STELLAR ASTRONOMY 401 



For in the magnitude of a star can be no reason for a predilection 

 of the direction of its motion. It is erroneous, however, to apply it 

 to stars of which the total proper motion has any particular value. 



For there are three reasons which will make the apparent proper 

 motions of a star considerable. 



(a) Considerable linear velocity; 



(6) Small distance from the solar system; 



(c) Near coincidence of the direction of the parallactic and peculiar 

 proper motion, whereby the effect of the two is added. 



Therefore if, for instance, we select stars of very considerable 

 proper motions, we are certain to give a certain amount of preference : 



To stars of great linear velocity and to stars of small distance 

 from the sun, but also to stars the peculiar motion of which favors 

 the direction of the parallactic motion, that is, the direction toward 

 the Antapex. 



This is also seen at once from Fig. 1, Q. The greatest proper motions 

 there are : Sa, Sb, Sc, Sm, SI corresponding to the peculiar mo- 

 tions SA, SB, SC, SM, SL, in Fig. 1, P, which motions evidently favor 

 the direction Sx towards the Antapex. 



It is the neglect of this consideration which has led several astro- 

 nomers into error. 



We have now to face the question : 



Can we derive the general traits of the structure of the stellar 

 system by the aid of the distances derived from the parallactic 

 motion. I am convinced that we can, arid it is the real purpose of 

 this lecture to show in what manner. 



The most direct, though not the only way, I think, is that \vhich 

 begins by determining the mean parallax of stars of a determined 

 magnitude and a determined amount of proper motion. 



Though, as I explained just now, we cannot derive the parallax 

 of stars of a determined proper motion from the parallactic motion, 

 we can still gain our end somewhat indirectly, but pretty satis- 

 factorily, if to the data furnished by that motion we add what we 

 know by direct determination of parallax. 



The results thus obtained were embodied in a simple formula, in 

 a paper published a few years ago. 



For the sake of brevity I will call the parallax of any star com- 

 puted by this formula from its magnitude and proper motion its 

 mean or theoretical parallax. 



If for any individual star the true parallax were equal to this 

 theoretical one, we should of course know at once the distribution 

 in space of all the stars of which we know the apparent magnitude 

 and the proper motion. 



It need not be said that they will be generally unequal. 



Without knowing the individual parallaxes we may still find out 



