418 ASTROMETRY 



ation, too, fails. Systematic motion of this kind will make the lines 

 of symmetry diverge from the great circles through the Apex. I 

 therefore investigated what becomes of our results if, for each of our 

 28 areas, I took for the line of symmetry, not the great circle through 

 the Apex, but the line which, for every particular area, satisfied rig- 

 orously the condition 2y=Q. 



Even with regard to these lines the character of the phenomenon 

 as shown by our table is not changed. This proves the inadmissibility 

 of an explanation by local common motion. As, moreover, in this 

 case the adopted position of the Apex plays no part whatever, it 

 proves, even more conclusively than the preceding consideration, 

 that the phenomenon exists independently of errors in the determin- 

 ation of the Apex. 



In order to find out, then, what may be the real cause of it, I finally 

 set to work as follows : 



I took in hand first the distribution of the numbers of the proper 

 motions over the angles of position counted from the line towards 

 the Antapex. The results found for all the regions lying nearly at the 

 same or at supplementary distances from the Apex (results which 

 would have been identical, had our fundamental hypothesis been 

 satisfied) were then combined. So, for instance, were the results of 

 12 such areas as those of Fig. 3, of which the sine of the distance from 

 the Apex lies between 0.90 and 1.00, summarized in a single set of 

 results. This set proved to be all but perfectly symmetrical and duly 

 gave the maximum frequency for the direction towards the Antapex. 

 For these reasons I felt myself justified in provisionally adopting 

 the set as representing the normal distribution for the corresponding 

 distance from the Apex. That is, I supposed that this distribution 

 would nearly represent the distribution corresponding to a set of 

 proper motions really fulfilling the fundamental hypothesis, cleared 

 of the inequalities which it is our purpose to find out. 



In the possession of this normal distribution we now at once 

 obtain these inequalities separately by simply subtracting the 

 normal number from the corresponding ones found directly from 

 observation for the separate regions. 



It thus appeared that these inequalities consist in a manifest 

 excess of proper motions in certain determinate angles of position. 



These favored directions have been carefully determined for each 

 of our 28 areas. The greater part of them clearly show two favored 

 directions; for a minority but one of the maxima is well developed. 

 Entering these favored directions on a globe, it appeared at once 

 that they all converge with considerable approximation towards 

 two points of the sphere. Here we have a clear indication that we 

 have to do with two star-streams parallel to the lines joining our 

 solar system with these two points. 



