opposite points, but simply that their components of motion parallel to this line are considerably greater, on the average, than the components in any other direction. We may visualize his ideas in the following manner:
Assume the existence, ages ago, of a great cluster or cloud of stars distributed more or less uniformly through a certain vast volume of space, whose individual motions were at random in both magnitude and direction. Assume the existence of an entirely similar group of stars, occupying another vast volume of space, whose internal motions were also at random. Assume, further, that these two groups of stars were traveling through space in such a way that they more or less completely interpenetrated, with the result that the two groups of stars have now become a single group. There are stars still moving in all directions, with speeds of all dimensions within certain limits, and yet there exists a preference for motion along and parallel to the line which originally joined the centers of the two groups. Assume now that our Sun is carrying the terrestrial observer through the combined group in a direction making a considerable angle with the line of preferential motion: the apparent motions of the individual stars, as observed from the solar system, would then have preferences for two directions very different from the line joining the two original positions of the groups; we should find a great number deviating by small angles from the two preferential directions, a small number deviating to a greater extent, and relatively few whose motions make large angles with the preferential directions; and this is as the apparent motions of the stars have been determined by many observers.
Kapteyn's results depend upon proper motion data; that is, upon their apparent motions on the surface of the sky. Spectroscopic observations of stellar motions of approach and recession confirm that the stars have preferential motions, but to a smaller degree than proper motion data had indicated.
No one doubts that preferential motions exist, but the explanation is another matter. Kapteyn does not insist that our stellar system has actually resulted from the intermingling of two star streams, yet he inclines more and more to this point of view, and the hypothesis does seem to accord better with the observed facts than any other hitherto proposed. A strong objection to it is its apparent improbability. It does not seem reasonable that two great clouds of stars, containing all the stars now in our sidereal universe, should have come together and interpenetrated so completely as to have produced in an age when we happen to be the observers a stellar system apparently spheroidal in form. When I look at the Milky Way, completely encircling the sky, my mind is filled with doubt. And if two great galaxies of stars have traveled far and come together, they will travel further and through each other and we shall have two galaxies again, moving away from each other. It does
