surface brilliancy as the Sun, would express the ratio of density of the stars to that of the Sun. Actually, it gives the product:
Density x (brilliancy).2
The numbers in the last column being all less than unity, it follows that either the stars are much less dense than the Sun or they are of much less surface brilliancy. Moreover, they belong to a selected list in which the numbers of the last column are larger than the average.
To form some idea of the result of a selection from the general average, we may assume that the average of all the measured distances between the components of a number of binary systems is equal to the average radius of their orbits, and that the observed annual motion is equal to the mean motion of the companion in its orbit. Taking a number of cases of this sort, I find that the number corresponding to the last number of the preceding table would be little more than one thousandth.
A very remarkable case is that of ξ Orionis. This star, in the belt of Orion, is of the second magnitude. It has a minute companion at a distance of 2".5. Were it a model of the Sun, a companion at this apparent distance should perform its revolution in fourteen years. But, as a matter of fact, the motion is so slow that even now, after fifty years of observation, it cannot be determined with any precision. It is probably less than 0°.1 in a year. The number expressing the comparison of its density and surface brilliancy with those of the Sun is probably less than .0001.
The general conclusion to be drawn is obvious. The stars in general are not models of our Sun, but have a much smaller mass in proportion to the light they give than our Sun has. They must, therefore, have either a less density or a greater surface brilliancy.
We may now inquire whether such extreme differences of surface brilliancy or of density are more likely. The brilliancy of a star depends primarily not on its temperature throughout, but on that of some region near or upon its surface. The temperature of this surface cannot be kept up except by continual convection currents from the interior to the surface. We are, therefore, to regard the amount of light