THOM AS G EO R G E COWLING
17 June 1906— 16 June 1990
THOM AS G EO R G E COWLING
17 June 1906— 16 June 1990
Elected F.R.S. 1947
BY L. MESTEL, F.R.S.
BACKGROUND, EDUCATION AND CAREER
THOM AS G E O R G E COW LING was born in Hackney, east London, the second son
of George and Edith Eliza (nee Nicholls). Several years ago, at his request, my wife
did some genealogical research into his ancestry. She found that his grandparents and
their antecedents were nearly all artisans, blue-collar workers or servants from London
and the home counties: the men including a cabman, a dock clerk, a milkman, a
bellows-maker, a tallow-chandler, a shoemaker and two weavers, the women a
housemaid and a boot-binder. One great-great-grandfather was a Cornish naval
s e a m a n . S o m e e x o tic g e n e s e n te r e d th e fam ily s to c k th ro u g h a
great-great-great-grandfather, a Swedish mariner named Janas Winnburg, whom one
is tempted to picture as a six-foot-plus red-headed Viking.
Tom described his father G eorge as a very intelligent person, with great
determination. Because of the early death of his father, George had to start work at
the age of 14 as an office boy earning five shillings a week, but continued his education
in evening classes, reaching finally the grade of executive engineer in the Post Office.
Although Tom’s mother Edith had trained as a teacher, she led a mainly domestic life,
devoted to the upbringing of their four sons. Both parents were ‘loyal members of
Baptist churches’, from whom their sons inherited the ‘Puritan work ethic’ (78)*.
The Cowling boys were of the generation first to benefit from the 1902 Education
Act. Tom won a county scholarship to Sir George Monoux Grammar School at
Walthamstow, a Tudor foundation which had been incorporated into the newly
established state-run system of secondary education. The school was particularly
strong in mathematics, and was special for that time in having laboratories for physics
and chemistry. Tom was in fact put into the arts sixth form, following the advice of a
family friend that to make oneself employable, training in mathematics and English
sufficed, and a pure science course would be too narrowing. Besides double
mathematics he therefore studied (non-examinable) French and Latin beyond what
Numbers in this form refer to entries in the bibliography at the end of the text.
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would now be called the O-level standard, but did no sixth-form chemistry and little
physics, something he later regretted. With general guidance from the overworked
senior mathematics master, he prepared himself for university entrance, winning an
open scholarship to Brasenose College, Oxford in 1924. Grants from Essex County
and the Ministry of Education matched the value of his scholarship, so relieving his
parents of any further financial burdens on his behalf.
His description of Oxford mathematics teaching in the 1920s is unflattering;
‘old-fashioned and run inadequately by tutors who had other responsibilities’. He was
nevertheless satisfied to be left to work from texts. His native mathematical ability
showed up through his winning the University Junior Mathematical Exhibition in 1925
and Scholarship in 1926. He recalls the inspiring undergraduate lectures by G.H.
Hardy, but his natural predilection was clearly towards theoretical physics, even
though the only such undergraduate course was an option in electromagnetism based
on Jeans’s treatise.
His first class degree was rewarded by a three-year postgraduate scholarship at
Brasenose. The year 1927-28 he spent working for the University Diploma in
Education, so fulfilling the condition on which had depended his undergraduate grant
from the Ministry of Education. He writes (78) that the diploma did little for his
subsequent career, but in his tutor’s opinion it was beneficial in widening his outlook
after a narrow mathematics course. Because of this year’s delay in beginning research
he was able to work under the supervision of E.A. Milne, the first incumbent of the
newly established Rouse Ball Chair of Mathematics, who arrived in Oxford in January
1929.
While Cowling was still an undergraduate his tutor had given him to read the journal
containing Schrodinger’s fundamental paper on wave mechanics. Although a lack of
training in Hamiltonian mechanics and inadequate German prevented him from a full
understanding, he had been stimulated into further reading. He therefore asked Milne
if he could work in atomic theory; however, Milne replied that his own knowledge of
that area was rusty, so a new research student would have to work on an astronomical
topic. This is the reason for the title ‘Astronomer by accident’ given by Cowling to his
Annual reviews o f astronomy and astroph
autobiographical essay in
In two areas - cosmical magnetism and stellar structure - Cowling soon established
himself as a sharp but constructive critic. Milne had asked Sydney Chapman for a
simple problem to give his new student. Chapman had written a paper to explain a
reported observed property of the solar magnetic field (which in fact turned out later
to be spurious). He suggested that Cowling could use his model to calculate the heights
of origin of the spectral lines exhibiting the Zeeman effect. Cowling’s studies enabled
him to show that Chapman’s explanation of the supposed field limitation was itself
spurious, as had been suggested by R.H. Fowler and others on thermodynamic
grounds. This early demonstration of his acumen seems to have been crucial for
Cowling’s subsequent career. It impressed Milne into withdrawing his highly
discouraging suggestion (made after only six months’ acquaintance) that Cowling
should think of a career in teaching rather than in research; and Chapman lost no time
Thomas George Cowling
107
in inviting Cowling to join the Mathematics D epartm ent at Imperial College as a
demonstrator, on expiry of his Brasenose scholarship. The ensuing collaboration with
Chapman was to lead to publication in 1939 of the now classical text, The mathematical
theory o f non-uniform gases. Vincenzo C.A. Ferraro (subsequently professor at Exeter
and Queen Mary College, London) was also on Chapm an’s staff, and he and Cowling
‘spent quite a time enthusiastically explaining his research to the other’ (78), the
beginning of a lifelong friendship.
Milne’s direct influence was to interest Cowling in the then lively controversy
between Sir A rthur Eddington, Sir James Jeans and Milne on the technicalities and,
indeed, the underlying philosophy of the theory of stellar structure. In his own words
he ‘kept his head down’, but the work he did at Oxford was the start of a series of
studies by himself, Ludwig Biermann and others that was both to vindicate the essence
of Eddington’s case and to introduce significant modifications.
W hen his untenured post at Imperial College came to an end, Cowling moved to
University College, Swansea, as assistant lecturer in mathematics (1933-37), followed
by a year as lecturer at University College, Dundee, and seven years as lecturer at
M anchester University. From 1945 to 1948 he was Professor of Mathematics at
University College, Bangor, moving to his last post as Professor of A pplied
Mathematics at Leeds University until his retirem ent in 1970, when he became
Emeritus Professor.
Over the three decades 1928-1958 Cowling made outstanding contributions to the
theory of stellar structure, cosmical electrodynamics, kinetic theory and plasma
physics, discussed in detail below. In his own words, with the completion of his
Interscience tract on magnetohydrodynamics (MHD), his original work was nearly
done. In the following years he wrote a few papers and several reviews, conference
r e p o r ts a n d p r e s id e n tia l a d d re s s e s , a n d he p r e p a r e d new e d itio n s o f
Magnetohydrodynamics and of Chapman & Cowling, but the work was consolidatory
and critical rather than trail-blazing. 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 in 1954, a slipped disk in 1957 and a mild heart attack in 1960 - caused a
slowing down of his activities well before his retirement.
Compared with most active academics today, Cowling spent comparatively little
time abroad. However, in 1951 he worked for three months at each of Caltech and
Princeton University Observatory, visits remembered with warmth by Horace Babcock
and Jesse L. Greenstein on the west coast and by Lyman Spitzer Jr and Martin
Schwarzschild on the east. The lectures he gave formed the basis of his article (38) on
‘Solar electrodynamics’. While in America he met the late Pol Swings and Paul Ledoux
from Liege. (Ledoux he had previously met in Belgian Air Force uniform at a Royal
Astronomical Society meeting during World War II; they shared a common interest
in problems of stellar stability.) As a consequence Cowling made several visits to Liege,
in particular contributing to the annual colloquia at the Institut d ’Astrophysique. His
public service included many years as Council member, Vice-President and President
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(1965-67) of the Royal Astronomical Society, and as President of the International
Astronomical U nion’s Commissions on Stellar Constitution (1955-58) and on
Magnetohydrodynamics (1964-67). In 1954 he went, together with Donald Sadler
(Director of the Nautical Almanac), as U.K. representative invited by the U.S.S.R.
Academy of Sciences to attend the ceremonial reopening of the Pulkovo Observatory
near Leningrad, destroyed by the Nazis during World War II.
Cowling was perhaps a little over-conscious of the limitations, for one whose
interests were mainly (though not exclusively) in astronomy, resulting from his having
spent his entire career in mathematics departments. He never had a formal education
in astronomy, and had few opportunities to give graduate courses in astrophysics.
Although, I think, recognizing that much research in astronomy would inevitably
continue to be done by faculty members whose main teaching responsibilities would
be in applied mathematics and physics, he approved of the plans for the establishment
of a National Institute of Theoretical Astronomy that were under discussion from very
soon after the War. The Institute of Astronomy at Cambridge and the Astronomy
Centre at Sussex finally emerged (somewhat indirectly) from these plans, but by then
his health problems discouraged him from considering a move to an astronomical
environment.
In addition to election in 1947 to the Royal Society, Cowling received several other
honours: the Johnson Memorial Prize at Oxford for original work in astronomy or
meteorology (1935), the Gold Medal of the Royal Astronomical Society (1956), the
Bruce Medal of the Astronomical Society of the Pacific (1985) and (two days before
his death) the Hughes Medal of the Royal Society (1990), an award given especially
for work in electrodynamics. In 1966 Brasenose elected him an Honorary Fellow.
Tom Cowling married Doris Marjorie Moffatt on 24 August 1935. She survives him
together with their daughters Margaret Ann Morrison and Elizabeth Mary Offord,
their son Michael John, and six grandchildren. The family connection with Brasenose
(continued by a nephew who read P.P.E.) has been further maintained by M argaret’s
son Alan who read mathematics, and now by Elizabeth’s son Ian who began reading
modern languages in October 1991.
The devoted support from Doris and family enabled Tom to battle against the
recurring bouts of ill-health that plagued him during the 1980s. He finally succumbed
one day before his 84th birthday, just too soon to learn of the award of the Hughes
Medal.
SCIENTIFIC WORK
(a) Stellar structure
To bring out the significance of Cowling’s contributions in this area, it is helpful to
summarize the early controversies. Cowling began his research career as Milne’s
student a few years after Eddington had published his celebrated Internal constitution
o f the stars (1926). Eddington modelled a typical homogeneous star as a sphere of gas
obeying the classical Charles law, with internal temperatures high enough for gas and
Thomas George Cowling
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radiation pressure jointly to balance self-gravitation. As first noted by Jeans, at these
tem peratures the gas is highly ionized, emitting and absorbing radiation efficiently, so
that the radiation field at each radius is very close to the Planck distribution for the
local tem perature. The heat flow to the surface down the gravitationally maintained
tem perature gradient is primarily by the slow leak of radiation through the opaque
gas. The principal source of opacity in addition to Thomson scattering had been
identified as photoelectric absorption, and tolerably accurate estimates for its
magnitude and its dependence on density, tem perature and composition were made
by H.A. Kramers, S. Rosseland and later by J.A. Gaunt. The theory of nuclear energy
liberation had not yet been developed; however by some ruthless approximation
Eddington was able to present his ‘standard model’ of a star with its mass-luminosity
relation, requiring just calibration against one star (Capella) to be applicable to all
other ‘main sequence’ stars.
Criticism of this picture came from Milne and Jeans. Both Milne and Eddington
had made important contributions to the theory of a stellar atmosphere, the outer
region of a star that includes the observed photosphere, in which the photon
mean-free-path increases sharply from the small value appropriate to the opaque
stellar interior to the infinite value for radiation streaming into the interstellar medium.
Eddington would (in present-day parlance) regard the interior and atmosphere
solutions as well-matched asymptotic approximations, whereas Milne believed that the
precise surface boundary conditions would affect strongly the whole internal structure
solution. Cowling wrote (78): ‘Milne’s basic idea was that since all that we know about
a star is in its surface properties we should seek relations involving only those
properties. H e even suggested the properties of the deep interior, being unobservable,
should be regarded as candidates for Occam’s razor.’ On reading Tom’s preprint
version of this essay (78), I expressed surprise that Milne should advance such an
extreme and naive brand of positivism. Tom replied: ‘In speaking of Occam’s razor I
was never sure w hether Milne had his tongue in his cheek or not. He certainly stated
his suggestion perfectly seriously, but perhaps he was simply meaning that the only
results that ultimately are useful are those that can be tested by observation.’ W hatever
the exact meaning of Milne’s stated philosophical stance, its practical upshot was to
make him look for stellar configurations other than those satisfying Eddington’s
mass-luminosity relation, and in which the interior structure is sensitive to the surface
boundary conditions. His views in part overlapped with those of Jeans, who had argued
against Eddington that not only the mass but also the luminosity was an independently
specifiable quantity. This divergence perhaps derived originally from differing ideas
as to the source of stellar energy. Jeans had advocated radioactive decay, a process
virtually unaffected by the tem perature and density of the material, whereas
Eddington (like H.N. Russell before him) argued that the energy sources are highly
temperature-sensitive, being virtually inactive until the tem perature reaches a critical
value, to be identified with the nearly constant central temperature inferred for the
observed main sequence stars.
Looked at from today, it is clear that Eddington could have emphasized that the
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Biographical Memoirs
radiative transfer equation yields a mass-luminosity-radius relation, but owing to the
fortuitous form of the opacity law the dependence on the radius is weak. His picture
was ultimately vindicated by the calculations of H.A. Bethe and C.F. von Weizsacker
in the late 1930s, which showed that thermonuclear energy generation is indeed highly
temperature-sensitive. A main sequence star thus contains an efficient thermostat
which fixes the radius and so also the central temperature at the value at which the
transport of radiation is balanced by energy from the fusion of hydrogen into helium.
As Eddington argued, Jeans’s hypothetical star with intense radioactivity would not
necessarily radiate faster than an ordinary star, but would use the surplus energy in
expanding.
In his later years, presumably influenced by the evidence for thermonuclear energy
generation, Jeans (1944) was ready to accept the essentials of Eddington’s picture;
something noted by W.H. McCrea in a radio broadcast but missed by Milne in his
biography of Jeans (1952). Around 1930, however, there was an apparent serious
difficulty with the theory of gaseous stars: it seemed impossible to ensure stability
against exponentially growing pulsations if the energy generation had even a modest
positive dependence on temperature and density. Eddington acknowledged this
implicitly by adopting for his standard model a nearly uniform source distribution
through the star. Jeans felt compelled to study ‘liquid stars’, meaning models in which
the internal equation of state deviated markedly from the classical gas law. And
Cowling’s supervisor, Milne, in attempting to construct non-Eddingtonian models,
suggested that main sequence stars might be degenerate in the Pauli-Fermi-Dirac
sense in their central regions.
Inevitably, Cowling’s first forays into the area of stellar structure were strongly
influenced by his supervisor’s opposition to Eddington’s picture, but his conclusions
in fact failed to help Milne’s case. Working independently, Cowling (3), Russell and
Bengt Stromgren (using the non-relativistic approximation to the degenerate equation
of state) and Subrahmanyan Chandrasekhar (using the unapproximated form) showed
that in homogeneous stars with main sequence radii, degeneracy was unimportant (in
contrast to white dwarf stars, for which R.H. Fowler, E.C. Stoner and Chandrasekhar
had shown that degeneracy is crucial (see Chandrasekhar 1939)). Cowling also worked
on a non-degenerate ‘point-source’ model (2), with energy sources strongly centrally
condensed, in contrast to Eddington’s standard model. When the Royal Astronomical
Society, in 1931, devoted a meeting to a discussion of Milne’s ideas, Cowling was asked
to speak on his work. He must have been uncomfortable at being looked on as a
supporter of Milne. He could not but agree with Eddington’s comment that the
point-source model was not the best for representing real stars. His computations on
this model in fact suggested that Eddington’s standard model was remarkably robust:
to get configurations of homogeneous stars very different from Eddington’s something
drastic must certainly happen near the centre, but these calculations showed that
degeneracy was irrelevant to the problem.
Cowling’s most important contributions came through his studies on stellar stability.
In 1934 he looked again at the vibrational stability of stars in radiative equilibrium
Thomas George Cowling
111
throughout (8). The oscillations will grow in amplitude if the extra thermonuclear
energy fed into the central regions during compression exceeds the extra energy
transfer during rarefaction. A proof of stability thus requires a careful treatm ent of
the outermost layers of the star where most of the damping occurs. The correct
procedure is to com pute the oscillation eigen-functions for the stellar model
considered, and then to construct the ‘coefficient of stability’ (in Rosseland’s
terminology). Earlier treatm ents had adopted the short cut of assuming the oscillation
amplitude to be proportional to the radius. Cowling showed that this grossly
underestimates the damping, as the actual amplitude is relatively much greater in the
outer regions.
Simultaneously came the realization that the tem perature gradient in the core of a
radiative star with strongly centrally condensed energy sources would exceed the local
adiabatic gradient and so would violate Karl Schwarzschild’s criterion for stability
against convection: a point that seems first to have been made by Harold Jeffreys.
Cowling estimated the maximum rate that energy generation could increase with
tem perature without the onset of convection near the centre, confirming that his
point-source models would indeed develop a convective core. This rounded off his
first studies on vibrational instability, for a fully radiative stellar model in which the
energy generation increased fast enough with tem perature to lead to vibrational
instability would already be convectively unstable in the centre.
Meanwhile, Ludwig Biermann in Germany had applied L. Prandtl’s idea of the
mixing-length - a macroscopic mean-free-path - to show that once a turbulent
convective core developed, the consequent energy transport would be so efficient that
the tem perature gradient would be super-adiabatic by no more than about 10“6. In a
second paper on stability (10) Cowling gave a more detailed discussion of energy
transport in a convective zone, confirming that a star with strongly centrally condensed
sources would have a convective core with a nearly adiabatic tem perature gradient.
In an appendix to this paper he constructed the ‘Cowling stellar model’. This important
modification to E ddington’s basic theory exploits the anticipated tem perature
sensitivity of energy generation in two ways. In the convective core the temperature
gradient is well approximated by the adiabatic value; whereas at the radius where the
convection dies out and purely radiative transport takes over, the tem perature is lower
by a factor two or so than the central value, so that local energy generation is negligible
and the rest of the star can be treated as a radiative ‘envelope’ with a Kramers opacity
law, carrying a constant luminosity to be radiated ultimately from the stellar surface.
The Cowling model is thus a physically acceptable modification of the earlier
point-source model. Cowling then extended his work on vibrational stability to this
model, showing again that the large damping effect of the outer layers offsets the
nuclear energy input into the oscillations in the core, unless the tem perature
dependence is far higher than anything expected. The results of both stability papers
require that the ratio of specific heats (y) be not too close to the value 4/3 at which
the star becomes secularly unstable. Violation of this will occur only for very massive
stars where the relative contribution of radiation pressure to the total pressure is large.
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Biographical Memoirs
The Cowling model stands out as a landmark in the development of the theory. The
su c c e ssfu l c o n s tr u c tio n o f a g a se o u s s te lla r m o d e l w ith a stro n g ly
temperature-sensitive energy source, but which is nevertheless vibrationally stable,
greatly strengthened the case for the overall philosophy behind Eddington’s treatment
of homogeneous stars. It also removed an implicit inconsistency, for the assumption
of a nearly uniform energy source distribution in Eddington’s standard model really
contradicts his own interpretation of the main sequence with its remarkable prediction
of temperature-sensitive energy generation (cf. 66).
In stars a little more massive than the Sun, fusion of hydrogen into helium occurs
via the highly temperature-sensitive carbon-nitrogen cycle, so for them the Cowling
model with its convective core is the appropriate paradigm. In the Sun and less massive
stars, the rather less sensitive direct fusion via deuteron formation dominates and
purely radiative transfer persists in the central regions. This difference is important
for the later evolution of stars of different mass, but the presence or absence of a
convective core in a main sequence star made comparatively little difference to the
temperature-density distribution. Cowling noted that his model deviated far less than
might have been expected from Eddington’s standard model, and Biermann
commented on the robustness of the mass-luminosity relation. The common interest
of Cowling and Biermann in stellar structure and cosmical magnetism (see below) led
to a vigorous correspondence over the years 1936-39. A. Unsold had earlier pointed
out that the latent heat of hydrogen ionization would yield an adiabatic index near
unity a short distance below the solar photosphere, so that again the Schwarzschild
criterion would fail and convective instability would set in (observable as the solar
granulation). Biermann’s detailed analysis showed that this outer convective zone
would be much deeper than was expected. He extended his work to the possible case
of a fully convective star, which at first sight seems to have the extra degree of freedom
that Milne had looked for in his attempt to construct non-Eddington stellar models.
Cowling (12, 13) pointed out that the luminosity of such a star is again not a free
parameter, but is fixed by conditions in the thin surface layer in which radiative
transport dominates (essentially by the temperature at the radius where the optical
depth is near unity, in accord with the M ilne-Eddington treatm ent of stellar
atmospheres). The profundity of this comment showed up many years later, in studies
of evolved, inhomogeneous red giant stars by F. Hoyle and M. Schwarzschild and of
contracting pre-main sequence stars by C. Hayashi (cf. Schwarzschild 1958,
Kippenhahn & Weigert 1990). These models (like those of lower main sequence stars)
have extensive outer convective zones and the correct choice of the adiabat (essentially
the entropy of the zone) is crucial for their overall structure.
In the earlier controversy Milne had objected to Eddington’s inference of the value
for the internal opacity from surface observations. Eddington’s procedure is in fact
adequate for primarily radiative stars, for which the surface layers are the ‘tail’, wagged
by the bulk of the star forming the ‘dog’. For cool giant and pre-main sequence stars,
with surface convection, the necessary precise treatment of the surface conditions
requires use of the appropriate local opacity in constructing the optical depth. R. Wildt
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113
showed that the dominant process is absorption by the negative hydrogen ion, which
yields a coefficient of opacity that increases with tem perature, in contrast to the
Kramers law appropriate to the interior, and this leads to very different evolutionary
tracks in the H ertzsprung-R ussell lum inosity-colour diagram, and to marked
deviations from Eddington’s mass-luminosity relation. It is also the case that Fermi
degeneracy does occur in the burnt-out central regions of inhomogeneous evolved
giant stars. It is certainly ironic that Milne’s objections to Eddington’s treatm ent and
his alternative proposals should turn out to be relevant, but to bodies very different
from those that both he and Eddington were considering. (However, when it comes
to the construction of inhomogeneous stellar models, the non-dimensional variables
introduced by Milne are admirably suited for the matching of interior and exterior
solutions (Schwarzschild 1958).)
A part from the joint paper with Biermann (15) on the effect of chemical composition
on vibrational stability, Cowling wrote no more papers on mainstream stellar structure
theory. All the early work could be done (laboriously) with the help of tables and
pre-electronic desk calculators. Though appreciative of the method for constructing
models quickly, devised by Christine and Hermann Bondi, he saw that once one started
to use accurate energy generation and opacity values, and to take account of the details
of stellar evolution, the electronic computer was an essential tool. By then, although
he had administrative responsibility to the Senate for the Leeds University Computing
Laboratory, he found himself without sufficient time to master the use of a computer,
due partly to his first bout of illness (DeVorkin 1978). However, over the years he
wrote several papers on cognate topics which show his characteristic soundness of
judgement.
In close binary systems with non-circular orbits the observed rotation of the apsidal
line can be used to estimate the degree of central condensation of the stars. The effect
is due to the non-Coulomb term in the gravitational potential arising from the mutual
tidal interactions of the stars. Earlier treatments suggested a density distribution much
more uniform than in an Eddington-type star. Cowling pointed out (14) that these
authors had assumed the stars to be quasi-rigid; a correct treatm ent yielded a central
condensation as required by Eddington’s theory and its modifications. (The formalism
in this paper is also useful for an elementary study of the internal motions within
non-synchronized binary systems and so for deriving a basic formula of G.H. Darwin’s
for the time-scale of synchronization by the action of turbulent friction.)
While on duty as an air-raid warden in 1941, Cowling took the opportunity to do
the numerical work for a paper (18) on non-radial oscillations of polytropic stars. His
m otivation was the feeling th at the local instability criterion given by Karl
Schwarzschild should emerge more rigorously from the discovery of exponentially
growing global non-radial modes of oscillation, analogues of the radial modes studied
earlier. To keep the problem manageable he made what is now known as the Cowling
approximation which neglects the modification to the gravitational field due to the
density fluctuations. This enabled him to identify two classes of non-radial oscillations,
the p modes driven essentially by pressure variations as in a sound wave, and the g
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Biographical Memoirs
modes, analogues of gravity waves in a stratified terrestrial atmosphere, the two classes
being separated by a (fundamental) / mode having no node. Later work has blurred
the separation between low order/? and
gmodes and
always so easily identified; Chandrasekhar and Lebovitz have been able to drop the
Cowling approximation. Cowling himself did not regard the paper as particularly
important, but it in fact turned out to be seminal for what is now known as
helioseismology (the probing of the solar interior by theoretical interpretation of the
spectrum of p modes at the solar surface). Such studies use the splitting of mode
frequencies to make inferences about the internal solar rotation: another pioneering
paper in this area is by Cowling and Newing (32).
The two-way interaction of rotation with convection remains an ongoing problem.
Cowling’s paper (36) inferred that the stabilizing effect of rotation for axisymmetric
systems (Rayleigh’s criterion) can be nullified in some non-axisymmetric modes, in
which ascending and descending columns exchange angular momentum by leaning on
each other. Thus rotation, uniform or non-uniform, allows instability as soon as the
Schwarzschild stability criterion is violated. A more difficult question is the extent to
which the efficiency of developed convection is affected by rotation.
(b) Cosmical magnetism
When Cowling began working with Chapman, the strongest cosmical magnetic fields
known were the several thousand Gauss fields of sunspots, discovered early in the
century by G.E. Hale through the Zeeman effect. Chapman had often quoted a paper
by Sir Joseph Larmor containing the suggestion that cosmical magnetic fields might
be maintained by ‘dynamo action’: motion of the conducting gas across an existing
field induces an emf which drives currents against the ohmic resistance of the gas, and
these currents could be just those required by Ampere’s law to maintain the assumed
field. Cowling began what he expected to be ‘a relatively routine piece of difficult
computation’ to see what sort of field could be maintained by the Larmor process. For
simplicity the field was chosen to be axisymmetric, with a circle of O-type neutral points
where the field B vanishes but the current density j a V x B remains finite. In this
geometry Larmor’s process requires that j = a(vxB ) at each point, where o is the
conductivity and v the bulk velocity of the gas, and this condition cannot be satisfied
near the neutral points. This is Cowling’s celebrated ‘anti-dynamo’ theorem, published
in the paper (7) entitled ‘The magnetic field of sunspots’. Cowling’s proof was
subsequently generalized by Chandrasekhar and Backus to encompass fields where
both B and j vanish at O, but with B necessarily vanishing to a higher order. E.C.
Bullard noted that strict axisymmetry is not necessary; a whole class of fields
topologically similar to Cowling’s possess a critical closed curve analogous to the
O-point circle and so can also be excluded from dynamo maintenance. Nowadays we
think in magnetohydrodynamic terms, with the motional induction term corresponding
to advection of the field lines by the moving fluid, whereas the ohmic term j/cr causes
diffusion of the field through the fluid. In fields covered by Cowling’s theorem, there
is a steady drain of magnetic flux onto the critical curve which could be offset only if
Thomas George Cowling
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the points on the curve are sources of gas. The same argument forbids the generation
of such fields by dynamo action.
For a while Cowling does seem to have surmised that there was waiting to be proved
a general anti-dynamo theorem, at least for homogeneous conductors. Later he felt
that too much emphasis was laid on his and other anti-dynamo theorems: their
significance is that those fields that can be dynamo-maintained - and the associated
motions - cannot be simple in structure or in mathematical formulation. Thus one can
write the dynamo requirem ent for a prescribed laminar velocity field as an eigen-value
problem, but because of the non-Hermitian nature of the relevant operator there is
no automatic guarantee of real eigenvalues (43). Cowling’s theorem was a challenge
to mathematicians: even though one could picture non-axisymmetric motions that
seemed to replace the flux being lost ohmically, there was need for rigorous existence
proofs (Backus, Herzenberg) before one felt confidence in pictorial argument or
numerical computations. Cowling set the scene for today’s veritable dynamo industry,
much of it owing to the insights of E.N. Parker in Chicago and M. Steenbeck, F. Krause
and K.-H. Radler in (erstwhile) East Germany.
A magnetic field that cannot be maintained by dynamo action, and without any other
sources of energy, will decay through ohmic dissipation of the currents. Cowling
discussed the decay eigen-modes of a dipolar stellar field (ignoring the effect of any
turbulent zones) (27), the mathematical problem being a generalization of one solved
in the last century by H. Lamb. H e found that the characteristic time of decay of the
largest-scale mode is of the order of the solar lifetime. Our knowledge of the solar
field - in particular its reversal along with the sunspot cycle - now precludes the idea
that the field is a ‘fossil’ relic of the field with which the Sun was born, and most workers
accept that what we observe in the Sun and other solar-type stars is quasi-periodic
dynamo action; but for those hotter stars (without strong outer convection zones) that
show strong surface fields, Cowling’s fossil theory (suitably modified to satisfy stability
criteria) remains a plausible candidate.
Several authors beginning with Biermann have shown that plasma microphysics can
sometimes yield the analogue of a ‘battery’, a non-electric force acting to accelerate
electrons relative to ions and so to build up a system of currents and its associated
magnetic field. Biermann’s battery term in a fully ionized gas is Eb = V/?e/«ec where
—e is the electronic charge and p e and ne the electron partial pressure and number
density. Cowling pointed out that the same enormous self-inductance of cosmical
systems that leads to the long decay time of fields without energy sources also yields
a long growth time before the field reaches the asymptotic value, given by balancing
energy input from the Biermann battery against ohmic dissipation. In his ‘Solar
electrodynamics’ article (38) Cowling noted the analogy with elementary circuit
theory. If no other effects intervene, then the Biermann-type process, acting alone,
can lead over cosmical timescales to strong stellar fields, but of azimuthal (‘toroidal’)
rather than meridional (‘poloidal’) structure. Most workers look upon cosmical
batteries rather as processes that generate seed flux, which can then be amplified by
dynamo action.
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Biographical Memoirs
Returning now to the 1930s: Cowling shelved temporarily the problem of the origin
of the general solar magnetic field and instead devoted much thought to the sunspot
phenomenon. His work on the dynamo problem led him to picture a spot forming
through local compression and twisting by mass motions of flux forming part of the
general solar field. On both mechanical and thermodynamic grounds he criticized the
argument put forward independently by Russell and Milne that the coolness of spots
is due to adiabatic cooling of rising material (9). Much stimulus came again through
correspondence with Biermann. Each came independently to the conclusion that the
lateral Lorentz force exerted by the concentrated flux in a spot is vital for balancing
the pressure difference between the hot gas outside and the cool gas inside the spot;
but Cowling emphasizes (78) that it was Biermann who suggested that the cause of
the spot coolness is magnetic interference with the efficiency of upward convective
heat transport into the spot region as compared with the unimpeded transport outside,
an explanation that convinced Cowling and that remains very widely accepted.
Cowling’s general physical discussion of magnetism and convection in the
Magnetohydrodynamics tract is particularly illuminating.
Although Cowling, Biermann, Ferraro and others in the 1930s were clearly moving
towards the ideas of MHD, it was Hannes Alfven in 1942 who gave a comprehensive
formulation of the two-way interaction between a magnetic field and a conducting
medium such as an ionized gas and who discovered the Alfven wave. He also
rediscovered Ferraro’s law of ‘isorotation’ - uniform rotation along individual poloidal
field lines - valid in a steady axisymmetric state with just rotatory motion. He pointed
out that if isorotation is violated then the system will execute torsional oscillations,
with energy interchange between the rotation and the toroidal magnetic field; an
example of the MHD wave in non-Cartesian geometry. In 1950 Alfven published his
Cosmical electrodynamics, which received a mixed reception: general approval for the
basic theory presented in the first four chapters, but reservations about some of his
specific cosmical applications.
Alfven had independently surmised that a sunspot field is not created or destroyed
in situ, but is a tran sien t local am plification by com pression of p a rt of a
quasi-permanent general solar field. Cowling’s estimate of 300 years for the growth
and decay time of fields in stationary media (simple extensions of his work on
large-scale fields) gave strong support to the MHD picture. But Alfven had also
attempted a general theory of the solar cycle in terms of his torsional oscillations along
a general dipole-like field. He pictured a spot pair appearing when a wave packet
reaches the solar surface, where it is reflected back into the interior. Cowling severely
criticized Alfven’s theory (30), summing up his rejection of it in the words (38): ‘Alfven
exceeds the number of ad hoc assumptions which can reasonably be allowed to the
author of a theory, and there are serious gaps and inconsistencies in his account.’
Looking back, one feels that Alfven and his collaborator C. Walen attempted to extract
too much from too simple a model. Nowadays we picture the solar cycle as a
quasi-periodic dynamo in which the generation of a toroidal field component by
non-uniform rotation plays certainly a crucial role, along with upward motion of flux
Thomas George Cowling
117
through magnetic buoyancy, and the conversion of a toroidal into a poloidal field
component by the Coriolis force acting on turbulent eddies.
The sunspot controversy was the second major interaction with Alfven involving
some approval but rather more criticism on Cowling’s part. Chapman and Ferraro had
put forward a model for the onset of geomagnetic storms as due to the emission from
the Sun of a highly conducting electron-ion stream which compresses the E arth’s field.
Their pioneering work was essentially hydromagnetic, with the degree of charge
separation fixed by the divergence of the electric field entering the equations of
motion. Over the years their model has inevitably been greatly modified. The
perm anent outflow of plasma from the Sun (the solar wind, predicted by Biermann
from observations of cometary ionic tails) implies a perm anent magnetospheric cavity
around the earth, with geomagnetic storms being sometimes associated with enhanced
surface activity on the Sun, such as flaring. Alfven pointed out that the wind will carry
frozen-in magnetic flux from the Sun, modifying significantly the interaction with the
magnetosphere; and there is an extended magneto-tail behind the Earth which has
observable effects near the E arth’s poles. But the attem pt to describe the basic
phenomenon as a collective plasma process remains well-advised. Alfven produced a
different theory which aimed more at explaining the later phases of a storm. He
assumed a stream of particles far more energetic than those in the Chapm an-Ferraro
streams which passed through the magnetic field of Sun and Earth without much
hindrance, with cooperative effects being ignorable. Chapman asked Cowling to
exercise his renowned critical faculties on Alfven’s theory (22). Cowling appreciated
Alfven’s development of the guiding-centre description of the motion of particles in
a magnetic field (a combination of gyration about a centre moving along a field line
with slow trans-field drifts superposed), but he objected strongly to the assumption
that it was enough to consider only individual particle motions.
Cowling wrote (78) that he regrets that his first encounter with Alfven was as a
‘bespoken critic’. H e also thought that the continuing assaults by Alfven on the
Chapman school were somewhat unjust, forcing him to rise to the defence. He clearly
felt that the polemic should cease, not least because ‘most workers in the field seem
now to believe that the ideas of Chapman and Alfven have been subsumed into a later
synthesis’. H e recalls with pleasure that in 1949 Alfven sent S. Lundquist to work with
him. H e suggested that Lundquist use the energy principle to study and in fact confirm
Alfven’s surmise that a magnetic flux rope when twisted too far becomes unstable to
loop formation. ‘This is the closest that Alfven and I have gotten to working together’
(78). As Cowling said to me more than once: ‘Alfven’s best ideas are very good indeed.’
In the late 1940s Horace Babcock discovered strong magnetic fields - typically a few
thousand Gauss, but in one case about 35 000 Gauss - in several early-type stars. Since
then the catalogue has been greatly extended. In virtually all cases the fields are found
to vary periodically, often reversing in overall polarity. Typical periods are 5-10 days,
and a few are very much longer. The simplest model is the ‘oblique rotator’, with the
magnetic and associated spectral and luminosity variations arising from a periodically
changing aspect as the star rotates about an axis inclined to the magnetic axis. Of the
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Biographical Memoirs
alternatives, a scaled-up solar cycle model is highly implausible for many reasons. The
remaining candidate was the magnetic oscillator, with the field variations resulting
again from the dragging of the field lines by the moving gas. However, Cowling showed
(37) that the periods of oscillation would normally be too short, and in any case a
correct treatment of the surface boundary condition virtually rules out the possibility
of field reversal, a conclusion confirmed in a subsequent study by P. A. Sweet. This left
the oblique rotator in possession of the field of combat, and it is now accepted both
by observers as a phenomenological model and by theorists as a generator of important
and interesting problems.
Of his review articles, etc., in this area, that on ‘Solar electrodynamics’ (38) is
particularly instructive. The crucial role of electromagnetic induction in large-scale
systems is clearly brought out in the discussion both of basic theory and of applications
to solar phenomena, even if in retrospect some of his critical comments seem
overstated. The Interscience tract Magnetohydrodynamics - like the complementary
volume Physics o f fully ionized gases by Spitzer (1956) - is a model of lucidity combined
with compactness and has been very influential. Th
reviews article (76) surveys
the developments in solar dynamo theory in the decade following a similar review by
Parker. The summary conclusion that ‘the dynamo theory of the Sun’s magnetic field
is subject to a number of unresolved objections, but alternative theories advanced so
far are open to much greater objections’ remains true a further decade later.
(c) Kinetic theory and plasma-physics
When Cowling moved to Imperial College, Chapman had on his shelves a ‘skeleton
of a book on gas theory’ and had been looking for someone with whom to complete
it. Two possible collaborators had already declined when they realized how much work
would be involved. Cowling was impressed by the manuscript’s ‘novelty and power’,
and was glad to accept Chapman’s subsequent invitation. The Enskog-Chapman
approach to the solution of Boltzmann’s equation enabled him ‘to see kinetic theory
as a developed whole, instead of the collection of approximations and tricks that had
been represented in Jeans’s work’ (the reference is to Jeans’s Kinetic theory o f gases).
Most of Cowling’s personal contribution was completed by 1935, but it took another
year before Chapm an had gone through the new manuscript and suggested
improvements, and the first edition of the Mathematical theory o f non-uniform gases
did not appear till 1939. The 1970 third edition had undergone a radical revision, but
is recognizably the same book. Largely because of its emphasis on mathematical
fundamentals, the book makes an awesome initial impression: one can imagine that a
physicist with literary talent might emulate Keats and write a sonnet entitled: ‘On first
looking in to ... ’
Over the years Cowling retained his interest in gases of electrically neutral particles
(19, 52, 64), interacting particularly with the chemists P. Gray and P.G. Wright (55),
but his main interest was in conducting gases permeated by a magnetic field (even
though the relevant chapter in Chapman & Cowling is only one eighth of the book.)
His early papers (1, 5) are noteworthy for their resolution of the sort of paradox that
Thomas George Cowling
119
arises if individual particle trajectories are used naively to predict macroscopic plasma
behaviour. His 1945 paper (26) on electrical conductivity derived from a discrepancy
noted by Chapman between the results from the Boltzmann equation treatm ent and
those from the simpler mean-free-path method. In characteristic style he responded
to Chapm an’s request that he ‘tidy up the problem’.
In the 1940s and 1950s there was some confusion about the effect of a magnetic
field on the conductivity of a plasma. The Galilean invariant form of Ohm’s law for a
simple moving conductor is j/cr = E, where E = E + v x B i s the electric field in a
frame moving with the local velocity v and cr is the usual conductivity. A simple kinetic
treatm ent of a fully ionized gas introduces into ‘Ohm’s law’ the Biermann battery term
Eb and also the Hall term - jx B
/n^e,which dominates over the oh
electrons ‘spiral freely about the magnetic field between collisions with the ions’. This
micro-anisotropy shows up if one solves the generalized Ohm’s law for j in terms of
the ‘effective electric field’ E' = E + Eb, and in (26) and (38), as in his earlier paper
(6), Cowling introduced differing conductivities for the directions respectively parallel
to B, E' xB and B x (E' xB). In parallel studies, Biermann and Arnulf Schliiter preferred
to eliminate the Hall term via the Lorentz force term jx B in the bulk equation of
motion of the plasma, so arriving back at the form j/cr = E " for Ohm’s law, but with
the new effective electric field E " that does not contain j and so apparently does not
imply an anisotropic conductivity. Cowling (38) responded that as the same equations
are being used, they must predict the same results: for a given component of j, the
unreduced conductivity o must imply the component of E " to be correspondingly
smaller. Though this is certainly true, it is not clear that the tensor conductivity
formulation is particularly helpful for the solution of specific problems. However, the
really important point - emphasized in particular by Schliiter - is that a reduced
trans-field conductivity does not imply an increased dissipation of magnetic energy:
with A m pere’s law fixing j by VB, the dissipation rate per unit volume is j 2/cr where o
is again the ordinary ‘unreduced’ conductivity. In the mean-free-path approximation
the magnetic field has no effect on the dissipation rate, while in the kinetic treatment
the modifications to the velocity distribution function cause a modest change in Ho by
up to a factor 2 (Spitzer 1956).
Things are very different in a lightly ionized gas, which can often be pictured as a
fully ionized component of electrons and ions (the ‘plasma’) nearly frozen into the
magnetic field, but forced to drift with respect to the neutral bulk at a rate fixed by
the balance of Lorentz force against ion-neutral friction. One can write the associated
dissipation of m agnetic energy as j 2/cr*, w here j x is the current com ponent
perpendicular to B, and Ho* oc B2 can be much larger than the ohmic resistivity due
to ion-electron collisions. This result appeared more or less simultaneously in
Cowling’s 1956 paper (44), in a paper by J.H. Piddington, and for the particular context
of star formation in a paper by Spitzer and myself. The possibility of this plasma drift
was foreshadowed in an earlier paper by Schliiter, who gave it the name ‘ambipolar
diffusion’. However, it does not seem to have been taken very seriously until
publication of the above papers and the discussions at the 1956 Stockholm IAU
120
Biographical Memoirs
Symposium 6 on ‘Electromagnetic phenomena in cosmical physics’. (For example, in
the 1953 Cambridge Symposium on ‘Gas dynamics of cosmic clouds’ there is no
reference to it even when lightly ionized gases are discussed.) Slightly adapting
Cowling’s words in (44), in the cases considered earlier the ion current due to
ambipolar diffusion (with its accompanying cancelling electron current) was supposed
not to flow, so that the enormously increased (B-dependent) dissipation was not found.
However, in the cases of interest in astronomy there is nothing to prevent the
ambipolar diffusion current from flowing, and today the process is universally accepted
as crucially important in galactic molecular clouds. A general discussion for all degrees
of ionization is given in (44) and reproduced in the Magnetohydrodynamics tract.
Neither the formal Enskog-Chapman development nor the simpler two and three
fluid models of fully and partially ionized gases are strictly applicable at very low
densities. The last sections both of Chapman & Cowling (1970) and of the second
edition of
Magnetohydrodynamics(1967) contain brief discussions of such ‘collisionless
plasmas’. Cowling wrote to me that he was less satisfied with the second edition than
with the original tract, because it ‘left a lot unsaid’; I presume that he felt he lacked
the physical strength necessary to attempt the writing of an essentially new book.
Cowling’s publications include several that do not fall into the above three
categories, for example, on boundary layers, waveguides and non-cosmical MHD. The
series concerned with the temperature of the atmosphere as affected by infrared
absorption and by eddy diffusivity (17, 23, 24, 33, 34) were clearly appreciated by the
meteorological community, including its doyen Sir David Brunt. His three historical
lectures on astrology (74, 75, 77) make interesting reading. His approach is to show
how astrology developed in the ancient world into a reasonable putative science tied
to a picture of the cosmos with regular motions, and indeed had some important
astronomical spin-off, but that Hipparchus’s discovery of the precession of the
equinoxes had already laid a time-bomb. Copernicus and Kepler destroyed the
cosmogonic frame of the early astrologers, even though Kepler (like Tycho Brahe)
believed in astrology and indeed derived part of his livelihood from casting horoscopes.
It remained for the discovery of stellar proper motions and the measurement of stellar
parallaxes to remove any remaining rational basis.
Per so n a l
r e m in is c e n c e s
Everyone knew Tom by sight; his red hair and his great height made him
conspicuous. (I recall during the 1952 IAU General Assembly in Rome his being
identified as ‘II signor alti-i-i-i-ssimo!’.) Most of us looked up to him also metaphorically
because of his justified reputation for kindliness combined with high critical standards,
which he applied as strictly to his own work as to that of others. If after discussion of
some work one succeeded in getting at least a ‘Nihil obstat’ from him, then it was
unlikely that any official referee would refuse the ‘Imprimatur’. His generosity to
younger workers is attested by several who have since acquired international
reputations, including Nigel Weiss and Eric Priest (one of Tom’s rather small number
Thomas George Cowling
121
of Ph.D. students).
As he himself admits (78), he sometimes overworked his critical faculties. He quotes
with approval Fred Hoyle’s rule that ‘when confronted by an attractive but possibly
dubious argument, he tries to pick out what part of it is satisfactory’, adding ‘I myself
have been too prone to see ideas as absolutely black or white, thereby justifying Milne’s
advice to me not to confuse scientific error with moral defects’. Although his
interventions at meetings were usually helpful, there were occasions in which he could
sound like a caricature of himself. H e certainly recognized that there is room and
indeed need for a variety of styles in the scientific endeavour, and that the same person
could advance the frontiers sometimes by a rigorous piece of mathematical analysis,
other times by throwing tentative ideas into the arena; but his instinct was to damp
down what he thought of as over-exuberant speculation. (On one occasion I countered
this only by unscrupulously quoting from Pilgrim's Progress: ‘Now Giant Despair had
a wife and her name was Diffidence.’) My feeling is that had he been prepared to relax
his standards a little, especially in his later years, his influence would have been still
greater. However, he would probably then have felt untrue to himself.
Tom’s dedication to science in no way lessened his concern with the problems of
our century, especially during the traumatic years before and during World War II.
He certainly could not be a pacifist in a war against the Nazis. For a time he was
involved by invitation in some defence-oriented mathematical work, but later to his
puzzlement he found his services no longer in demand. He learned after the War that
he was regarded as one who ‘could not be entrusted with state secrets because of
unreliable associates’. His pen-friendship with Biermann in Germany persisted up to
the outbreak of war, his last ‘carefully worded letter’ concluding: ‘With all good wishes,
whatever may transpire during the next few days.’ However, he did not think this
association was the reason for the security wall, but surmised rather that it arose
because of his friendship at M anchester with the Hungarian cosmic ray physicist L.
Janossy who was a known Communist, and with the minister of his church who was a
keen pacifist. At the risk of being wise after the event, one does wonder at the
ineptitude of the security services. The upshot was that Tom spent the war years
teaching applied mathematics at M anchester and doing service as an air-raid warden.
Tom remained an active member of the Baptist Church throughout his life. He
taught in Sunday school at Manchester, Bangor and Leeds, became a Life Deacon at
Leeds and served on the committee of Rawdon Baptist College for several years until
its amalgamation with M anchester College to form the Northern Baptist College. He
also spent much time as a scout leader.
His approach to theological and biblical studies was with the same scholarly
commitment as in his scientific work. Combined with his strict intellectual honesty, this
ensured that his religious beliefs were non-fundamentalist. Nevertheless, in my
contacts with him up to his retirement, I wondered whether he still lived with some of
that compartmentalism that persists in many scientists with a traditional religious
upbringing. If so, the walls had broken down by the beginning of his last decade, when
during a bout of illness he started a correspondence which carried on for a few years.
122
Biographical Memoirs
In his own words:
For years I have been oppressed by the comparison between the size of and power of the
Universe and man’s littleness, but did not think too much about the problem, perhaps hoping it
would go away or solve itself. At the start of the illness I had a dream (vision, nightmare) in which
I met the problem with literally blinding clarity. The form of the dream was probably due to a
high temperature; its subject was significant in uncovering to me what I had in the back of my
mind. I had a lot of time to think about this in the next few weeks, when I barely slept. The
problem was one of reconciling my traditional belief in the goodness and loving-kindness of God
with the existence of a universe in which humanity is an almost irrelevant detail.
My lengthy responses were not much help to him, except insofar that he recognized
- from his own experience - symptoms of the need to get things off one’s chest. In
wrestling with these problems he was following in the footsteps of Jeans, Eddington
and Milne. I think they would have agreed with his conclusion that the will to believe
takes over: ‘Ultimately one’s decision about one’s religion is a matter of commitment
rather than pure reason; one has to make a conscious personal decision.’ He described
himself as ‘getting closer to mysticism rather than to a religion of set creeds’.
Tom’s neighbour Dr B.S.J. Isserlin of the Leeds Department of Semitic Studies
writes:
Among the residents in Leeds-Headingley, Professor Cowling was a notable and pleasant figure.
One encountered him, usually briefly, on his walk to and from home; walking along purposefully,
if more slowly in his last years, but always willing to stop and to be engaged in a brief conversation
or to answer a question, always agreeable and never giving any indication this might not be
convenient. His powerful intellect and wide erudition were obvious, but never a barrier. Talk
ranged widely: occasionally it was on Biblical and related subjects which, in different ways,
interested us both. Here his erudition was on occasion almost frightening. I remember once
meeting him in the University Senior Common Room. We came to talk about the Book of Job:
he was fully apprised of the subject. Yet this was not one that concerned him professionally, and
one was left with the feeling ‘If he knows so much about a field that is not his professionally, what
will he not know about those subjects that are in his own academic field!’. Occasionally one might
ask for his advice: it was worth having. I remember his looking at something I had written: he
found it too abstract for the public in view. He will be much missed: intellectual power combined
with humanity are not so often met combined as one might wish, and one has to be all the more
grateful for having had the chance of benefiting from the combination, which he made available
to so many.
In Roger Tayler’s words, with his death the Royal Astronomical Society has lost one
of its most distinguished and well-loved Fellows, as has the Royal Society. I certainly
count myself fortunate on both scientific and personal grounds to have begun my
research career first as a student of Fred Hoyle’s, followed by a period as research
fellow with Tom Cowling, whom I shall always think of as representing the best in the
British Puritan tradition.
Acknow ledgem ents
Doris Cowling and Margaret Morrison (nee Cowling) read the draft and checked it for accuracy.
I had helpful comments on the scientific questions and some personal glimpses from my Sussex
colleagues Sir William McCrea, Robert Smith and Roger Tayler and from Sir Hermann Bondi, Allin
Goldsworthy, Douglas Gough, Peter Gray, Sir Fred Hoyle, Ben Isserlin, Eric Priest, Lyman Spitzer
Thomas George Cowling
123
Jr, Peter Sweet and Nigel Weiss. Louise Mestel did the genealogical research quoted.
The portrait photograph was taken by Walter Bird.
B ib l io g r a p h y
(1)
1929
(2)
1930
1931
(3)
(4)
(5)
1932
(6)
(7)
(8)
(9)
1933
1934
1935
(10)
(11)
(12)
1936
(13)
(14)
1938
( 15)
1939
(16)
1940
( 17)
1941
(18)
(19)
(20)
1942
(21)
(22)
(23)
(24)
(25)
1943
(26)
1945
(27)
(28)
1946
(29)
On the radial limitation of the Sun’s magnetic field. Mon. Not. R. astr. Soc. 90,
140-154.
On a point-source model of a star. Mon. Not. R. astr. Soc. 91, 92-108.
Note on the fitting of polytropic models in the theory of stellar structure . Mon.
Not. R. astr. Soc. 91, 472-478.
The radii of stellar models. Z. Astrophysik 4, 331-338.
Diamagnetism and drift currents in the solar atmosphere. Mon. Not. R. astr. Soc.
92, 407-413.
The electrical conductivity of an ionised gas in the presence of a magnetic field.
Mon. Not. R. astr. Soc. 93, 90-98.
The magnetic field of sunspots. Mon. Not. R. astr. Soc. 94, 41-48.
The stability of gaseous stars. Mon. Not. R. astr. Soc. 94, 768-782.
The structure of sunspots. Mon. Not. R. astr. Soc. 96,15-20.
The stability of gaseous stars (second paper). Mon. Not. R. astr. Soc. 96, 42-60.
Convection in stars. Observatory 58, 243-247.
Remarks on L. Biermann’s paper ‘Konvection im Innern der Sterne’.
Nachr.
258,133-134.
The stability of convective stars. Mon. Not. R. astr. Soc. 98, 528-535.
On the motion of the apsidal line in close binary systems. Mon Not. R. astr. Soc.
98, 734-744.
(With L. BlERMANN) Chemische Zusammensetzung und dynamische Stabilitat
der Sterne. Z. Astrophysik 19,1-9.
On certain expansions involving products of Legendre functions. Q. JIMath. 11,
222-224.
(With A. WHITE) The eddy diffusivity and the temperature of the lower layers of
the atmosphere. Q. Jl R. met. Soc. 67, 276-286.
The non-radial oscillations of polytropic stars. Mon. Not. R. astr. Soc. 101, 367-373.
(With S. CHAPMAN) The velocity of diffusion in a mixed gas; the second
approximation. Proc. R. Soc. Lond. A 179,159-169.
The influence of diffusion on the propagation of shock waves. Phil. Mag. 33,
61-67.
The theory of stellar structure, 1932-42. Observatory 64, 224-228.
On Alfven’s theory of magnetic storms and of the aurora. Terr. Magn. atmos.
Elect. 209-214.
The absorption of infra-red radiation in the atmosphere. Q. Jl R. met. Soc. 68,
197-200.
The absorption of water vapour in the far infra-red. Rep. Prog. Phys. 9, 29-41.
Hitherto unidentified absorption bands of water vapour. Nature, Lond. 152,
694-695.
The electrical conductivity of an ionized gas in a magnetic field, with applications
to the solar atmosphere and the ionosphere. Proc. R. Soc. Lond. A 182, 453-479.
On the Sun’s general magnetic field. Mon. Not. R. astr. Soc. 105,166-174.
The growth and decay of the sunspot magnetic field. Mon. Not. R. astr. Soc. 106,
218-224.
(With J.T. A l l a n s o n & R. COOPER) The theory and experimental behaviour of
right-angled junctions in rectangular section wave guides. / Inst. elec. Engrs 93,
Biographical Memoirs
124
(30)
(31)
(32)
(33)
(34)
(35)
1951
(36)
(37)
1952
(38)
1953
1948
1949
1950
(39)
(40)
(41)
(42)
1955
(43)
(44)
1956
(45)
1957
(46)
(47)
(48)
(49)
(50)
1958
1960
(51)
(52)
1961
(53)
(54)
1962
1963
(55)
(56)
(57)
(58)
1964
1965
(59)
(60)
(61)
(62)
1966
1967
1968
177-187.
Alfven’s theory of sunspots. Mon. Not. R. astr. Soc. 106, 442-456.
Electrical conductivity of the ionospheric D-layer. Nature, Lond. 161, 515-516.
(With R.A. NEWING) The oscillations of a rotating star.
J. 109,149-158.
Atmospheric absorption of heat radiation by water vapour.
Mag. 41,109-123.
The calculation of radiative temperature changes. Cent. Proc. R. met. Soc. 19-25.
A new method of numerical integration of the equations of the laminar boundary
layer. A.R.C.Reports and Memoranda no. 2575.
The condition for turbulence in rotating stars.
J. 114, 272-286.
The oscillation theory of magnetic variable stars. Mon. Not. R. astr. Soc. 112,
527-539.
Solar electrodynamics. In The Sun (ed. G.P. Kuiper), chapter 8. University of
Chicago Press.
(With H.W. BABCOCK) General magnetic fields in the Sun and stars. Mon. Not.
R. astr. Soc. 113, 357-381.
Le champ magnetique de la Galaxie. Ciel et Terre.
Nuclear processes and stellar structure; general survey. Mem. Soc. R.
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