416 ASTROMETRY 



completely by Bradley (over 2400 stars). They are distributed over 

 two thirds of the whole of the sky. This surface has been divided up 

 into 28 areas. From the stars contained on each area I have derived 

 the distribution of the proper motions corresponding to the centre 

 of the area. How this was done need not be here explained. The 

 whole of the materials were thus embodied in 28 figures like those of 

 Fig. 3. 



Not to overburden this figure, I have only included ten of the figures 

 for which the phenomenon to which I wish to draw your attention is 

 most marked. 



It is very suggestive that these lie all near to the poles of the 

 Milky Way. 



The figures have been constructed as follows. A line has been 

 drawn making the angle of 15 with the great circle through the Apex, 

 the length of which represents the sum of all the proper motions, 

 making angles of between and 30 with that circle. 



In the same way the radius vector at 45 represents the sum of 

 all the motions between 30 and 60, and so on. 



For the sake of uniformity all the results have been reduced to 

 what they would have been had the total number of stars been the 

 same for all the 28 areas. That part of the figure between the radii- 

 vectors making angles of zero and 60, +60 and +180, have been 

 blackened. 



The position adopted for the Apex is practically that found by 

 a variety of methods, all more or less akin to that described a moment 

 ago. 



If our fundamental hypothesis were satisfied, and if, in con- 

 sequence thereof, the symmetry of our figures were complete, the 

 blackened parts of the figure would have been equal to the correspond- 

 ing lighter-tinted parts. (This ideal case is represented in Fig. 1, R.) 



The real state of things is something quite different, and, what is 

 all-important, we see at once that the divergences are strikingly 

 systematic. The figures at each pole of the Milky Way show them in 

 nearly every particular of the same character. Near the North Pole 

 the blackened parts are invariably much greater; at the South Pole 

 the case is reversed. 



At a first glance the difference of the more extensive parts on the 

 side of the Antapex is probably more conspicuous. As a matter of 

 fact, however, the difference between the smaller parts is by no means 

 less important. 



For many of you the way in which the second of the above con- 

 ditions is fulfilled, or rather not fulfilled, will be still more convincing. 



For each of the 28 regions the mean value of the x component 

 of the proper motions has been computed, separately for those lying 

 on the two sides of the great circle through the Apex. Let X R , X L 



