[Footnote 1: Fig. 1 is from a photograph taken by Mr. Evershed at Kodaikanal Observatory, Madras. Fig. 2 is from the Mount Wilson Observatory, California.]
[Footnote 2: I am indebted to Professor C. T. R. Wilson for Figs. 3-6.]
[Footnote 3: Primarily it is the electric charge and not the high speed of particles which determines their appearance in these photographs. But a high-speed particle leaves behind it a trail of electrically charged particles--the victims of its furious driving--so that it is shown indirectly by its line of victims.]
[Footnote 4: Other substitutions for silver do not as a rule cause greater change, and the differences are likely to be toned down by mixture of many elements. Excluding hydrogen, the most extreme change is from 48 particles for silver to 81 particles for an equal mass of helium. But for hydrogen the change is from 48 to 216, so that hydrogen gives widely different results from other elements.]
[Footnote 5: The mean density of Capella is nearly the same as the density of the air.]
[Footnote 6: Unless otherwise indicated ‘gaseous’ is intended to mean ‘composed of _perfect_ gas’.]
[Footnote 7: For this prediction it is unnecessary to know the chemical composition of the stars, provided that extreme cases (e. g. an excessive proportion of hydrogen) are excluded. For example, consider the hypotheses that Capella is made respectively of (_a_) iron, (_b_) gold. According to theory the opacity of a star made of the heavier element would be 2½ times the opacity of a star made of iron. This by itself would make the golden star a magnitude (= 2½ times) fainter. But the temperature is raised by the substitution; and although, as explained on p. 23, the change is not very great, it increases the outflow of heat approximately 2½ times. The resultant effect on the brightness is practically no change. Whilst this independence of chemical constitution is satisfactory in regard to definiteness of the results, it makes the discrepant factor 10 particularly difficult to explain.]
[Footnote 8: Observation shows that the sun is about 4 magnitudes fainter than the average diffuse star of the same spectral class, and Krueger 60 is 10 magnitudes fainter than diffuse stars of its class. The whole drop was generally assumed to be due to deviation from a perfect gas; but this made no allowance for a possible difference of mass. The comparison with the curve enables the dense star to be compared with a gaseous star _of its own mass_, and we see that the difference then disappears. So that (if there has been no mistake) the dense star is a gaseous star, and the differences above mentioned were due wholly to differences of mass.] [Footnote 9: Rougher estimates were made much earlier.]
[Footnote 10: The observed period of Algol is the period of revolution, not of rotation. But the two components are very close together, and there can be no doubt that owing to the large tidal forces they keep the same faces turned towards each other; that is to say, the periods of rotation and of revolution are equal.]
[Footnote 11: It may be of interest to add that although the proper light of Algol B is inappreciable, we can observe a reflection (or re-radiation) of the light of Algol A by it. This reflected light changes like moonlight according as Algol B is ‘new’ or ‘full’.]
[Footnote 11: The mass-luminosity relation was not suspected at the time of which I am speaking.]
[Footnote 13: My references to ‘_perfect gas_ of the density of platinum’ and ‘_material_ 2,000 times denser than platinum’ have often been run together by reporters into ‘perfect gas 2,000 times denser than platinum’. It is scarcely possible to calculate what is the condition of the material in the Companion of Sirius, but I do not expect it to be a perfect gas.]
[Footnote 14: Photographed by Dr. W. H. Wright at the Lick Observatory, California.]
[Footnote 15: Nos. 43, 61, 75 are recent discoveries and may require confirmation. There now remain only two gaps (85 and 87) apart from possible elements beyond uranium.]
[Footnote 16: It does not give _both_ temperature and pressure, but it gives one if the other is known. This is valuable information which may be pieced together with other knowledge of the conditions at the surface of the stars.]
[Footnote 17: Hydrogen (being element No. 1) has only one planet electron.]
[Footnote 18: Fig. 9 is a photograph of the ‘flash spectrum’ of the sun’s chromosphere taken by Mr. Davidson in Sumatra at the eclipse of 14 January 1926.]
[Footnote 19: The helium line in the Ring Nebula on which we have already commented is not a member of the Pickering Series, but it has had the same history. It was first supposed to be due to hydrogen, later (in 1912) reproduced by Fowler terrestrially in a mixture of helium and hydrogen, and finally discovered by Bohr to belong to helium.]
[Footnote 20: This, of course, is found from the other lines of the spectrum which genuinely belong to the star and shift to and fro as it describes its orbit.]
[Footnote 21: As the word temperature is sometimes used with new-fangled meanings, I may add that 15,000° is the temperature corresponding to the individual speeds of the atoms and electrons--the old-fashioned gas-temperature.]
[Footnote 22: Photograph taken by E. T. Cottingham and the author in Principe at the total eclipse of 29 May 1919.]
[Footnote 23: We refer to calcium as it occurs in the chromosphere, i. e. with one electron missing.]
[Footnote 24: There is an awkwardness in applying the term ‘apparent’ to something too small to be seen; but, remembering that we have armed ourselves with an imaginary telescope capable of showing the disk, the meaning will be clear.]
[Footnote 25: Densities below that of air have been found for some of the Algol variables by an entirely different kind of investigation, and also for some of the Cepheid variables by still another method. There are also many other examples of stars of bulk comparable with that of Betelgeuse.]
[Footnote 26: From a photograph taken at the Royal Observatory, Cape of Good Hope.]
[Footnote 27: For comparison, the nearest fixed star is distant 4 light years. Apart from clusters we rarely deal with distances above 2,000 light years.]
[Footnote 28: One cannot always be sure that what is true of the cluster stars will be true of stars in general; and our knowledge of the nearer stars, though lagging behind that of the stars in clusters, does not entirely agree with this association of colour and brightness.]
[Footnote 29: The term nebula covers a variety of objects, and it is only the nebulae classed as spirals that are likely to be outside our stellar system.]
[Footnote 30: This can be checked because uranium lead has a different atomic weight from lead not so derived. Ordinary lead is a mixture of several kinds of atoms (isotopes).]
[Footnote 31: You may wonder why, having said that the sun contains 2,000 quadrillion tons of energy _at the most_, I now assume that it contains just this amount. It is really only a verbal point depending on the scientific definition of energy. All mass is mass of _something_, and we now call that something ‘energy’ whether it is one of the familiar forms of energy or not. You will see in the next sentence that we do not assume that the energy is convertible into known forms, so that it is a terminology which commits us to nothing.]
[Footnote 32: Aston in his latest researches has been able to detect that the oxygen atom is just appreciably lighter than the four helium atoms.]
[Footnote 33: A measurement of the heat observed to flow from a continuous fountain of heat is a measurement of the output of the fountain, unless there is a storing of energy between the output and the outflow. The breakdown of the Kelvin time-scale indicates that the storing in the stars (positive or negative) and consequent expansion or contraction is negligible compared to the output or outflow.]
[Footnote 34: The stars all put together cover an area of the sky much less than the apparent disk of the sun, so that unless their surface-layers are generating this radiation very much more abundantly than the sun does, they cannot be responsible for it.]
[Footnote 35: The term ‘dwarf stars’ is not meant to include _white dwarfs_.]
[Footnote 36: We can scarcely suppose that all stars after reaching the main series pass through _precisely_ the same stages. For example, Algol, when it has become reduced to the mass of the Sun, may have slightly different density and temperature. But the observational evidence indicates that these individual differences are small. The main series is nearly a linear sequence; it must have some ‘breadth’ as well as ‘length’, but at present the scatter of the individual stars away from the central line of the sequence seems to be due chiefly to the probable errors of the observational data and the true breadth has not been determined.]
[Footnote 37: Exhaustion of supply without change of mass would cause the star to contract to higher density; it would thus have a combination of density and mass which (according to observation) is not found in any actual stars.]
[Footnote 38: This increase was assumed in our detailed description of the automatic adjustment of the star, and it will be seen that it was essential to assume it.]
