[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.
[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.
[5] The mean density of Capella is nearly the same as the density of the air.
[6] Unless otherwise indicated ‘gaseous’ is intended to mean ‘composed of perfect gas’.
[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.
[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.
[9] Rougher estimates were made much earlier.
[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.
[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’.
[11] The mass-luminosity relation was not suspected at the time of which I am speaking.