558 ANNUAL, REPORT SMITHSONIAN INSTITUTION, 1923 



together in pairs or even in large groups were known. As early 

 as 1896, however, Kapteyn had noticed that the distribution of mo- 

 tion was not at random, but it was not until 1904 that he showed 

 that there is a fundamental peculiarity in these motions and that 

 they are not moving even approximately in a haphazard way. In- 

 stead of moving in all directions, as a random distribution would 

 require, the stars tend to move in two preferential directions. That 

 this tendency was so long overlooked by those who were working 

 on a determination of the solar motion is principally due to the 

 fact that they used the mean motions of all the stars in certain parts 

 of the sky. Kapteyn, however, went to work in a different way, 

 plotting the proper motions for limited regions of the sky. If for 

 convenience sake we assume all the stars in a certain region to be 

 located in the same point S of the sphere, then with a random dis- 

 tribution of the motus peculiaris alone, we find about the same num- 

 ber and about the same total motion in each direction. A motion 

 of the observer, such as we have as a result of the sun's motion 

 through space, will add to each star a parallactic motion in the direc- 

 tion of the antapex. While this of course will disturb the symmetry of 

 the motions around the point S, we still will have bilateral symmetry, 

 the line of symmetry evidently passing through the point S and the 

 apex. This evident condition of bilateral symmetry would probably 

 furnish the best means of determining the apex, as these lines of 

 symmetry for the different parts of the sky must all intersect in two 

 points, the apex and the antapex. In applying this idea to the 

 proper motions of about 2,400 Bradley stars, divided into 28 regions, 

 Kapteyn derived the distribution of the proper motions correspond- 

 ing to the center of the areas. The whole of the material was thus 

 embodied in 28 figures, like those in Figure 2, each of which shows 

 at a glance the distribution of the proper motions for one particular 

 region of the sky. This figure 2 is the same as the one shown by 

 Kapteyn at the Cape meeting of the British Association for the 

 Advancement of Science in 1905. Not to overburden the plate, only 

 10 of the 28 regions are included. If the hypothesis of random dis- 

 tribution were true, all these figures should be symmetrical with 

 respect to the line through the center of each field and the apex. 

 It is clear that this is not the case; each figure shows two preferen- 

 tial deviations. Kapteyn showed that the assymetry as shown in 

 the figure can be explained neither by an uncertainty in the preces- 

 sion, nor by systematic errors in the proper motions, nor by an erro- 

 neous position of the apex. As all the lines of favored directions 

 for the two sets seem to converge, approximately, to two points, 

 some 140° apart, the one 7° south of a Orionis, the other a few de- 

 grees south of y] Sagittarii, Kapteyn came to the conclusion that we 



