retirement in 1970, to live in Kent with her beloved sister, she continued her teaching for a time in the Open University. She was elected an Emeritus Fellow of St Hugh's in 1970 and in 1984 an anonymous donor endowed the Ida Busbridge Fellowship in Mathematics.
Ida played a very important part in college life generally. She was a committed Christian and a pillar of the college chapel. On the Governing Body her informed judgement and robust realism were invaluable. The gardens of St Hugh's College have always been a special feature: she was Custos Hortulorum for many years and was in her element in that role. In retirement she and her sister Evelyn continued to maintain their large garden at home. St Hugh's College has had a long-standing association with the St Margaret's House Settlement, Bethnal Green and after Miss Gwyer (College Principal 1924-46) retired Ida took over the responsibility for that connection. She was a most useful member of the House Committee and this included generous personal donations when funds were low!
Notwithstanding her dedication to her work as College Fellow and Tutor, which she felt to have the first claim on her time and energy, Ida produced an impressive amount of original work as the accompanying account of it shows. This will stand to her memory as a research worker: by many she will be remembered also as an inspired teacher and a dear friend.
M.G.ADAM
___________________________________________________________
Miss Busbridge was elected Fellow of the Society in 1948 and willingly served with diligence and professional skill as a referee of mathematical papers, particularly in the theory of radiative transfer in which she became a leading authority. Originally, she worked on the Theory of Fourier Integrals and related topics, and later applied this work to problems in radiative transfer. Her friendship with Dr M.G.Adam at St Hugh's College, Oxford, was no doubt responsible for the interest that Miss Busbridge began to show in some of the problems in solar work in progress at the University Observatory under the direction of Professor H.H.Plaskett. It was in 1936 that he published his well-known paper on Solar Granulation in which he solved the integral equation of radiative transfer numerically, using a modification of a method due to Eddington, and found an isothermal region in the solar photosphere near the top of the zone in which granular convection streams were believed to occur. This result was challenged by several people on general physical grounds although Plaskett had produced a specific physical argument in support of the inferred temperature distribution. The onset of the Second World War only created a momentary truce in the controversy.
Miss Busbridge declined an invitation to work during the War in the Board of Trade because she felt very strongly that it was more important as a contribution to the war effort to provide physicists and engineers with the basic tools of mathematics. However, in spite of her heavy teaching load at St Hugh's College, she managed to make time for research and turned her attention to the problem of the inversion of the Laplace transform of the source function, which was at the root of the problem tackled numerically by Plaskett. Using the limb-darkening data of Moll, Burger and van der Bilt, meticulously prepared for her by Miss Adam, she found an ingenious representation of the data for different wavelengths which satisfied strictly the mathematical conditions required for the inversion. This led to her first paper in Monthly Notices for 1941, 'On the Solution of the Equation of Radiative Transfer', which soon became well known, and a detailed account of it appeared in Chapter XII of Waldmeier's book Einführung in die Astrophysik, published in 1948 by Birkhäuser of Basel. In that paper, she found no evidence for Plaskett's isothermal layer, and suggested that his result might have been due to the mesh size used in the numerical inversion.
However, he demonstrated forthwith that the isothermal layer persisted in the same region of the photosphere in calculations with a different division of the atmosphere into layers, and he suggested that its absence in her analysis might have arisen from the circumstance that the mathematical method required her empirical representation of the limb-darkening ratio to hold not only over the observable range of emergent angles but also in an observationally inaccessible range. It appears that the controversy was resolved a decade later by J.B.Sykes who showed that the empirical representation used by Miss Busbridge was physically unsound, as it involved an implicit assumption that the Sun was completely darkened at the limb, and that as a consequence the source function would be zero at the surface of the photosphere. However, the source function calculated by Miss Busbridge was found to agree with the detailed calculations of Sykes for optical depths greater than 0.3, thereby disproving the existence of the isothermal layer. It is interesting that Miss Busbridge had produced results that were mathematically correct although the function used for the empirical fit to the limb-darkening data was physically unsound. In another paper, published in the Astrophysical Journal for 1950, which also aroused some controversy, Miss Busbridge proved by rigorous use of Laplace transform methods that some useful results in radiative transfer, deduced by Menzel and Sen by operational methods, were only correct in form although some aspects of the mathematical treatment were shown by her to be unsound. Menzel took strong exception to some remarks in her paper until the present writer suggested to him that the role of their physical intuition, which led to correct results, might not have been fully appreciated and that a salutary reminder to authors of the need for rigour in the use of operational methods was not out of place, and also drew his attention to the role that Miss Busbridge had played in the limb-darkening controversy almost a decade earlier. Apart from these two isolated but important instances, the research contributions of Miss Busbridge were entirely devoid of controversy. She was not in any sense a controversial person: she stated clearly any assumptions that she made, stood firm on the rigour of her mathematics, and encouraged others to do the same. She was, in fact, always a kindly, courteous and stimulating colleague.
There is no doubt that her interest in the theory of radiative transfer was stimulated by her association with Professor V.Kourganoff of the University of Paris in the collaborative work that she did on his book Basic Methods in Transfer Problems published at the Clarendon Press in 1952. The first draft of Kourganoff's General Introduction, as well as the list of contents of his proposed book, was translated by Plaskett and submitted to the Delegates of the Oxford University Press who agreed to publish the work in their International Series of Monographs in Physics, edited by N.F.Mott. Miss Busbridge was introduced to Kourganoff by Plaskett and she consented to translate the manuscript into English. However, in the course of her work on the book, she became much more than a translator, and her substantial contributions can be summarized most appropriately by quoting Kourganoff who wrote in his Preface as follows: "I found in Dr Busbridge not only an excellent translator but also a most stimulating collaborator. She suggested new developments, rectified several mistakes, wrote some sections of the book, helped with the correction of the proofs, and provided general assistance of inestimable value." There is no doubt whatever that the mathematical rigour and clarity of exposition in much of the book owes a great deal to Miss Busbridge. There is also no doubt that her work with him was a great stimulus for her further work, as is evident from the fact that, setting aside the span of time, she had only written three papers on radiative transfer before working on the Monograph but had fifteen more publications in that field to her credit before retirement, including her own book entitled The Mathematics of Radiative Transfer, published in 1960 by Cambridge University Press as No. 50 in their series Cambridge Tracts in Mathematics and Mathematical Physics. She submitted this work, together with other work, to Oxford University for the DSc Degree. The submission was examined by Titchmarsh and Stibbs, and the Degree was awarded in 1961.
Detailed study of her Tract is a rewarding experience not only in the elegant use of rigorous mathematics, which she appears to have found easy, but also as a revelation of what she appears to have found difficult. It is evident from the Tract, as well as from some of her publications, that physical intuition was all right for those gifted with it, but that it was necessary to verify mathematically many of the things that those so gifted took for granted. A case in point is the development of Principles of Invariance by Chandrasekhar on the basis of the early work by Ambartsu-mian who had used a physical approach to problems in diffuse reflection. At the beginning of Chapter 6 of her Tract, Miss Busbridge makes the following assertion: "The application of these principles is not easy, and until a precise statement is given of the physical conditions which are sufficient to ensure their truth, any solution based on them ought to be verified in another way. In one of her publications, in Monthly Notices for 1955, Miss Busbridge carefully verifies mathematically the principle of invariance as applied to the case of completely non-coherent scattering and interlocked multiplet lines in the theory of line formation. Again, in the case of anisotropic scattering, which is treated in Chapter 10 of her Tract, she comments: "Chandrasekhar's method employs 'principles of invariance'. The equations for anisotropic scattering are derived and these are then reduced to H equations (if the atmosphere is semi-infinite) by an inspired insight denied to the reader." Towards the end of the same Chapter, she derives the law of diffuse reflection from the mathematical foundations of the subject in preference to it being regarded as a physical law to be called upon when required and, finally, she gives a mathematical derivation of one of the invariance equations, for an atmosphere with a constant net flux, otherwise known as an invariance arising from the asymptotic solution at infinity, which is perhaps one of the most difficult of the invariance equations to grasp. This leaves the reader with the impression that whereas Miss Busbridge might have been to some extent envious of those who had inspired physical insight, she nevertheless felt it to be in some sense suspect and, in any case, unnecessary to use it when techniques are available to deduce the results with mathematical rigour from the fundamental equations of the problem.
Some of the more formal aspects of the research that Miss Busbridge did in radiative transfer theory appeared in the Oxford Quarterly Journal of Mathematics for 1950, 1955 and 1957, in some of which the departure from physical applicability appears to be substantial and some of the notation is definitely unusual. For example, in her 1950 paper the integro-exponential function with a complex index is an interesting but curious generalization; and in her 1955 paper χ is used for the albedo instead of the standard symbol and the physical relevance of some expansions is difficult to appreciate. In her Cambridge Tract, the appearance of the notation ω instead of ω(bar) for albedo was as surprising to herself as to her readers. Unfortunately, her manuscript notation was misread by the Press and with great toleration she accepted the proofs, probably without demur. Of her seven papers published in Monthly Notices of the Society, the one in 1941 is the limb-darkening paper already referred to; her 1953, 1954 and 1955 papers are concerned with line formation in semi-infinite stellar atmospheres with coherent and non-coherent scattering, the 1954 paper being written jointly with Stibbs; and there is a fine series of three papers on finite atmospheres with isotropic scattering in 1955, 1956 and 1957. The Astrophysical Journal published six of her papers, the last two, written in collaboration with E.C.Orchard and published in 1967 and 1968, on the reflection and transmission of light by thick atmospheres, being of relevance to geometrically thin but optically thick layers of paint! Her published work on radiative transfer theory in solar, stellar and other contexts is an enduring testimonial to her uncompromisingly high standards and enviable versatility as a mathematician.
D.W.N.STIBBS
Ida Winifred Busbridge's obituary appeared in Monthly Notices of the Royal Astronomical Society 33:4 (1992), 455-459.