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almost precisely with the observed one. This process has been carried out, more or less as here described, for a considerable number of regions of the sky, and from it results our knowledge of the velocities and directions of the streams. It is necessary to remark that what here concerns us is motion projected on the sky, that is transverse motion. As attention is turned from one region of the heavens to another, the stream motions will present themselves in different aspects. For example, there are two points of the sky where the transverse motions of the two streams are identical, and the only difference is in the radial motions, with which we are not here concerned. At these points it would be impossible to detect the presence of two streams, and the individual motions would seem to be haphazard. The full information as to the streams can only be found by comparing results from different parts of the sky.
In order to form a clearer view of the significance of the phenomena now revealed, let us abandon the solar system, which has hitherto served as the reference point, and transfer ourselves to the centre of gravity of the stars here considered. Looked at from this point the streams must be moving in directions exactly opposite to one another. It is perhaps not easy to realise that the inclination of the two star-streams is a purely relative phenomenon depending entirely on the point of reference chosen; but this is the case. If we divest our minds of all standards of rest, and contemplate simply two objects in space, the two star-streams, all that can be said is that they are moving towards or away from or through one another along a certain line. This line, the direction of relative motion of the two streams, is a very important and fundamental axis; for it is an axis of symmetry of distribution of stellar motions. The points in which it meets the celestial sphere are called the Vertices. If, as seems to be the case, the number of stars belonging to the two streams is the same, the velocities of the two streams referred to the mean of the stars must be equal. The results, regarded from this new standpoint, can be given numerically. Each star has a streamvelocity of about 26 kilometres per second directed towards R. A. 5h 44m, Dec. 24°, or towards the opposite point according as it belongs to Stream I or to Stream II: in addition it has its own peculiar motion, equally likely to be in any