Our use of Jeans' data interposes another and equally insuperable difficulty to any tidal hypothesis. Four billion miles is a very short distance in the eyes of an astronomer. At that distance a star twice the size of the sun would attract the outer planets more strongly than the sun itself, and might capture them. If a star should come within four billion miles of the sun, its effect in distorting the orbits of all the planets would be great. If this had happened often enough to cause all the glaciations known to geologists, the planetary orbits would be strongly elliptical instead of almost circular. The consideration here advanced militate so strongly against the tidal hypothesis of solar disturbances that it seems scarcely worth while to consider it further. Let us turn now to the electrical hypothesis. Here the conditions are fundamentally different from those of the tidal hypothesis. In the first place the electrostatic effect of a body has nothing to do with its mass, but depends on the area of its surface; that is, it varies as the square of the radius. Second, the emission of electrons varies exponentially. If hot glowing stars follow the same law as black bodies at lower temperatures, the emission of electrons, like the emission of other kinds of energy, varies as the fourth power of the absolute temperature. In other words, suppose there are two black bodies, otherwise alike, but one with a temperature of 27 deg. C. or 300 deg. on the absolute scale, and the other with 600 deg. on the absolute scale. The temperature of one is twice as high as that of the other, but the electrostatic effect will be sixteen times as great.[115] Third, the number of electrons that reach a given body varies inversely as the square of the distance, instead of as the cube which is the case with tide-making forces. In order to use these three principles in calculating the effect of the stars we must know the diameters, distances, temperature, and number of the stars. The distances and number may safely be taken as given by Jeans in the calculations already cited. As to the diameters, the measurements of the stars thus far made indicate that the average mass is about twice that of the sun. The average density, as deduced by Shapley[116] from the movements of double stars, is about one-eighth the solar density. This would give an average diameter about two and a half times that of the sun. For the dark stars, we shall assume for convenience that they are ten times as numerous as the bright ones. We shall also assume that their diameter is half that of the sun, for being cool they must be relatively dense, and that their temperature is the same as that which we shall assume for Jupiter.