308 ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1908. 



WHAT WE KNOW ABOUT STAR DISTANCE. 



By direct measurement we know the distance of some hundred 

 individual stars. 



For the rest we know the average distance of any fairly numerous 

 group of stars of determinate apparent magnitude and apparent 

 motion.'^ 



The question is: Can this imperfect knowledge of the distances 

 be considered as in any wise sufficient for obtaining an insight into 

 the real arrangement of the stars in space? 



I tliink it can, and I will now try to show in what manner. 



LOCALIZATION OF THE STARS IN SPACE BY A SORTING PROCESS. 



The method may be best explained as a sorting process. The proc- 

 ess was not actually followed ; it would have been too laborious and 

 would have met with some difficult3\'^ But the difference is imma- 

 terial, and the present description has, I think, the advantage in 

 point of clearness. 



Let each of the stars of the second, third, etc., to the eighth mag- 

 nitudes be represented by a little card on which are inscribed the 

 apparent magnitude and the apparent proper motion of the star. 



Then imagine three sets of boxes. 



CLASSIFICATION ACCORDING TO MAGNITUDE. 



First set. Ayparent magnitude boxes represented in fcjure 1. 



In the box for the second apparent magnitude, as many cards are 

 put as there are stars of the second nnignitude in the sk}'. The total 

 numbers of stars for each magnitude are inscribed on the lid. We 

 thus see that there are in the Avhole of the sky 46 stars of the second 

 magnitude, 134 of the third, and so on. 



•^At the preseut moment some objection might certainly still be made against 

 the generality of this statement. In fact, the scarcity of spectroscopic data is the 

 cause that, though the determination of the solar motion separately for such 

 .groups as the stars of determinate magnitude and proper motion is quite pos- 

 sible, it has not yet been carried through. As a consequence the results used in 

 what follows still rest on the assumption that the centers of gravity of all the 

 groups considered are at rest relative to each other. That this assumption 

 must be probably true, follows from the near identity of the direction of the 

 sun's motions, furnished by the several groups. 



^ For many of the stars used the proper motion is still not known. What is 

 known, however, is the percentage of the stars of each magnitude having a 

 determined proper motion. This knowledge enables us to put in every box the 

 required number of cards showing a determined proper motion, and this is all 

 that is wanted in what follows. 



