may be vastly greater than we have described it; but this consideration would not act to increase the radius of the actual stellar system in the direction of the poles of the galaxy by any appreciable amount.
Investigations conducted principally at the Harvard and Greenwich Observatories indicate that the number of stars visible in our largest telescopes is of the order of 60,000,000 or 70,000,000, and that the number which can be recorded on photographic plates by means of long exposures with our largest reflecting telescopes is several times as great.
Investigations by Newcomb and Kelvin upon the gravitational power of the stellar universe to produce the observed velocities of the stars give indications that the visible stars contain in reality only a fraction, perhaps one fifth, of the gravitating materials concerned, and they conclude that more material exists in dark and invisible stars than in the visible ones. I am inclined to regard their estimates of dark material as of questionable accuracy, on account of the purely arbitrary assumptions involved.
It is necessary that we consider briefly the motions of the stars, including that of our own star. It has been found that all celestial bodies, as far as they have been studied, are in motion with reference to the entire system, and with reference to each other. Our Sun is no exception to the rule: it is traveling rapidly through the stellar system, carrying its planets and their satellites along with it. The apparent motions of the individual stars are not in general their real motions: they are a compound of the real motions and of our motion. If the other stars were really at rest in the great system, they would still seem to be moving because our star is carrying us past them, so to speak: the nearer stars would seem to be moving rapidly, and the more distant stars less rapidly, away from that point in the sky which we are approaching. Since the stars are really moving in a great variety of directions, with a great variety of speeds, their apparent motions are also in a great variety of directions, but the prevailing tendency of their motions is away from our goal.
By studying these compounded motions, Herschel, in 1783, and a long line of distinguished investigators following Herschel, have established that our solar system is traveling toward a point in distant space about on the boundary line between the constellations Hercules and Lyra. If the solar system is moving rapidly toward that point, the stars in that vicinity should, on the average, seem to be approaching us, and the stars in the opposite region of the sky should, on the average, seem to be receding from us. The spectrograph enables us to measure the rates of approach and recession of the individual stars. It has been found that while the hundreds of bright stars in the Hercules-Lyra region are traveling, some away from us and some toward us, with