In the stellar problem, we are dealing with very different lengths of time; collisions only occur at intervals of thousands of millions of millions of years. If the stars only redistributed their energy when actual collisions occurred, we might surmise that a close approximation to equipartition of energy would not be attained until after each star had experienced eight or ten collisions, and this would require a really stupendous length of time. Actually no such length of time is needed because the numerous gravitational pulls, even between stars which are at a considerable distance apart, equalise energy far more efficiently and expeditiously than the very rare direct hits. Every time that two stars happen to pass even fairly near to one another in their wanderings, each pulls the other a bit out of its course, and the directions and speeds of motion of both stars are changed—by much or little according as the stars pass quite close to one another or keep at a substantial distance apart. In brief, each approach of stars causes an interchange of energy, and after sufficient time, these repeated interchanges of energy result in the total energy being shared equally, on the average, between the stars, regardless of differences in their weights. Now the crux of the situation, to which all this has been leading up, is that observation shews that stars of different weights are moving with different average speeds, these average speeds being such that equipartition of energy already prevails among the stars—not absolutely exactly, but to a tolerably good approximation. The question of how long the stars must have interacted to reach such a condition now becomes one of absolutely fundamental importance, for _the answer tells us the ages of the stars_. STELLAR VELOCITIES. We have already seen (p. 48) how stars which form binary systems can be weighed, such weighings disclosing weights ranging from about a hundred times the weight of the sun to only a fifth of its weight. The speeds of motion of binary systems can be measured in precisely the same way as the speeds of single stars. As far back as 1911, Halm, with an accumulation of such measurements before him, pointed out that the heaviest stars moved the most slowly. He found that, on the average, the heaviest of known stars had approximately the same energy of motion as the lightest, the high speeds of the latter just about making up for the smallness of their weights, and so suggested that the velocities of the stars, like those of the molecules of a gas, might be found to conform to the law of equipartition of energy. It appeared to be a case of Brownian movements on a stupendous scale.