308 Professor Dr. J. G. Kapteya [May 22, 



2" per century, etc. For the larger motions the limits have been taken 

 somewhat wider. In the 11th box the motions 10" to 15" are 

 contained ; in the 13th those between 20" and 30" ; and so on. The 

 number of star-cards in each box has been inscribed on the lower 

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

 that there are in the sky 90 stars of the 5th magnitude, having a 

 proper motion between 0" and 1" per century. We have thus 

 arranged the stars according to both the rougli 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 letters MD 

 prefixed. 



Already we may see now how incorrect it is to imagine all the 

 stars of the 5th 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 11 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 86 stars in our 6tli box (see Fig. 3) are at an average distance 

 of 248 light-years. Are we compelled to stop here and to assume 

 that the real distance of all the individual 86 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 5th magnitude, that 

 is, the whole of the 28 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 

 hind, and it would be impossible to say in how far the results 

 definitively to be obtained would be influenced. 



Happily there is an escape. 



For our last classification, the classification in the distance-boxes, 

 it is of no particular advantage that every individual star gets in its 

 proper distance-box. It will be sufficient to know how many stars 

 will finally be found in each distance-box. If this result is obtained, 

 we shall presently see how easy it becomes to study the problem put 

 at the beginning of this lecture. Our aim will be evidently reached 

 if we can find out how many per cent, of the stars in any one box 

 have such and such a distance. Now, in order to determine these 

 percentages, it will be sufficient to investigate a sample of our stars. 



