Author name code: milne ADS astronomy entries on 2022-09-14 author:"Milne, Edward Arthur" ------------------------------------------------------------------------ Title: Sir James Jeans Authors: Milne, E. A. Bibcode: 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. Title: Newtonian Universes and the Curvature of Space Authors: McCrea, W. H.; Milne, E. A. Bibcode: 2000GReGr..32.1949M Altcode: No abstract at ADS Title: A Newtonian Expanding Universe Authors: Milne, E. A. Bibcode: 2000GReGr..32.1939M Altcode: No abstract at ADS Title: The Maxima of Absorption Lines in Stellar Spectra Authors: Fowler, R. H.; Milne, E. A. Bibcode: 1994JApA...15..241F Altcode: No abstract at ADS 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. Bibcode: 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. 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. Bibcode: 1978opat.conf..130C Altcode: No abstract at ADS 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. Bibcode: 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. Title: Selected papers on the transfer of radiation Authors: Menzel, Donald Howard; Milne, Edward Arthur Bibcode: 1966sptr.book.....M Altcode: 1966QB817.M4....... No abstract at ADS Title: Modern cosmology and the Christian idea of God. Authors: Milne, Edward Arthur Bibcode: 1952mcci.book.....M Altcode: 1952QB981.M77...... No abstract at ADS Title: Gravitation and magnetism Authors: Milne, E. A. Bibcode: 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. Title: The vertex of star-streaming Authors: Milne, E. A. Bibcode: 1949Obs....69..107M Altcode: No abstract at ADS Title: The Luminosity-Velocity Relation for Pulsating Stars Authors: Milne, E. A. Bibcode: 1949MNRAS.109..517M Altcode: No abstract at ADS Title: II. -Motion in an extended distribution of Matter Authors: Milne, E. A. Bibcode: 1948MNRAS.108..316M Altcode: No abstract at ADS Title: Star-streaming and the Stability of Spiral Orbits in Spiral Nebulae. I. -Motion round a point-nucleus Authors: Milne, E. A. Bibcode: 1948MNRAS.108..309M Altcode: No abstract at ADS Title: Kinematic relativity; a sequel to Relativity, gravitation and world structure. Authors: Milne, Edward Arthur Bibcode: 1948krsr.book.....M Altcode: 1948QB500.M49...... No abstract at ADS Title: La Cinquantenaire de l'Observatoire Yerkes Authors: Ledoux, P.; Milne, E. A.; Minnaert, M. Bibcode: 1948LAstr..62...46L Altcode: No abstract at ADS Title: The Equation to the Arm of a Spiral Nebula. Authors: Milne, E. A. Bibcode: 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 Title: On the spiral character of the external galaxies Authors: Milne, E. A. Bibcode: 1946MNRAS.106..180M Altcode: No abstract at ADS Title: Kinematical Relativity Authors: Milne, E. A. Bibcode: 1945Natur.156..747M Altcode: MY attention has been directed to Prof. H. Dingle's recent letter in Nature1. 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 myself2 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. Title: Kinematical Relativity and the Nebular Red-Shift Authors: Milne, E. A. Bibcode: 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. Title: The Ageing of Light Authors: Milne, E. A. Bibcode: 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. Title: (Presidential Address) ,on presenting the Gold Medal to Professor Bengt Edlén Authors: Milne, E. A. Bibcode: 1945MNRAS.105..138M Altcode: No abstract at ADS Title: The natural philosophy of stellar structure (Presidential Address, 1945) Authors: Milne, E. A. Bibcode: 1945MNRAS.105..146M Altcode: No abstract at ADS Title: Obituary: Ralph Howard Fowler Authors: Milne, E. A. Bibcode: 1944Obs....65..245M Altcode: No abstract at ADS Title: Prof. H. F. Newall, F.R.S. Authors: Milne, E. A. Bibcode: 1944Natur.153..455M Altcode: No abstract at ADS Title: On the nature of universal gravitation (Presidential Address, 1944) Authors: Milne, E. A. Bibcode: 1944MNRAS.104..120M Altcode: No abstract at ADS Title: On “Absolute Acceleration” Authors: Milne, E. A. Bibcode: 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. Title: Cosmological Theories. Authors: Milne, E. A. Bibcode: 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 Title: Physical Sciences: Reversibility of the Equations of Classical Dynamics Authors: Milne, E. A.; Whitrow, G. J. Bibcode: 1938Natur.141..905M Altcode: IN a recent series of papers, one of us has derived the equation of motion1 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 graduated2 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 form3 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 shown4 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. Title: On a linear equivalence discussed by L. PAGE. Mit 1 Abbildung. Authors: Milne, E. A.; Whitrow, G. J. Bibcode: 1938ZA.....15..342M Altcode: No abstract at ADS 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. Bibcode: 1938ZA.....15..263M Altcode: No abstract at ADS Title: Stellar luminosity and the opacity in the outer layers of a star Authors: Milne, E. A. Bibcode: 1937MNRAS..98...21M Altcode: No abstract at ADS Title: Stellar luminosity and photospheric pressure Authors: Milne, E. A. Bibcode: 1937MNRAS..97..513M Altcode: No abstract at ADS Title: The Constant of Gravitation Authors: Milne, E. A. Bibcode: 1937Natur.139..409M Altcode: WITH regard to Prof. P. A. M. Dirac's recent letter to NATURE1, I have shown, in various contexts2 that the relation between γ, the `constant' of gravitation, and t, the epoch, is given by where M0 is the apparent mass of the fictitious homogeneous universe. (The actual mass must be infinite.) With t = 2 × 109 years, this gave M0 = 2.4 × 1055 grams = mass of 1.5 × 1079 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. Title: Kinematics, Dynamics, and the Scale of Time Authors: Milne, E. A. Bibcode: 1937RSPSA.158..324M Altcode: No abstract at ADS Title: The Background of the Galaxies Authors: Milne, E. A. Bibcode: 1936Natur.138...38M Altcode: IN NATURE of May 30, M. Leontovski1 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 background2. Combining these results, we see that the background realizes the poet's dream of ``A rose-red city, half as old as time.''3 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. Bibcode: 1936MNRAS..96..207M Altcode: No abstract at ADS 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. Bibcode: 1936MNRAS..96..195M Altcode: No abstract at ADS Title: The Pressure in the interior of a star Authors: Milne, E. A. Bibcode: 1936MNRAS..96..179M Altcode: No abstract at ADS 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. Bibcode: 1936MNRAS..96..184M Altcode: No abstract at ADS Title: Stellar kinematics and the K-effect Authors: Milne, E. A. Bibcode: 1935Obs....58..248M Altcode: No abstract at ADS Title: Stellar kinematics and the K-effect Authors: Milne, E. A. Bibcode: 1935MNRAS..95..560M Altcode: No abstract at ADS Title: Reviews, reviewers and reviewed Authors: Milne, E. A. Bibcode: 1935Obs....58..124M Altcode: No abstract at ADS Title: Origin of the Cosmic Rays Authors: Milne, E. A. Bibcode: 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 universe1. The arguments required are purely kinematical, and involve no appeal to any specific theory of gravitation, or any arbitrary hypotheses. Title: The configuration of stellar masses Authors: Milne, E. A. Bibcode: 1935Obs....58...52M Altcode: No abstract at ADS Title: Relativity, gravitation and world-structure Authors: Milne, Edward Arthur Bibcode: 1935rgws.book.....M Altcode: 1935QB500.M5....... 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. Bibcode: 1935MiPul..14A.202M Altcode: No abstract at ADS Title: A method of analysing stellar variability Authors: Milne, E. A. Bibcode: 1934MNRAS..94..418M Altcode: No abstract at ADS Title: On the theory of the cosmical constant Authors: Milne, E. A. Bibcode: 1934Obs....57...99M Altcode: No abstract at ADS Title: World-models and the world-picture Authors: Milne, E. A. Bibcode: 1934Obs....57...24M Altcode: No abstract at ADS Title: A Newtonian expanding Universe Authors: Milne, Edward Arthur Bibcode: 1934QJMat...5...64M Altcode: No abstract at ADS Title: Newtonian Universes and the curvature of space Authors: McCrea, William Hunter; Milne, Edward Arthur Bibcode: 1934QJMat...5...73M Altcode: No abstract at ADS Title: World-relations and the "cosmical constant," Authors: Milne, E. A. Bibcode: 1933MNRAS..94....3M Altcode: No abstract at ADS Title: Remarks on world-structure Authors: Milne, E. A. Bibcode: 1933MNRAS..93..668M Altcode: No abstract at ADS Title: Correction to the paper: ``World-Structure etc. " Authors: Milne, E. A. Bibcode: 1933ZA......6..244M Altcode: No abstract at ADS Title: Note on H. P. Robertson's paper on World-Structure. Authors: Milne, E. A. Bibcode: 1933ZA......7..180M Altcode: No abstract at ADS Title: World-Structure and the Expansion of the Universe. Mit 6 Abbildungen. Authors: Milne, E. A. Bibcode: 1933ZA......6....1M Altcode: No abstract at ADS Title: The Expanding Universe Authors: Milne, E. A. Bibcode: 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. Title: World Structure and the Expansion of the Universe Authors: Milne, E. A. Bibcode: 1932Natur.130....9M Altcode: No abstract at ADS Title: The analysis of stellar structure, II Authors: Milne, E. A. Bibcode: 1932MNRAS..92..610M Altcode: No abstract at ADS Title: The white dwarf stars; being the Halley lecture, delivered on 19 May 1932 Authors: Milne, Edward Arthur Bibcode: 1932wdsb.book.....M Altcode: 1932QB903.M5....... No abstract at ADS Title: Note on the boundary Temperature of a Star. Authors: Milne, E. A. Bibcode: 1932ZA......5..328M Altcode: No abstract at ADS Title: Ionization in stellar atmospheres, Part III Authors: Milne, E. A.; Chandrasekhar, S. Bibcode: 1932MNRAS..92..150M Altcode: No abstract at ADS Title: The Theory of Stellar Structure II (Energy-generation). Authors: Milne, E. A. Bibcode: 1932ZA......5..337M Altcode: No abstract at ADS Title: The Theory of Stellar Structure. Authors: Milne, E. A. Bibcode: 1932ZA......4...75M Altcode: No abstract at ADS Title: The Internal Temperature of White Dwarf Stars. Authors: Milne, E. A. Bibcode: 1931Natur.128..999M Altcode: IT has recently been discovered by S. Chandrasekhar,1 B. Swirles,2 and R. C. Majumdar,3 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 Atkinson4 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, Jeans5 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 Jeans6 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''. Title: Contributions to a British Association Discussion on the Evolution of the Universe. Authors: Milne, E. A. Bibcode: 1931Natur.128..715M Altcode: No abstract at ADS Title: The configuration of stellar masses Authors: Milne, E. A. Bibcode: 1931Obs....54..243M Altcode: No abstract at ADS Title: Emden's equation: Note on steady-state distributions which are given by solutions of Emden's differential equation Authors: Milne, E. A. Bibcode: 1931MNRAS..91..751M Altcode: No abstract at ADS Title: Dense stars Authors: Milne, E. A. Bibcode: 1931Obs....54..140M Altcode: No abstract at ADS Title: Note on "equations of fit" in the theory of stellar structure Authors: Milne, E. A. Bibcode: 1931MNRAS..91..479M Altcode: No abstract at ADS Title: [Letters to the Editor] Authors: Milne, E. A. Bibcode: 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. Title: Über die Frage der Opazität der Sternmaterie. (Eingegangen am 18. Juli 1931) Authors: Milne, E. A. Bibcode: 1931ZA......3..253M Altcode: No abstract at ADS Title: Stellar Structure and the Origin of Stellar Energy. Authors: Milne, E. A. Bibcode: 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 ­ 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. Bibcode: 1930MNRAS..91....4M Altcode: No abstract at ADS Title: The analysis of stellar structure Authors: Milne, E. A. Bibcode: 1930Obs....53..305M Altcode: No abstract at ADS Title: The connection of mass with luminosity for stars Authors: Milne, E. A. Bibcode: 1930Obs....53..238M Altcode: No abstract at ADS Title: Stellar Structure and the Origin of Stellar Energy. Authors: Milne, E. A. Bibcode: 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. Bibcode: 1930MNRAS..90..769M Altcode: No abstract at ADS Title: The Problem of Stellar Luminosity. Authors: Milne, E. A. Bibcode: 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. Bibcode: 1930MNRAS..90..678M Altcode: No abstract at ADS Title: Temperature-gradients and molecular weight in the Sun's atmosphere Authors: Milne, E. A. Bibcode: 1930Obs....53..119M Altcode: No abstract at ADS Title: Preliminary note on the structure of sunspots Authors: Milne, E. A. Bibcode: 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. Bibcode: 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. Bibcode: 1930thst.book.....M Altcode: No abstract at ADS Title: Theory of Pulsating Stars Authors: Milne, E. A. Bibcode: 1930HDA.....3..804M Altcode: No abstract at ADS Title: Thermodynamics of the Stars Authors: Milne, E. A. Bibcode: 1930HDA.....3...65M Altcode: No abstract at ADS Title: The Radiative Equilibrium of a Planetary Nebula. With 3 figures. Authors: Milne, E. A. Bibcode: 1930ZA......1...98M Altcode: No abstract at ADS Title: Anomalous effects in astrophysics Authors: Milne, E. A. Bibcode: 1929Obs....52..358M Altcode: No abstract at ADS Title: The masses, luminosities, and effective temperatures of the stars Authors: Milne, E. A. Bibcode: 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. Bibcode: 1929BHarO.870....1M Altcode: No abstract at ADS Title: Integral theorems on the equilibrium of a star Authors: Milne, E. A. Bibcode: 1929MNRAS..89..739M Altcode: No abstract at ADS Title: A derivation of the equations of radiative viscosity Authors: Milne, E. A. Bibcode: 1929MNRAS..89..518M Altcode: No abstract at ADS Title: Bakerian Lecture: The Structure and Opacity of a Stellar Atmosphere Authors: Milne, E. A. Bibcode: 1929RSPTA.228..421M Altcode: No abstract at ADS Title: Absolute Magnitude Effects in Stellar Spectra Authors: Milne, E. A. Bibcode: 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. Bibcode: 1928MNRAS..89..157M Altcode: No abstract at ADS Title: The theoretical contours of a absorption lines in stellar atmospheres Authors: Milne, E. A. Bibcode: 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. Bibcode: 1928MNRAS..89...17M Altcode: No abstract at ADS Title: Pressure of Calcium in the Sun's Atmosphere Authors: Milne, E. A. Bibcode: 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 × 1010 atoms per cm.2. Title: A reply to Prof. Anderson Authors: Milne, E. A. Bibcode: 1928Obs....51..196M Altcode: No abstract at ADS Title: The effect of collisions on monochromatic radiative equilibrium Authors: Milne, E. A. Bibcode: 1928MNRAS..88..493M Altcode: No abstract at ADS Title: The total absorption in the Sun's reversing layer Authors: Milne, E. A. Bibcode: 1928Obs....51...88M Altcode: No abstract at ADS Title: Pressures in the calcium chromosphere and reversing layer Authors: Milne, E. A. Bibcode: 1928MNRAS..88..188M Altcode: No abstract at ADS Title: Stellar equilibrium and the influence of the distribution of energy-production Authors: Milne, E. A. Bibcode: 1927MNRAS..87..708M Altcode: No abstract at ADS Title: Selective radiation-pressure and the structure of a stellar atmosphere Authors: Milne, E. A. Bibcode: 1927MNRAS..87..697M Altcode: No abstract at ADS Title: Some Recent Advances in Astrophysics Authors: Milne, E. A. Bibcode: 1926Natur.118..738M Altcode: No abstract at ADS Title: The reflection effect in eclipsing binaries Authors: Milne, E. A. Bibcode: 1926MNRAS..87...43M Altcode: No abstract at ADS Title: The equilibrium of the calcium chromosphere (Second and third papers) Authors: Milne, E. A. Bibcode: 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. Bibcode: 1926MNRAS..86..459M Altcode: No abstract at ADS Title: The equilibrium of the calcium chromosphere (Second and third papers) Authors: Milne, E. A. Bibcode: 1925MNRAS..86....8M Altcode: No abstract at ADS Title: The theory of planetary nebulae Authors: Milne, E. A. Bibcode: 1925Obs....48..317M Altcode: No abstract at ADS Title: The width of Fraunhofer lines: a reply to Professor Stewart Authors: Milne, E. A. Bibcode: 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. Bibcode: 1925MNRAS..85..768M Altcode: No abstract at ADS Title: The stellar absorption coefficient Authors: Milne, E. A. Bibcode: 1925MNRAS..85..750M Altcode: No abstract at ADS Title: Note on Rosseland's integral for the stellar absorption coefficient Authors: Milne, E. A. Bibcode: 1925MNRAS..85..979M Altcode: No abstract at ADS Title: The height of the chromosphere Authors: Milne, E. A. Bibcode: 1925Obs....48..145M Altcode: No abstract at ADS Title: Astrophysics without Mathematics Authors: Milne, E. A. Bibcode: 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. Bibcode: 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. Bibcode: 1924MNRAS..84..499F Altcode: No abstract at ADS Title: The Temperature of Reversing Layers of Stars Authors: Milne, E. A. Bibcode: 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 T1 and subject on the other side to no radiation, lies between T1 and 12T1 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 T1), 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 T1 and 12T1 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. Bibcode: 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. Bibcode: 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. Bibcode: 1923MNRAS..83..403F Altcode: No abstract at ADS Title: Stars of type O and the theory of high-temperature ionisation Authors: Milne, E. A. Bibcode: 1923Obs....46..113M Altcode: No abstract at ADS Title: The equilibrium of a rotating star Authors: Milne, E. A. Bibcode: 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. Bibcode: 1923RSPTA.223..201M Altcode: No abstract at ADS Title: Recent work in stellar physics Authors: Milne, E. A. Bibcode: 1923PPSL...36...94M Altcode: No abstract at ADS Title: The temperature in the outer atmosphere of a star Authors: Milne, E. A. Bibcode: 1922MNRAS..82..368M Altcode: No abstract at ADS Title: Ionization in stellar atmospheres Authors: Milne, E. A. Bibcode: 1921Obs....44..261M Altcode: No abstract at ADS Title: Spectroscopy, Astronomical, Radiative equilibrium: the effect of a strong absorption line Authors: Milne, E. A. Bibcode: 1921MNRAS..81..510M Altcode: No abstract at ADS Title: Spectroscopy, Astronomical, Radiative equilibrium and spectral distribution Authors: Milne, E. A. Bibcode: 1921MNRAS..81..375M Altcode: No abstract at ADS Title: Radiative equilibrium in the outer layers of a star Authors: Milne, E. A. Bibcode: 1921MNRAS..81..361M Altcode: No abstract at ADS