( 528 ) 



follows. It is a well-known fact that the astronomical proper motions 

 of the helium stars are small. We conclude that their distance must 

 be considerable. The mean distance of the stars of different spectral 

 type, for which the existence of the two star-streams has been 

 demonstrated, is undoubtedly much smaller. He concludes: "The 

 "two star stream.s probably involve at least half a million of the 

 "stars around us; but there has never been any evidence that thej 

 "prevail in the extremely remote parts, where the helium stars are 

 "thinly scattered." 



He thinks that the helium-stars must be almost entirely at rest. 

 The stream-motion which thev show, when the velocity is considered 

 relative to the sun, is entirely due to the motion of the solar system 

 itself. 



The theory is very attractive. The more so because it furnishes a 

 natural explanation of the fact, already mentioned, that the motion 

 of the helium-stars coincides, at least approximately, with that of the 

 centre of gravity of the two streams for the other stars. In our 

 theory this fact is not so easily explained. 



It is for this reason, tliat 1 kept back the preceding remarks, till 

 I should have found an occasion of testing Eddington's theory. Such 

 a test which seems to me ]>retty decisive, is possible in the following- 

 way. From the same materials which served Eddington for his last 

 investigation, i. e. from the stars of Boss' Preliminary Catalogue (the 

 helium-stars being excluded) I extracted the stars the proper motion 

 of which lies between 0".030 and 0".079. The average proper motion 

 is equal to that of those helium-stars — 40 percent of the total — 

 which have a proper motion ^ 0".030. There is every reason to 

 assume that the two classes of stars are approximatelj' at the same 

 distance. We thus have to find out whether or not these stars still 

 show the phenomenon of the two star-streams. The execution of this 

 plan led to the conclusion that the phenomenon is clearly shown; 

 it [is but little less evident than for the whole of the stars. That it 

 is 'somewhat less evident is probably sufficiently accounted for by the 

 greater influence of the errors of observation. Graphical representations 

 show the matter at a single glance. They are however too extensive 

 for this communication. 



Meanwhile we may demonstrate the matter almost as well hy 

 giving the quantities 



n. 4- n. 



e — iog-^JL-1 



n^ + ^4 

 for the several parts of the sky. The letter n^ represents the number 

 of stars for a determined region of the sky, for which the proper 



