1908] on Recent Researches in the Structure of the Universe. 307 



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



Localisation of the Starr in Space by a Sorting Process. 



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

 process was not actually followed, it would have been too laborious 

 and would have met with some difficulty.* But the difference is 

 immaterial, and the present description has, I think, the advantage 

 in point of clearness. 



Let each of the stars of the 2nd, 8rd, etc., to the 8th magnitudes 

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

 magnitude and the apparent proper motion of the star. 



Then imaojine thi'ee sets of boxes. 



Classification according to Magnitude. 



\st Set. — Apparent magnitude boxes represented in Fig. 1. — In the 

 box for the 2nd apparent magnitude, as many cards are put as there 

 are stars of the 2nd magnitude in the sky. The total numbers of 

 stars for each magnitude are inscribed on the lid. We thus see that 

 there are in the whole of the sky, 46 stars of the 2nd magnitude, 

 134 of the 3rd, and so on. 



According to Magnitude and Proper Motion. 



2nd Set. — Magnitude-motion boxes (Fig. 3). The stars in each of 

 the former series of boxes are redistributed over a series of boxes, 

 each of them containing stars of a determined apparent motion. By 

 way of an example, Fig. 3 shows this new classification for the stars of 

 the fifth apparent magnitude. There is of course another such series 

 for each one of the apparent magnitudes. Those for the fifth have 

 been distributed over 28 new boxes. In the first have been collected 

 the cards representing the stars with a proper motion of 0" to 1" per 

 century. The average motion is 0*5, and this has been inscribed 

 on the lid. The little arrow indicates that this number represents a 

 motion. The number 5 surrounded by a star refers to the fact that 

 we have exclusively to do with stars of the fifth apparent magnitude. 

 The second box contains the stars with proper motion between 1" and 



* 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 numher of cards showing a determined proper motion, and this is all 

 that is wanted in what follows. 



X 2 



