The only stars whose weights can be measured directly are the components of binary systems, and these are relatively few in number. Seares found, however, that the weights of binary systems conformed to the law of equipartition of energy already explained in Chapter III, so that it is highly probable that other stars which are not binary also conform, for it is difficult to imagine any reason why binary systems should attain to a state of equipartition sooner than other stars. It will be remembered that this state is defined by a purely statistical law connecting the weights and speeds of motion of stars, so that the fact that a system of stars has attained this state can give no information as to the weight of an individual star whose speed is known, but it makes it possible to determine the average weight of any group of stars in terms of their average speeds of motion. In this way Seares has determined the average weights of stars of different assigned luminosities and spectral types—in other words, the average weights of the stars represented at the various points in the diagram of fig. 22. The results he obtained are shewn by the thick curved lines in fig. 23. The arrangement of these curves confirms the inference we have drawn from a few selected stars; the weight of main-sequence stars falls off steadily as we pass down the sequence from high luminosity to low. These curved lines specify the average weight of the stars represented at each point in the Russell diagram, and the diameters are already known from fig. 22. From these two data the mean density of the star can of course be calculated. The mean densities as calculated by Seares are shewn by the broken lines in fig. 23. [Illustration: Fig. 23. Stellar weights and densities in the Russell diagram, according to Seares.] This completes our collection of observational material. We now turn to the far more difficult problem of discussing what it all means. Here we leave the firm ground of ascertained fact, to enter the shadowy morasses of conjecture, hypothesis and speculation. The questions we shall discuss are some of the most interesting in the whole of astronomy, to which it must be admitted that science has so far obtained only lamentably dusty answers. The reader who is hot for certainties may prefer to read something other than the remainder of the present chapter. THE PHYSICAL CONDITION OF THE STARS The foregoing collection of observational data has provided abundant proof that stars to certain specifications do not exist at all. To put the same thing in another way, there are certain regions in the Russell diagram which are wholly unoccupied by stars.