a basis, our best course is to examine the most plausible hypotheses we can make as to the distribution of the stars which do not belong to the galaxy, and see which agrees best with observation.
Let Fig. 2 represent a section of the galactic ring or belt in its own plane, with the sun near the center S. To an observer at a vast distance in the direction of either pole of the galaxy, the latter would appear of this form. Let Fig. 3 represent a cross section as viewed by an observer in the plane of the galaxy at a great distance outside of it. How would the stars that do not belong to the galaxy be situated? We may make three hypotheses:
1. That they are situated in a sphere (A B) as large as the galaxy itself. Then the whole universe of stars would be spherical in outline, and the galaxy would be a dense belt of stars girdling the sphere.
2. The remaining stars may still be contained in a spherical space
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(K L), of which the diameter is much less than that of the galactic girdle. In this case our Sun would be one of a central agglomeration of stars, lying in or near the plane of the galaxy.
3. The non-galactic stars may be equally scattered throughout a flat region (M N P Q), of the grindstone form. This would correspond to the hypothesis of Herschel and Struve.
There is no likelihood that either of these hypotheses is true in all the geometric simplicity with which I have expressed them. Stars are doubtless scattered to some extent through the whole region M N P Q, and it is not likely that they are confined within limits defined by any geometrical figure. The most that can be done is to determine to which of the three figures the mutual arrangement most nearly corresponds.
The simplest test is that of the third hypothesis as compared with the other two. If the third hypothesis be true, then we should see the
