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Author name code: milne
ADS astronomy entries on 2022-09-14
author:"Milne, Edward Arthur"
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Title: Sir James Jeans
Authors: Milne, E. A.
2013sjj..book.....M Altcode:
Memoir by S. C. Roberts; 1. Merchant Taylor's and Cambridge;
2. Princeton, 1905-9; 3. Return to England. The Adams Prize essay,
1909-19; 4. Secretary of the Royal Society, 1919-29; 5. Popular
exposition, 1929-30; 6. Later years, 1931-46; 7. Science in Jeans's
boyhood; 8. The partition of energy; 9. Rotating fluid masses; 10. Star
clusters; 11. The equilibrium of the stars; 12. Jeans and philosophy;
Bibliography; Index.
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Title: Newtonian Universes and the Curvature of Space
Authors: McCrea, W. H.; Milne, E. A.
2000GReGr..32.1949M Altcode:
No abstract at ADS
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Title: A Newtonian Expanding Universe
Authors: Milne, E. A.
2000GReGr..32.1939M Altcode:
No abstract at ADS
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Title: The Maxima of Absorption Lines in Stellar Spectra
Authors: Fowler, R. H.; Milne, E. A.
1994JApA...15..241F Altcode:
No abstract at ADS
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Title: Image resolution through atmospheric turbulence.
Authors: Crittenden, E. C., Jr.; Cooper, A. W.; Milne, E. A.; Rodeback,
G. W.; Kalmbach, S. H.; Armstead, R. L.
1978SPIE..134...34C Altcode: 1978peor.conf...34C
The effects of atmospheric turbulence on imaging systems, and beam
projection systems such as laser designators, can be evaluated and
the performance predicted in terms of a properly path-weighted value
of the turbulence structure constant, Cn2. An operating system for
direct field determination of this weighted value with a portable slit
scanning telescope and on-line data reduction minicomputer system will
be described. This system utilizes a point laser source located in
the vicinity of the target and scans the image of that source from the
opposite end of the optical path. The on-line computer system combines
data, for the system on test, with the data taken on the atmosphere
at the instant of test firing, utilizing Fourier and Abel transform
techniques, to provide a prediction of behavior of the system on test,
or an evaluation of the effects of the atmosphere on that test. The
results can be presented in a variety of forms, including immediate
hard copy plots of the MTF of the atmosphere, of the overall system
being tested, or plots of predicted radial distribution of intensity on
target for the system on test. The slit scanning telescope can track a
slowly moving target, with internal optical tracking. A gyro platform
is under development which can provide operation from shipboard or
other unstable platform.
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Title: Effects of turbulence on imaging through the atmosphere.
Authors: Crittenden, E. C., Jr.; Cooper, A. W.; Milne, E. A.; Rodeback,
G. W.; Kalmbach, S. H.; Armstead, R. L.
1978opat.conf..130C Altcode:
No abstract at ADS
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Title: Image resolution /OTF/ through atmospheric turbulence over
the ocean
Authors: Crittenden, E. C., Jr.; Copper, A. W.; Milne, E. A.; Rodeback,
G. W.; Kalmbach, S. H.; Armstead, R. L.
1977SPIE..124...19C Altcode:
The optical transfer function (OTF) of the atmosphere has been measured
over the ocean for four wavelengths from visible to far-IR, using laser
sources and a slit scanning telescope. The effects of diffraction,
finite slit width, and aberrations have been removed by digital
Fourier processing. The shapes of the curves of long-term average
OTF and the image-centered (tracked) OTF, as well as the magnitude of
the wander variance, all agree well with a theoretical model by Fried
(1966). Comparisons of the path-integrated values of the square of the
turbulence structure constant for index of refraction (Cn-squared)
obtained from the OTF with the path-integrated values of Cn-squared
obtained from the square of thermal fluctuations indicate that for
nonuniform Cn-squared the weighting of Cn-squared as a function of
position on the path behaves as predicted. This weighting heavily
emphasizes the part of the path nearest the telescope for imaging
devices, whereas scintillation emphasizes the path center. The
weighting that applies to imaging devices also applies to beam-forming
or projection systems, with the heavily emphasized part near the
projection optics. Measurement with a scanning telescope thus yields
directly the properly weighted value for such systems.
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Title: Selected papers on the transfer of radiation
Authors: Menzel, Donald Howard; Milne, Edward Arthur
1966sptr.book.....M Altcode: 1966QB817.M4.......
No abstract at ADS
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Title: Modern cosmology and the Christian idea of God.
Authors: Milne, Edward Arthur
1952mcci.book.....M Altcode: 1952QB981.M77......
No abstract at ADS
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Title: Gravitation and magnetism
Authors: Milne, E. A.
1950MNRAS.110..266M Altcode:
t is shown by the methods of kinematic relativity that there should be
a onnection between gravitation and magnetism of the type suggested by
the empirical formulae of Blackett and Wilson, multiplied however by
certain dimensionless ratios. The field of a rotating system cannot
be represented by a dipole. The derivation only applies rigorously
to a rotating system like a galaxy, with its centre at a fundamental
particle. The results obtained suggest that for a given mean density
and given angular momentum, a highly flattened system should have an
effective magnetic moment greater than a less flattened system.
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Title: The vertex of star-streaming
Authors: Milne, E. A.
1949Obs....69..107M Altcode:
No abstract at ADS
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Title: The Luminosity-Velocity Relation for Pulsating Stars
Authors: Milne, E. A.
1949MNRAS.109..517M Altcode:
No abstract at ADS
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Title: II. -Motion in an extended distribution of Matter
Authors: Milne, E. A.
1948MNRAS.108..316M Altcode:
No abstract at ADS
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Title: Star-streaming and the Stability of Spiral Orbits in Spiral
Nebulae. I. -Motion round a point-nucleus
Authors: Milne, E. A.
1948MNRAS.108..309M Altcode:
No abstract at ADS
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Title: Kinematic relativity; a sequel to Relativity, gravitation
and world structure.
Authors: Milne, Edward Arthur
1948krsr.book.....M Altcode: 1948QB500.M49......
No abstract at ADS
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Title: La Cinquantenaire de l'Observatoire Yerkes
Authors: Ledoux, P.; Milne, E. A.; Minnaert, M.
1948LAstr..62...46L Altcode:
No abstract at ADS
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Title: The Equation to the Arm of a Spiral Nebula.
Authors: Milne, E. A.
1947ApJ...106..137M Altcode:
The equation which should represent the arm of a spiral nebula on the
basis of kinematical relativity, on a certain hypothesis, is deduced
by a simple method and is shown to depend on the epoch 1, reckoned
from the natural zero of time. Its relation to various forms of the
equation to the orbits of the indi- vidual members of the nebula is
obtained. It is shown to represent to a close approximation the most
general form of spiral arm to be expected
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Title: On the spiral character of the external galaxies
Authors: Milne, E. A.
1946MNRAS.106..180M Altcode:
No abstract at ADS
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Title: Kinematical Relativity
Authors: Milne, E. A.
1945Natur.156..747M Altcode:
MY attention has been directed to Prof. H. Dingle's recent letter in
Nature<SUP>1</SUP>. His supposed refutation of kinematical relativity
is on a par with Dr. Samuel Johnson's refutation of metaphysics; my
failure to reply to him directly is due to my reluctance to engage
in such trivialities. I have already given him all the answer he
needs by referring him to my mathematical papers, where the case
of the collision of equivalent particle-observers is fully dealt
with. You cannot wantonly re-graduate any casual clock and expect to
secure a consistent physics. Kinematical relativity does not do so. In
kinematical relativity it is shown that for consistent time-keeping to
be possible, the various particle-observers whose temporal experiences
constitute clocks must be members of equivalences. Regraduation
is applied only to such equivalences; and it was shown by Whitrow
and myself<SUP>2</SUP> that if two members of an equivalence ever
coincide, then all members coincide at the same event. This technical
point is well known to all who have studied time-keeping in relation to
equivalences; it is fundamental, for example, in some recent unpublished
work by A. G. Walker. In its application, it means that in a contracting
universe of time-keepers, there would be a singularity which would be
the counterpart of `creation' in an expanding universe. Prof. Dingle
is concerned with the timing of `subsequent events' there would be no
subsequent events-Prof. Dingle would not survive the catastrophe-just
as in an expanding universe there are no events anterior to
`creation'. There are other objections to a contracting universe,
but the `absurdity' which preoccupies Prof. Dingle is a monster of
his own construction which simply adds point to the absurdity of a
contracting universe. As the universe is observed to be expanding,
Prof. Dingle's difficulties never arise.
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Title: Kinematical Relativity and the Nebular Red-Shift
Authors: Milne, E. A.
1945Natur.155..511M Altcode:
PROF. DINGLE makes Prof. Haldane's contribution to kinematical
relativity the occasion for what he thinks is an attack on its
foundations. He is very simply answered: the red-shifts in the spectra
of the galaxies are described in kinematic relativity as a Doppler
effect due to recession. The consequences of this in relation to the
ageing of light and Prof. Haldane's work have been discussed by me in
a letter to Nature written before I saw Prof. Dingle's letter.
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Title: The Ageing of Light
Authors: Milne, E. A.
1945Natur.155..234M Altcode:
RED-SHIFTS in the spectra of the galaxies are usually interpreted as
Doppler effects consequent on recession. Alternatively, they have been
interpreted as an `ageing' of light with time, by which the wavelength
of a photon steadily increases. That the two interpretations are
substantially equivalent can be seen from the following strikingly
simple calculation. I adopt the kinematic model of the expanding
universe.
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Title: (Presidential Address) ,on presenting the Gold Medal to
Professor Bengt Edlén
Authors: Milne, E. A.
1945MNRAS.105..138M Altcode:
No abstract at ADS
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Title: The natural philosophy of stellar structure (Presidential
Address, 1945)
Authors: Milne, E. A.
1945MNRAS.105..146M Altcode:
No abstract at ADS
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Title: Obituary: Ralph Howard Fowler
Authors: Milne, E. A.
1944Obs....65..245M Altcode:
No abstract at ADS
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Title: Prof. H. F. Newall, F.R.S.
Authors: Milne, E. A.
1944Natur.153..455M Altcode:
No abstract at ADS
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Title: On the nature of universal gravitation (Presidential Address,
1944)
Authors: Milne, E. A.
1944MNRAS.104..120M Altcode:
No abstract at ADS
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Title: On “Absolute Acceleration”
Authors: Milne, E. A.
1942Natur.150..489M Altcode:
IT is of interest to consider, in this the year of Newton's
tercentenary, the present position of acceleration in Newtonian
mechanics. The Newtonian equations of motion of a particle in free
space are unaltered in form, as is well known, on transformation to
any other frame in uniform relative motion, but this is not true for
transformations to relatively accelerated frames. Hence the notion
of “inertial frames”-frames for which the Newtonian dynamics holds
good-frames for the existence of which, according to Einstein and Infeld
in their book, “The Evolution of Physics”, physics has been unable
to account. The existence of inertial frames appears to indicate that
any particle in the universe possesses an absolute acceleration.
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Title: Cosmological Theories.
Authors: Milne, E. A.
1940ApJ....91..129M Altcode:
The present report is mainly concerned with a careful analysis of the
fundamental ideas, methods, and postulates which underlie current
approaches to the cosmological problem. In particular, the methods
of general relativity and the author's kinematical relativity are
contrasted. In the later method all the fundamental notions ("uniform
time," "rigid length scale") are carefully scrutinized and emphasis
is laid on the methods by which two arbitrary observers can set up
"congruent" clocks and distance measures by dispatching and receiving
light-signals. A linear equivalence, defined as a class of observers
possessing congruent clocks, is then analyzed. This leads to the
considera- tion of the two scales of time, t and `r = t0 log t/t0 + t0,
such that a uniform motion equivalence in the scale of I becomes one
at relative rest in the scale of r. The physical significance of the
two scales of time are then further discussed. The methods by which
the dynamical equations of motion are to be set up by projecting a
"free" test particle in the presence of a density distribution and
specified equivalence are then considered. The fundamental problem
here is the determination of the motion of a free particle for an
equivalence satisfying the cosmological principle, i.e., the case when
the equivalence is such that the statistical description of the whole
equivalence from any one member of the equivalence coincides with that
from any other member. The solu- tion of the cosmological problem which
the consideration of this problem leads to is then discussed; particular
attention is here given to the degree of arbitrariness which is left at
each stage of the solution of the problem and how the arbitrariness is
then later removed. The kinematic arguments are shown to lead to (i) the
law of inertia for a substratum (i.e., a density distribution satisfying
the cosmological principle), (2) the existence of "gravitational" mass,
and (~) the inverse-square character of "gravita- tional force." Further
problems which can be treated by the methods outlined in this paper
are also indicated. The importance of the two time scales, that of
I and that of `r, in answering questions about the universe (e.g.,
whether the universe is expanding or is nonexpanding) is pointed out
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Title: Physical Sciences: Reversibility of the Equations of Classical
Dynamics
Authors: Milne, E. A.; Whitrow, G. J.
1938Natur.141..905M Altcode:
IN a recent series of papers, one of us has derived the equation
of motion<SUP>1</SUP> of a free particle in the presence of the
expanding universe by a priori methods, and constructed an associated
dynamics. The observers' clocks were supposed so graduated<SUP>2</SUP>
that the expansion appeared uniform, and the resulting scale of
time was called the t-scale. But the equations of motion reduced
to their classical form<SUP>3</SUP> only if observers' clocks were
regraduated from t to τ where and all derived measures correspondingly
changed. Accordingly, the `uniform time' of mechanics was identified as
τ-time. In this measure of time, the universe appears as a stationary,
non-expanding system, and the red-shift is shown<SUP>4</SUP>
to be attributable to an acceleration of atomic absorption- or
emissionfrequency with time in τ-measure, so that the light, emitted
long ago by a distant nebula, appears relatively displaced to the
red. In a joint paper about to appear in Zeitschrift für Astrophysik,
we have analysed generally all monotonic graduations of our temporal
experience, that is, all possible modes of clock-graduation, and
shown that of these there is just one, τ-measure, which reduces the
members of any `linear equivalence' to relative rest. This again we
have identified as the time of mechanics.
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Title: On a linear equivalence discussed by L. PAGE. Mit 1 Abbildung.
Authors: Milne, E. A.; Whitrow, G. J.
1938ZA.....15..342M Altcode:
No abstract at ADS
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Title: On the meaning of uniform time, and the kinematic equivalence
of the extra-galactic nebulae. Mit 3 Abbildungen.
Authors: Milne, E. A.; Whitrow, G. J.
1938ZA.....15..263M Altcode:
No abstract at ADS
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Title: Stellar luminosity and the opacity in the outer layers of
a star
Authors: Milne, E. A.
1937MNRAS..98...21M Altcode:
No abstract at ADS
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Title: Stellar luminosity and photospheric pressure
Authors: Milne, E. A.
1937MNRAS..97..513M Altcode:
No abstract at ADS
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Title: The Constant of Gravitation
Authors: Milne, E. A.
1937Natur.139..409M Altcode:
WITH regard to Prof. P. A. M. Dirac's recent letter to
NATURE<SUP>1</SUP>, I have shown, in various contexts<SUP>2</SUP>
that the relation between γ, the `constant' of gravitation, and t,
the epoch, is given by where M<SUB>0</SUB> is the apparent mass
of the fictitious homogeneous universe. (The actual mass must be
infinite.) With t = 2 × 10<SUP>9</SUP> years, this gave M<SUB>0</SUB>
= 2.4 × 10<SUP>55</SUP> grams = mass of 1.5 × 10<SUP>79</SUP>
protons. Two points of interest (amongst others) emerge from the
treatments I have given. First, (1) is a purely macroscopic formula,
having no connexion with atomicity. It is derived from purely
kinematic considerations, involving no appeal to any empirical
dynamical laws, still less to atomic laws. In papers already
communicated for publication, I have extended the application of (1)
to all local gravitational situations and derived the inverse square
law of gravitation in relativistic form in flat space, again without
recourse to empirical appeals, by kinematic methods.
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Title: Kinematics, Dynamics, and the Scale of Time
Authors: Milne, E. A.
1937RSPSA.158..324M Altcode:
No abstract at ADS
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Title: The Background of the Galaxies
Authors: Milne, E. A.
1936Natur.138...38M Altcode:
IN NATURE of May 30, M. Leontovski<SUP>1</SUP> shows that “To a
most sensitive eye, the background of the galaxies would appear as
a dark red.” Since the irresolvable background consists of nebulæ
receding with nearly the speed of light, the age of these nebulæ,
as observed, reckoned in our own time-scale, must be approximately
one half the present age of our own surroundings; that is, if t is
the conventional value of the age of the universe, ½t is the age of
the observed background<SUP>2</SUP>. Combining these results, we see
that the background realizes the poet's dream of “A rose-red city,
half as old as time.”<SUP>3</SUP>
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Title: Polytropic equilibrium. I. The radii of configurations under
given external pressure. II. The pressure in the photosphere of a
star. III. The luminosity of a star
Authors: Milne, E. A.
1936MNRAS..96..207M Altcode:
No abstract at ADS
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Title: Polytropic equilibrium. I. The radii of configurations under
given external pressure. II. The pressure in the photosphere of a
star. III. The luminosity of a star
Authors: Milne, E. A.
1936MNRAS..96..195M Altcode:
No abstract at ADS
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Title: The Pressure in the interior of a star
Authors: Milne, E. A.
1936MNRAS..96..179M Altcode:
No abstract at ADS
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Title: Polytropic equilibrium. I. The radii of configurations under
given external pressure. II. The pressure in the photosphere of a
star. III. The luminosity of a star
Authors: Milne, E. A.
1936MNRAS..96..184M Altcode:
No abstract at ADS
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Title: Stellar kinematics and the K-effect
Authors: Milne, E. A.
1935Obs....58..248M Altcode:
No abstract at ADS
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Title: Stellar kinematics and the K-effect
Authors: Milne, E. A.
1935MNRAS..95..560M Altcode:
No abstract at ADS
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Title: Reviews, reviewers and reviewed
Authors: Milne, E. A.
1935Obs....58..124M Altcode:
No abstract at ADS
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Title: Origin of the Cosmic Rays
Authors: Milne, E. A.
1935Natur.135..183M Altcode:
FROM the properties of the kinematic world-models which I have been
investigating during the past two and a half years, it can be shown that
any unimpeded free particle, at large in inter-galactic space, undergoes
acceleration as reckoned by an observer located on any arbitrary nebula,
and attains the speed of light at some finite epoch in the experience
of that observer. It then decelerates. It can also be shown that at
any arbitrary epoch, in any arbitrary domain of inter-galactic space,
there will occur some particles possessing velocities arbitrarily close
to that of light. If such a particle, of atomic dimensions, happens to
undergo a collision during this phase of its trajectory, it will give
rise to effects similar to those observed in cosmic ray experiments. I
therefore identify the primary agency responsible for cosmic rays with
highspeed particles accelerated to the vicinity of the speed of light
by the gravitational pull of the rest of the universe<SUP>1</SUP>. The
arguments required are purely kinematical, and involve no appeal to
any specific theory of gravitation, or any arbitrary hypotheses.
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Title: The configuration of stellar masses
Authors: Milne, E. A.
1935Obs....58...52M Altcode:
No abstract at ADS
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Title: Relativity, gravitation and world-structure
Authors: Milne, Edward Arthur
1935rgws.book.....M Altcode: 1935QB500.M5.......
No abstract at ADS
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Title: Radiative Equilibrium: The relation between the spectral
Energy Curve of a Star and the Law of Darkening of the Disc towards
the Limb, with Special Reference to the Effects of Scattering and
the Solar Spectrum
Authors: Milne, E. A.
1935MiPul..14A.202M Altcode:
No abstract at ADS
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Title: A method of analysing stellar variability
Authors: Milne, E. A.
1934MNRAS..94..418M Altcode:
No abstract at ADS
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Title: On the theory of the cosmical constant
Authors: Milne, E. A.
1934Obs....57...99M Altcode:
No abstract at ADS
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Title: World-models and the world-picture
Authors: Milne, E. A.
1934Obs....57...24M Altcode:
No abstract at ADS
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Title: A Newtonian expanding Universe
Authors: Milne, Edward Arthur
1934QJMat...5...64M Altcode:
No abstract at ADS
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Title: Newtonian Universes and the curvature of space
Authors: McCrea, William Hunter; Milne, Edward Arthur
1934QJMat...5...73M Altcode:
No abstract at ADS
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Title: World-relations and the "cosmical constant,"
Authors: Milne, E. A.
1933MNRAS..94....3M Altcode:
No abstract at ADS
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Title: Remarks on world-structure
Authors: Milne, E. A.
1933MNRAS..93..668M Altcode:
No abstract at ADS
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Title: Correction to the paper: “World-Structure etc. "
Authors: Milne, E. A.
1933ZA......6..244M Altcode:
No abstract at ADS
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Title: Note on H. P. Robertson's paper on World-Structure.
Authors: Milne, E. A.
1933ZA......7..180M Altcode:
No abstract at ADS
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Title: World-Structure and the Expansion of the Universe. Mit
6 Abbildungen.
Authors: Milne, E. A.
1933ZA......6....1M Altcode:
No abstract at ADS
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Title: The Expanding Universe
Authors: Milne, E. A.
1932Natur.130..508M Altcode:
IT is very satisfactory to find that the explanation I have given of
the phenomena of the expanding universe can be freed from some of
the restrictions which were introduced. The essential point in the
explanation, as I pointed out, is that we have to do with an unenclosed
system; if the system contains some high velocity particles, it will
necessarily expand. Mr. Kosambi points out that the expansion and
recession to infinity may also occur under more general conditions. But
Mr. Kosambi is scarcely correct in saying that in my explanation “the
material particles that form the universe are taken initially to have
been enclosed in some finite space”. I used the finite occupied sphere
surrounded by infinite empty space as the most striking illustration
of the principle (it was the way the explanation originally occurred to
me), but as I explicitly pointed out, any `initial' density distribution
with a concentration towards one region will give rise to the expansion
phenomenon; and for the particular relativistic world-structure which
I outlined the initial density-distribution extends throughout infinite
Euclidean space.
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Title: World Structure and the Expansion of the Universe
Authors: Milne, E. A.
1932Natur.130....9M Altcode:
No abstract at ADS
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Title: The analysis of stellar structure, II
Authors: Milne, E. A.
1932MNRAS..92..610M Altcode:
No abstract at ADS
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Title: The white dwarf stars; being the Halley lecture, delivered
on 19 May 1932
Authors: Milne, Edward Arthur
1932wdsb.book.....M Altcode: 1932QB903.M5.......
No abstract at ADS
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Title: Note on the boundary Temperature of a Star.
Authors: Milne, E. A.
1932ZA......5..328M Altcode:
No abstract at ADS
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Title: Ionization in stellar atmospheres, Part III
Authors: Milne, E. A.; Chandrasekhar, S.
1932MNRAS..92..150M Altcode:
No abstract at ADS
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Title: The Theory of Stellar Structure II (Energy-generation).
Authors: Milne, E. A.
1932ZA......5..337M Altcode:
No abstract at ADS
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Title: The Theory of Stellar Structure.
Authors: Milne, E. A.
1932ZA......4...75M Altcode:
No abstract at ADS
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Title: The Internal Temperature of White Dwarf Stars.
Authors: Milne, E. A.
1931Natur.128..999M Altcode:
IT has recently been discovered by S. Chandrasekhar,<SUP>1</SUP>
B. Swirles,<SUP>2</SUP> and R. C. Majumdar,<SUP>3</SUP> independently,
that the opacity of a degenerate gas is very small compared with
what would be computed for a classical gas at the same density
and temperature, the ratio being an inverse power of Sommerfeld's
degeneracy-criterion parameter. This discovery seriously affects
estimates of the internal temperatures in white dwarf stars. It has
previously been held that interiors of the white dwarf stars are
amongst the hottest of stellar interiors; for example, Russell and
Atkinson<SUP>4</SUP> remark that their internal temperatures must be
of the order of 50 times those of a main sequence star built on the
`diffuse' model. Again, Jeans<SUP>5</SUP> says “it appears that the
central temperatures of the white dwarfs must be enormously high, while
those of giant stars of large radius must be comparatively low”. This
has given rise to the paradox that the coolest stellar interiors
appeared to be the best generators of stellar energy, the hottest the
worst. To quote Jeans<SUP>6</SUP> again, “...many of the hottest and
densest stars are entirely put to shame in the matter of radiation by
very cool stars of low density, such as Antares and Betelgeuse”.
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Title: Contributions to a British Association Discussion on the
Evolution of the Universe.
Authors: Milne, E. A.
1931Natur.128..715M Altcode:
No abstract at ADS
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Title: The configuration of stellar masses
Authors: Milne, E. A.
1931Obs....54..243M Altcode:
No abstract at ADS
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Title: Emden's equation: Note on steady-state distributions which
are given by solutions of Emden's differential equation
Authors: Milne, E. A.
1931MNRAS..91..751M Altcode:
No abstract at ADS
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Title: Dense stars
Authors: Milne, E. A.
1931Obs....54..140M Altcode:
No abstract at ADS
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Title: Note on "equations of fit" in the theory of stellar structure
Authors: Milne, E. A.
1931MNRAS..91..479M Altcode:
No abstract at ADS
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Title: [Letters to the Editor]
Authors: Milne, E. A.
1931Natur.127..269M Altcode:
REFERRING to Sir James Jeans's letter in NATURE of Jan. 17, p. 89,
I may say that I fully acknowledged in my paper of November 1929
(Mon. Not. Roy. Ast. Soc., 90, p. 20) that Sir James was the first to
recognise the principle that the mass M and luminosity L of a star are
independent variables as regards steady state considerations. On p. 53
of that same paper (a page of which Jeans himself quotes in another
connexion) I made a general reference of obligation to his work. In my
last paper (Mon. Not. Roy. Ast. Soc., 91) I build on Jeans's permanent
contributions to science in three places, mentioning him by name (pp. 4,
9, 51). I could not, however, adduce any of the specific results of
his theory of stellar equilibrium in support of my conclusions, for
they are totally different; and I could not contrast his results with
mine without venturing to discuss his mathematics.
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Title: Über die Frage der Opazität der Sternmaterie. (Eingegangen
am 18. Juli 1931)
Authors: Milne, E. A.
1931ZA......3..253M Altcode:
No abstract at ADS
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Title: Stellar Structure and the Origin of Stellar Energy.
Authors: Milne, E. A.
1931Natur.127...16M Altcode:
PERHAPS the most striking general characteristic of the stars is that
they can be divided into two groups of widely differing densities. In
the first group, which comprises the majority of the known stars,
the densities are of ?terrestrial? order of magnitude? that is to say,
their mean densities are of the order of the known densities of gases,
liquids, and solids. They range from one-millionth of that of water to
ten or, in rare cases, perhaps fifty times that of water. In the second
group the densities are of the order of 100,000 times that of water. Of
the second group, the 'white dwarfs?? only a few examples are known,
but they are all near-by stars, and it is generally agreed that they
must be of very frequent occurrence in Nature, though difficult of
discovery owing to their faintness. Whether stars exist of intermediate
density remains for future observation. The possibility of the existence
of matter in this dense state offers no difficulty. As pointed out by
Eddington, we simply have to suppose the atoms ionised down to free
electrons and bare nuclei. At these high densities the matter will
form a degenerate gas, as first pointed out by R. H. Fowler. But this
leaves entirely unsolved the question of why, under stellar conditions,
matter sometimes takes up the 'normal? density and sometimes the
high density. Owing to the probable great frequency of occurrence of
dense stars, it might reasonably be asked of any theory of stellar
constitution that it should account for dense stars in an unforced
way. There are two main theories of stellar structure at the present
moment. That of Sir James Jeans accounts for the existence of giants,
dwarfs, and white dwarfs, but only at the cost of ad hoc hypotheses
quite outside physics. It assumes stars to contain atoms of atomic
weight higher than that observed on earth, and it assumes them to be
relentlessly disappearing in the form of radiation ? it appeals to
discontinuous changes of state consequent on successive ionisations,
for which there is little warrant. I think it is true to say that
the majority of astronomers do not accept this theory. The theory
of Sir Arthur Eddington does not claim to account for the observed
division of stars into dense stars and stars of ordinary density? nor
does it establish the division of ordinary stars into giants and
dwarfs. On the other hand, it claims to establish what is known as
the mass-luminosity law from considerations of equilibrium only,
that is, without introducing anything connected with the physics
of the generation of energy. It claims to show that the observed
fact that the brighter stars are the more massive can be deduced
from the conditions expressing that the star is in a steady state,
mechanically and thermally. It does this by making the hypothesis that
the stars (giants and ordinary dwarfs) consist of perfect gas. Closer
consideration of the actual formul used by the theory shows that it
scarcely bears out the claims made for it by its originator. The
'formula for the luminosity? of a star makes the luminosity very
nearly proportional to its effective temperature, and so the so-called
proof of the mass-luminosity law involves a semi-empirical element,
namely, an appeal to the observed effective temperatures of the stars,
for the observed values of which the theory fails to account. Another
difficulty encountered by the theory is that it makes the interiors of
the more luminous (giant) stars cooler than those of the fainter stars,
and it makes the interiors of both too cool for the temperature to
have any appreciable influence on the rate of generation of energy,
by stimu-lating, for example, the production of radioactive elements
or the conversion of matter to radiation. The claim to establish
the mass-luminosity law from mere equilibrium considerations cannot,
however, be sustained for a moment. We may regard a star in a steady
state as a system provided with an internal heating apparatus (the
source of energy). It adjusts itself?state of aggregation, density
distribution, temperature distribution?until the surface emission equals
the internal generation of energy L. But provided the luminosity L is
not too large (in order that the mass shall not burst under radiation
pressure), it is clear that a given mass M can adjust itself to suit
any arbitrary value of L. If, starting with one steady state, we then
alter L (upwards or downwards) by altering the rate of supply of energy,
the star will simply heat up or cool down until the surface emission
is equal to the new volume of L?precisely like an electric fire. L and
M are thus independent variables so far as steady-state considerations
are concerned. The fact that L and M show a degree of correlation in
Nature must be connected with facts of an altogether different order,
namely, with the physics of energy-generation. It is essential to
recognise the difference between the formal independence of L and M as
regards steady-state considerations and the observed correlation of
L with M in Nature. The observed mass-luminosity law must depend on
the circumstance that in some way the more massive star contrives to
provide itself with a stronger set of sources. The claim to establish
the mass-luminosity law from equilibrium considerations only appears to
me a philosophical blunder. Further, it is unphilosophical to assume
the interior of a gas to be a perfect gas ? either knowledge of the
interior is for ever unattainable or we should be able to infer it
from the observable outer layers. When we dispense with the perfect
gas hypothesis and at the same time recognise the independence of
L and M as regards steady-state considerations, it is found that a
rational analysis of stellar structure automatically accounts for the
existence of dense stars without special hypothesis. Further, it shows,
as common sense would lead us to expect, that the more luminous stars
must have the hotter interiors. Here the temperatures are found
to range up to 1010 degrees or higher, de pending on luminosity?a
temperature sufficient to stimulate the conversion of matter into
radiation. In addition, it shows that the central regions of stars
must be very dense, ranging up to 107 grams cm.-3 or higher. Thus the
difficulties met by earlier theories fall away as soon as the ground
is cleared philosophically. The foregoing ideas suggest the following
as the fundamental problems of stellar structure: (1) What are the
configurations of equilibrium of a prescribed mass M as its luminosity L
ranges from 0 upwards, M remaining constant ? (2) What is the effective
temperature T, associated with a given pair (M, L) in a steady state
? (3) What is the value of L which will actually occur for the physical
conditions disclosed by the answer to problem (1) ? We observe that
the outer parts of a star are gaseous. Consequently we can solve the
problem of the state of any actual star by integrating the equations
of equilibrium from the boundary inwards ? we are entitled to assume
the gas laws to go on holding until we find that the conditions are
incompatible with them. We then change to a new equation of state,
and carry on as before. We change our equation of state as often
as may be necessary until we arrive at the centre. The answer to
the first of the problems formulated above has been worked out, for
certain types of source-distribution and opacity, by the method of
inward integration. The results are sufficiently alike to be taken
as affording insight into the nature of stellar structure in general,
and are as follows. For a given mass M? of prescribed opacity, there
exist two critical luminosities L1 and L0 (L1>L0) such that for
L>L1 no configurations of equilibrium exist? for L1> L>
L0 the density and temperature increase very rapidly as the centre
is approached (T ocrÂ1 Â log------), so that in the centre there
is a region of very high temperatures and densities where the gas
laws are violated; for L = L0 a diffuse perfect gas configuration
is possible? for L0>L>0 the only perfect gas configuration is
a hollow shell provided with an internal, rigid supporting surface
of spherical shape. Since in Nature no internal supporting surface
is provided, to find the actual configuration when L0>L>0 we
construct the artificially supported hollow configuration and then
remove the supporting surface. The mass must collapse, and collapse
will proceed until a steady-state is attained in which, except for a
gaseous outer fringe, the gas laws are violated. Such configurations
may be termed 'collapsed?. Configurations for which L >L>L0 may be
termed 'centrally-condensed?. The physical origin of the different types
of configuration is simply the varying effect of fight-pressure. For
L = L0 the fight -pressure due to L is just sufficient to distend the
star against its self-gravity and maintain it in the form of a perfect
gas. For L1>L>.L0 light-pressure is so high that for equilibrium
to be maintained gravity at any given distance from the centre must
be assisted by concentrating as much matter as possible inside the
sphere in question? when this process is carried out for all spheres,
we get a central condensation. For L0>L>0, light-pressure due to
L is so low that the mass cannot support itself against its own weight
in the form of perfect gas, and collapse sets in until the gas-laws
are disobeyed. The diffuse configurations L = L0 are unstable with
respect to small changes of L. Figs. 1 and 2.?The linear series of
steady-state configurations of a mass M, of prescribed opacity, as
its luminosity L varies. (The ' white dwarfs' are the ' collapsed'
con¬figurations of the general theory. The ' Emden-Eddington
polytropes' are the gaseous diffuse configurations of the general
theory; they are unstable, in general, with regard to deviations of
L on either Bide of the value La. The * centrally-condensed ' series
has not been fully worked out?it awaits the construction of certain
tables? but It may be provisionally identified with stars in the state
of giants and ordinary dwarfs. The diagram is to be understood as
classificatory, not evolutionary.) (pe~ central density, r1=external
radius.) For collapsed or centrally-condensed configurations the centre
will be occupied by a gas in a degenerate state. When the mean densities
or effective temperatures of collapsed configurations are calculated,
using the Fermi-Dirac statistics for the degenerate gas, they are found
to agree with the observed order of magnitude for white dwarfs. Thus,
collapsed configurations may be identified with white dwarfs. A white
dwarf is thus a dense star simply because its luminosity is too low,
and its light-pressure accordingly too low, for it to support its own
mass against its own gravity. From another point of view the calculation
affords an observational verification of the numerical value of the
'degenerate gas constant? the co efficient K in the degenerate
gas law p=Kpi, and so a check on the Fermi-Dirac statistics. If
collapsed configurations may be identified with white dwarfs,
centrally-condensed configurations may be provisionally identified
with ordinary giants and dwarfs, though the full determination of the
properties of centrally-condensed configurations awaits the construction
of certain tables. Centrally-condensed configurations appear to have the
properties that as L decreases from L1 to L0 the effective temperature
rises to a maximum and then decreases again. This would correspond to
the observed division into giants and dwarfs. I give this deduction
with some caution, as it is not yet demonstrated rigorously in the
absence of the tables above mentioned. A point not yet settled is the
question of the continuity of the series of centrally-condensed con
figurations with the collapsed configurations (Figs. 1 and 2). There
are indications that as L passes through L0 from above to below, the
external radius of the configuration may decrease discontinuously, the
gaseous envelope collapsing on to the dense core. If this is confirmed,
it would follow that a star, when its steady-state luminosity L falls
through a certain critical value (depending on its mass), exhibits the
phenomena of a nova or temporary star. For it would have to disengage
a large amount of gravitational potential energy in a short time,
so that the actual emission would under go a temporary increase,
falling again to a value just below its previous value. It would be
highly interesting to have observational data as to the densities of
a nova before and after the outburst. The early-type spectrum of the
later stage of a nova may indeed be taken to indicate a high effective
temperature, and so a small radius and high density, in accordance
with our prediction. The important point about all the foregoing
analysis is that it involves at no stage any special properties of
matter or special assumptions. The observed features of the stars are
thus found to depend only on the most general properties of matter
in association with light-pressure. A question logically distinct
from these is the origin of stellar energy. Here we require to know
something of the physics of energy-generation. The following suggestions
are frankly of a speculative character. Let us assume, in accordance
with a hypothesis first made by Jeans (not his later hypothesis of
super-radioactive atoms), that protons and electrons can unite to form
radiation. Then thermodynamic considerations show that the process
must be reversible?photons can generate matter. We know that matter at
ordinary temperatures is stable. Hence we may postulate the existence
of a critical temperature above which the process can go on in either
direction. Suppose this critical temperature has been passed at 1011
degrees. Calculation then shows that at 1011 degrees almost the whole
of the mass in an enclosure would be in the form of radiation? and
further, that lowering of the temperature of the enclosure would
result in more of the surviving matter present disappearing in the
form of radiation. The process is in fact the thermodynamic opposite
of evaporation: steam condenses to water with emission of energy, and
the process is accordingly encouraged by cooling? matter 'evaporates'
(to radiation) with emission of energy, and the process is encouraged
by cooling. Now, the centre of a star is a sort of thermodynamic
enclosure with a slight leak. It follows that if (as the steady-state
theory indicates) the central region of a fairly luminous star is at
a temperature of 1011 degrees and a high density, then this central
region is effectively a reservoir of very dense radiant energy,
with a mere sprinkling of ordinary matter present. Natural cooling
of this reservoir provides the star's emission to space, and the
reservoir is itself maintained by the con version of matter into
radiation inside it and on its confines. Calculations based on this
idea are consistent with the usually accepted evolutionary timescale,
and predict a rate of 'generation' of energy ? per gram of the 4c2 d?T
right order, namely, ? = - -~- -57 throughout the mass of the core,
where -dT/dt is the rate of cooling. The rate of loss of mass is
given by the usual formula -n- = - -¾. By combination of these
formul it is found possible in principle to establish a relation
linking M with Te (the central temperature)? this is the additional
relation which, by expression of Tc in terms of L and M by means of
the steady-state theory, must lead in due course to a mass-luminosity
correlation. Whether it agrees with the observed mass luminosity law
remains for future investigation, but it is a final satisfaction that,
after first considering L and M as independent variables, we are able to
use the equilibrium configurations thus disclosed to arrive in outline
at a solution of the problem of the actual correlation of mass and
luminosity in Nature. It is to be noted that the star's generation of
energy is naturally non-explosive, for it is simply a con sequence of
the natural tendency of the star to cool. The star behaves, in fact,
simply like a freely cooling body containing a central region of very
high specific heat?namely, a pool of intense radiant energy, which is
gradually drained away though partially reinforced by the conversion
of matter. From this point of view, it is not that a star descends an
evolutionary path because its rate of generation of energy slackens? it
is rather that the act of evolving and the act of radiating energy
are identical. These suggestions as to the origin of stellar energy
and the mode of stellar evolution are not to be pressed. They are to
be sharply distinguished from the steady-state theory, which by the
rational process of proceeding from the known stellar exterior step
by step into the unknown interior indicates an inevitable series of
configurations which correspond to the observed bifurcation of celestial
objects into 'ordinary' stars and 'dense' stars. Note.?The fundamental
result of the rational method of analysis of stellar structure described
in the foregoing article is the division of con figurations into two
types, the 'collapsed' and the 'centrally-condensed'. The existence of
these two types can be demonstrated without complicated mathematics
by the following argument. Let r1 be the radius of a configuration,
arbitrarily assigned beforehand. Let us endeavour to construct a gaseous
configuration with this radius. If such a con figuration be capable
of being constructed, let us in imagination take a journey inwards
to the centre, starting from the boundary. Let M be the total mass,
M(r) the 'surviving' mass left inside the sphere of radius r when we
have reached the distance r from the centre. Then M - M(r) is the mass
already traversed. Consider now the influence of light-pressure. If L
is large, light-pressure will be large and will balance an appreciable
fraction of gravity, and accordingly the density-gradient will be
small. But if L is small, light-pressure will be small, and the
density-gradient will be large. Thus, when L is large, we shall have
traversed a smaller mass M - M(r) in the shell between r1 and r than
when L is small. Consequently, when L is large, M(r) will be larger
than when L is small. In other words, as we journey inwards, when L
is small we 'consume our mass' faster than when L is large. If L is
sufficiently small, we may have consumed our whole mass M before we
arrive at the centre? in that case the only configuration of radius r1
and mass M is a hollow shell internally supported by a rigid spherical
surface. If L is sufficiently large, we shall, however, tend to have an
appreciable mass M(r) surviving unconsumed how ever near we approach
the centre, and this surviving mass M(r) can only be packed inside
r at the cost of high density with violation of the gas laws. Thus
these configurations for large L must be centrally condensed. For
small L, on the other hand, no configurations of radius r1 and mass
M, unsupported, can exist, and the actual configurations must be
'collapsed' ones. 'Collapsed' configurations prove to be much more
nearly homogeneous than 'centrally-condensed' ones. * Substance of
lectures delivered at the Royal Institution on Dec. 2 and Dec. 9, 1930.
---------------------------------------------------------
Title: The analysis of stellar structure
Authors: Milne, E. A.
1930MNRAS..91....4M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The analysis of stellar structure
Authors: Milne, E. A.
1930Obs....53..305M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The connection of mass with luminosity for stars
Authors: Milne, E. A.
1930Obs....53..238M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Stellar Structure and the Origin of Stellar Energy.
Authors: Milne, E. A.
1930Natur.126..238M Altcode:
THE generally accepted theory of the internal conditions in stars,
due to Sir A. S. Eddington, depends largely on a special solution of
the fundamental equations, and according to this a definite calculable
luminosity is associated with a given mass. If this were the only
solution of the equations it would conflict, as I have repeatedly
shown in recent papers, with the obvious physical considerations
which show that we can build up a given mass in equilibrium so
as to have an arbitrary luminosity (not too large) whatever the
assumed physical properties of the material. I have recently noticed
that the fundamental equations possess a whole family of solutions,
corresponding to arbitrarily assigned luminosit for given mass. These
solutions show immediately that Eddington's solution is a special
solution and corresponds to an unstable distribution of mass. In the
stable distributions the density and temperature tend to very high
values as the centre is approached, theoretically becoming infinite
if the classical gas laws held to unlimited compressibility.
---------------------------------------------------------
Title: The dissociation formula according to the Fermi-Dirac
statistics
Authors: Milne, E. A.
1930MNRAS..90..769M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Problem of Stellar Luminosity.
Authors: Milne, E. A.
1930Natur.125..708M Altcode:
THOUGH I have the very greatest respect for anything written by my
friend and teacher Prof. Eddington, I cannot see that in his letter
in NATURE of Mar. 29 he meets my arguments.
---------------------------------------------------------
Title: The masses, luminosities, and effective temperatures of the
stars (Second paper)
Authors: Milne, E. A.
1930MNRAS..90..678M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Temperature-gradients and molecular weight in the Sun's
atmosphere
Authors: Milne, E. A.
1930Obs....53..119M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Preliminary note on the structure of sunspots
Authors: Milne, E. A.
1930MNRAS..90..487M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Atomic Physics and Related Subjects.: Communications to
Nature.: The Problem of Stellar Luminosity.
Authors: Milne, E. A.
1930Natur.125..453M Altcode:
SIR JOSEPH LARMOR, who raised certain interesting points concerning the
validity of my recent work on stellar luminosity in NATURE of Feb. 22,
has kindly allowed me to see some further exposition on these points
which he proposes to publish in the Observatory. With his further
analysis of the situation I am in complete agreement. As regards the
question which he thinks still outstanding, the work of Sir James Jeans
and of J. Woltjer, together with my own investigations, shows that 1-β,
the ratio of radiation pressure to total pressure varies very slowly
in the photospheric layers of a star on plausible assumptions as to
the absorption coefficient. It therefore satisfies his requirement of
being independent of the precise surface at which it is evaluated. But
it is necessary to explain the discrepancy with other existing theories.
---------------------------------------------------------
Title: Thermodynamics of the stars
Authors: Milne, E. A.
1930thst.book.....M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Theory of Pulsating Stars
Authors: Milne, E. A.
1930HDA.....3..804M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Thermodynamics of the Stars
Authors: Milne, E. A.
1930HDA.....3...65M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Radiative Equilibrium of a Planetary Nebula. With
3 figures.
Authors: Milne, E. A.
1930ZA......1...98M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Anomalous effects in astrophysics
Authors: Milne, E. A.
1929Obs....52..358M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The masses, luminosities, and effective temperatures of
the stars
Authors: Milne, E. A.
1929MNRAS..90...17M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A "Null-Effect" in the Theory of the Influence of Absolute
Magnitude on Stellar Spectra
Authors: Milne, E. A.
1929BHarO.870....1M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Integral theorems on the equilibrium of a star
Authors: Milne, E. A.
1929MNRAS..89..739M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A derivation of the equations of radiative viscosity
Authors: Milne, E. A.
1929MNRAS..89..518M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Bakerian Lecture: The Structure and Opacity of a Stellar
Atmosphere
Authors: Milne, E. A.
1929RSPTA.228..421M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Absolute Magnitude Effects in Stellar Spectra
Authors: Milne, E. A.
1928Natur.122..840M Altcode:
IT is known from the fundamental work of Adams and Kohlschütter and
their followers that certain pairs of lines in stellar spectra change
in relative intensity with absolute luminosity, and this has formed
the basis of the method of `spectroscopic parallaxes.' The method has
been hitherto empirical, stars of known luminosity being used as a
basis to determine the luminosities of other stars from calibration
curves. Saha's researches on high-temperature ionisation, whilst not
removing the empirical basis, afforded a general qualitative explanation
of many of the results observed. They showed that the lowered value
of surface gravity g in giant stars as compared with dwarfs must
cause reduced pressures in the atmospheres of giants with consequent
increased ionisation and hence increased intensity of enhanced lines
(Pannekoek, B.A.N., 19).
---------------------------------------------------------
Title: Ionization in stellar atmospheres. Part II. : Absolute
magnitude effects
Authors: Milne, E. A.
1928MNRAS..89..157M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The theoretical contours of a absorption lines in stellar
atmospheres
Authors: Milne, E. A.
1928MNRAS..89....3M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Ionization in stellar atmospheres. Part I. : Generalised
Saha formulæ, maximum intensities, and the determination of the
coefficient of opacity
Authors: Milne, E. A.
1928MNRAS..89...17M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Pressure of Calcium in the Sun's Atmosphere
Authors: Milne, E. A.
1928Natur.121.1017M Altcode:
IN a recent interesting investigation, A. Unsöld has estimated
the total number of atoms of various kinds in the solar atmosphere
which give rise to Fraunhofer lines of the observed width and depth
(Zeits. für Phys., 46, 765; 1928). The theoretical curves he has
calculated reproduce with remarkable fidelity the contours of such
lines as those of sodium, calcium, strontium, and barium. They give, it
is true, too small values for the residual intensities in the centres
of the lines, but in the wings, where the theory seems unquestionably
trustworthy, they agree exceedingly well with observation. With the
aid of the Saha theory of ionisation, Unsöld has deduced the total
number of atoms of a given species per square centimetre column above
the `photosphere.' The results as regards the relative abundances of
atoms of different kinds are in agreement with Miss Payne's estimates
of relative abundances in stellar atmospheres, but Unsöld's method
leads to an absolute determination. For example, for calcium he finds
2.3 × 10<SUP>10</SUP> atoms per cm.<SUP>2</SUP>.
---------------------------------------------------------
Title: A reply to Prof. Anderson
Authors: Milne, E. A.
1928Obs....51..196M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The effect of collisions on monochromatic radiative equilibrium
Authors: Milne, E. A.
1928MNRAS..88..493M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The total absorption in the Sun's reversing layer
Authors: Milne, E. A.
1928Obs....51...88M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Pressures in the calcium chromosphere and reversing layer
Authors: Milne, E. A.
1928MNRAS..88..188M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Stellar equilibrium and the influence of the distribution
of energy-production
Authors: Milne, E. A.
1927MNRAS..87..708M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Selective radiation-pressure and the structure of a stellar
atmosphere
Authors: Milne, E. A.
1927MNRAS..87..697M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Some Recent Advances in Astrophysics
Authors: Milne, E. A.
1926Natur.118..738M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The reflection effect in eclipsing binaries
Authors: Milne, E. A.
1926MNRAS..87...43M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The equilibrium of the calcium chromosphere (Second and
third papers)
Authors: Milne, E. A.
1926MNRAS..86..578M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the possibility of the emission of high-speed atoms from
the sun and stars
Authors: Milne, E. A.
1926MNRAS..86..459M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The equilibrium of the calcium chromosphere (Second and
third papers)
Authors: Milne, E. A.
1925MNRAS..86....8M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The theory of planetary nebulae
Authors: Milne, E. A.
1925Obs....48..317M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The width of Fraunhofer lines: a reply to Professor Stewart
Authors: Milne, E. A.
1925MNRAS..85..739M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Absorption coefficients and the pressure of radiation in the
photospheric layers of a star
Authors: Milne, E. A.
1925MNRAS..85..768M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The stellar absorption coefficient
Authors: Milne, E. A.
1925MNRAS..85..750M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Note on Rosseland's integral for the stellar absorption
coefficient
Authors: Milne, E. A.
1925MNRAS..85..979M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The height of the chromosphere
Authors: Milne, E. A.
1925Obs....48..145M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Astrophysics without Mathematics
Authors: Milne, E. A.
1925Natur.115..193M Altcode:
I AM sorry that my review has caused Prof. Dingle so much pain;
and I must beg him to accept my assurance that purely scientific
considerations were in my mind. My review contains evidence that there
were portions of the book which I read with pleasure, and I take this
occasion to say so explicitly. I cannot see that my criticisms were
outside the province of a reviewer, but I deeply regret that they should
have been expressed in language which Prof. Dingle finds discourteous.
---------------------------------------------------------
Title: The equilibrium of the calcium chromosphere
Authors: Milne, E. A.
1924MNRAS..85..111M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The maxima of absorption lines in stellar spectra (Second
paper)
Authors: Fowler, R. H.; Milne, E. A.
1924MNRAS..84..499F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Temperature of Reversing Layers of Stars
Authors: Milne, E. A.
1924Natur.113R.534M Altcode:
THE question of the relation of the temperature of a reversing
layer of a star to the star's effective temperature is raised by
Dr. J. Q. Stewart in NATURE of March 15. In the investigation of
mine to which Dr. Stewart refers (Mon. Not. R.A.S., 82, 368, 1922)
it was shown that the temperature of an indefinitely thin layer in
radiative equilibrium, subject on one side to black radiation of
effective temperature T<SUB>1</SUB> and subject on the other side to
no radiation, lies between T<SUB>1</SUB> and 12T<SUB>1</SUB> whatever
the selective absorption of the thin layer. As Dr. Stewart points out,
this result cannot be applied as it stands to a stellar atmosphere,
for the atmosphere as a whole is not “optically thin”. If we adopt
for its lower boundary a surface at such a depth that the radiation
incident on it from below is black (say of temperature T<SUB>1</SUB>),
a temperature gradient will exist between its lower and upper boundaries
and produce absorption lines. On the ordinary thermodynamic theory of
radiation it can then be shown that if the atmosphere is in radiative
equilibrium, the temperature of its lower boundary must lie between
T<SUB>1</SUB> and 12T<SUB>1</SUB> but the temperature of its upper
boundary may have any value whatever lying below that of the lower
boundary, according to the selective absorption.
---------------------------------------------------------
Title: An astrophysical determination of the average life of an
excited calcium atom
Authors: Milne, E. A.
1924MNRAS..84..354M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: XVIII. Statistical equilibrium in relation to the
photo-electric effect, and its application to the determination of
absorption coefficients
Authors: Milne, E. A.
1924PMag...47..209M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The intensities of absorption lines in stellar spectra,
and the temperatures and pressures in the reversing layers of stars
Authors: Fowler, R. H.; Milne, E. A.
1923MNRAS..83..403F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Stars of type O and the theory of high-temperature ionisation
Authors: Milne, E. A.
1923Obs....46..113M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The equilibrium of a rotating star
Authors: Milne, E. A.
1923MNRAS..83..118M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative Equilibrium: The Relation between the Spectral
Energy Curve of a Star and the Law of Darkening of the Disc towards
the Limb, with Special Reference to the Effects of Scattering and
the Solar Spectrum
Authors: Milne, E. A.
1923RSPTA.223..201M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Recent work in stellar physics
Authors: Milne, E. A.
1923PPSL...36...94M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The temperature in the outer atmosphere of a star
Authors: Milne, E. A.
1922MNRAS..82..368M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Ionization in stellar atmospheres
Authors: Milne, E. A.
1921Obs....44..261M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Spectroscopy, Astronomical, Radiative equilibrium: the effect
of a strong absorption line
Authors: Milne, E. A.
1921MNRAS..81..510M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Spectroscopy, Astronomical, Radiative equilibrium and spectral
distribution
Authors: Milne, E. A.
1921MNRAS..81..375M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative equilibrium in the outer layers of a star
Authors: Milne, E. A.
1921MNRAS..81..361M Altcode:
No abstract at ADS
