We may accordingly feel every confidence in the calculated diameters of all stars, even when these cannot be checked by direct measurement. Indeed a discrepancy between the true and calculated diameters could only arise in one way. The diameters are calculated on the assumption that the stars emit their full temperature-radiation. If the stars had been partially transparent like the nebulae, or solid bodies like the moon, this assumption would have been false, and its falsity would at once have been shewn by discordances between the calculated and measured diameters of the stars. The fact that no large discordances appear suggests that the stars emit nearly full temperature-radiation throughout the whole range of size from the largest to the smallest. THE VARIETY OF STARS Observation shews that the physical characteristics of the stars vary enormously, so that it is easy, as we shall soon see, to tell a sensational story by contrasting extremes, setting the brightest against the dimmest, the biggest against the smallest, and so on. This would, however, give a very unfair impression of the inhabitants of the sky; it would be like judging a nation from the giants and dwarfs, the strong men and the fasting men, seen inside the showman’s tent. We shall obtain a more balanced impression of the actual degree of diversity shewn by the stars as a whole if we consider the physical states of those stars which are nearest the sun. By taking these precisely in the order in which they come, we avoid any suspicion of going out of our way to introduce stars merely because they are bizarre or exceptional. The small group of stars obtained in this way may be expected to form a fair sample of the stars in the sky, although of course it will not be a large enough sample to include extremes. We need not discuss the sun itself in detail because it will figure as our standard star, with reference to which all comparisons are made. _The System of α Centauri._ This system consists of three constituent stars, which are believed to be our three nearest neighbours in space. The brightest, α Centauri _A_, is very similar to the sun. It is of the same colour and spectral type, but weighs 14 per cent. more and is about 12 per cent. more luminous. Being of the same colour as the sun, it emits the same amount of radiation per square inch. Thus its 12 per cent. greater luminosity shews that it must have a surface 12 per cent. greater, and therefore a diameter 6 per cent. greater, than the sun.