420 ASTROMETRY 



diametrically opposite. For the sake of brevity I shall call the points 

 of the sphere toward which the star-streams seem to be directed 

 the vertices of the stellar motion. 



The apparent vertices were thus provisionally found to lie south 

 of a Orionis and r) Sagittarii. Knowing with some approximation 

 both the velocity of the sun's motion and the mean velocity of the 

 stars, it is easy to derive from the apparent position of the vertices 

 their true position, which must lie at diametrically opposite points 

 of the sphere. 



Having once got what I considered to be the clue to the system- 

 atic divergences in the proper motions, and having at the same time 

 obtained an approximation for the position of the vertices, I have 

 made a more rigorous solution of the problem. 



The existence of two main stream-lines does not imply that the 

 real motions of the stars are all exclusively directed to either of the 

 two vertices; there only is a decided preference for these directions. 

 I have assumed that the frequency of other directions becomes 

 regularly smaller as the angle with the main stream becomes greater, 

 according to the most simple law of which I could think, which makes 

 the change dependent on a single constant. 



I have as yet only finished a first approximation to this solution. 

 The result is that one of the vertices lies very near to Orionis. 

 (a mo =6 n 2 m ; <5 mo = +135). The other, diametrically opposite, is 

 not near any bright star. They have been represented by the letter 

 V in Fig. 3. They lie almost exactly in the central line of the Milky 

 Way. Adopting Gould's coordinates of the pole of this belt, I find 

 the galactic latitude to be two degrees. I shall pass over the other 

 quantities involved. I shall only mention that the way in which 

 I conducted the solution points to the conclusion that all the stars 

 without exception belong to one of the two streams. 



To my regret I cannot give the detailed comparison of theory 

 and observation, because the detailed determination of the distri- 

 bution of the proper motions from the data of our solution is such 

 a laborious question that I have not yet made it, and would rather 

 defer it till the real existence of the streams shall have been put 

 beyond reasonable doubt by other observations presently to be con- 

 sidered. I shall only state that by this provisional solution the total 

 amount of dissymmetry for our 28 regions is reduced for the x com- 

 ponents as well as for the y components to about a third of the 

 amount they reach in the hypothesis of the random distribution of 

 the directions. Moreover, they have lost their systematic character. 



The observations alluded to are those of the radial velocities. 



I suspect that the materials for a crucial test of the whole theory 

 by means of these radial velocities are even now on hand in the 

 ledgers of American astronomers. Alas, not yet in published form. 



