234 



NA TURE 



[July 9, igoS 



RECENT RESEARCHES IN THE STRUCTURE 



OF THE UNIVERSE.' 



II. 



Localisation of the Stars in Space by a Sorting Process. 



nPHE 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 



diflicultv.- But the difference is immaterial, and the 



K^.i. 



present description has, I think, the advantage in point 

 of clearness. Let each of the stars of the second, third, 

 &c., to the eighth magnitudes be represented by a little 

 card on which are inscribed the apparent magnitude and 

 the apparent proper motion of the star. 

 Tlien imagine three sets of bo.\es. 



Classification according to Magnitude. 



ist Set.^ — .Apparent magnitude bo.\es re- 

 presented in Fig. I. — In the box for the 

 second apparent magnitude, as many cards 

 are put as there are stars of the second 

 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 forty-six stars of the 

 second magnitude, 134 of the third, and 

 so on. 



According to Magnitude and Proper 

 Motion. 



2nd Set. — Magnitude-motion bo.xes (Fig. 

 3). The stars in each of the former series 

 of boxes are re-distributed 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 twenty-eight 

 new boxes. In the first have been collected 

 the cards representing the stars witli a 

 proper motion of o" to i" 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 Discourse delivered at the Royal Institution on Friday, May 22, by 

 Prof. J. C. Kapteyn. Continued from p. 212. 



- 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 

 s all that is wanted in what follows. 



NO. 2019, VOL. 78] 



i" and 2" per century, S:c. For the larger motions the 

 limits have been taken somewhat wider. In the eleventh 

 box the motions 10" to 15" are contained, in the thirteenth 

 those between 20" and 30", and so on. The number of 

 star-cards in each bo.x has been inscribed on the lower 

 right-hand corner of the lid. The figure thus shows, for 

 instance, that there are in the sky ninety stars of the 

 fifth magnitude having a proper motion between o" and i" 

 per centurv. We h.ave thus arranged the stars according 

 to both the rough criteria of distance 

 at our disposal ; for we know perfectly 

 well that in a very general way the 

 fainter the stars and the smaller their 

 apparent motion the further they must 

 be away. 



For each of the groups thus obtained 

 we are now able, according to what has 

 been said before, to derive the mean 

 distance. This determination being 

 made, we obtain the mean distances 

 expressed in light-years which have 

 been inscribed on the lid with the letter 

 MD prefixed. .Already we may see now 

 how incorrect it is to imagine all the 

 stars of the fifth magnitude to be 

 placed at one and the same distance, 

 as Struve did. According to the 

 numbers in our figure, the distance 

 varies from 1670 light-years for the 

 stars of the first box to eleven light- 

 years for those of the last. It is true 

 that just the data for these extreme 

 boxes are the most uncertain ; still, it is 

 evident that even in these mean distances there must be 

 an enormous range. 



But to proceed. The eighty-six stars in our sixth box 

 (see Fig. 3) are at an average distance of 248 light-years. 



ric2. 



Are we compelled to stop here and to assume that the 

 real distance of all the individual eighty-six stars is 248 

 light-years? If it were so we would surely still have 

 gained a considerable advantage over Struve. For, owing 

 to want of other data, he saw himself compelled to treat 

 all the stars of the fifth magnitude, that is, the whole of 

 the twenty-eight groups in our boxes, as if they were all 

 at the mean distance of the whole. But yet there would 

 remain in our solution a defect of the same kind, and it 



