312 



ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1908. 



nitiicle in each of the rows. The stars of the boxes of figure 2 are 

 thus, of course, all contained in the vertical row of boxes, correspond- 

 ing to apparent magnitude 5 in figure 4. 



DISTEIBUTION ACCORDING TO DISTANCE ILLUSTRATED BY EXAMPLE. 



In order to illustrate by an example how the stars of the boxes in 

 our figure 3 are distributed over our different shells, that is over our 

 distance boxes of figure 2, take the seventh box. It contains 77 stars 

 at a mean distance of 220 light years. Our countings on the sample 

 showed that about one-fifth of the stars have true distances which are 



Fig. 3. — Distance Boxos. 



between 37 and 59 per cent of their mean distance (derived from their 

 apparent magnitude and proper motion). Therefore about one-fifth 

 of our 77 stars must have true distances between 37 and 59 per cent 

 of 220 light years; that is, between 82 and 130 light years; or, finally, 

 15 stars of our box must find their place in the fifth shell of figure 1; 

 that is, in the box corresponding to the fifth apparent magnitude in 

 that shell. In precisely the same way I find that 21 of them must be 

 placed in the sixth shell, 18 in the seventh, 10 in the eighth, and so on. 

 If, after that, we repeat the process for all the remaining boxes of 

 figure 2, we get, for the fifth apparent magnitude, the numbers in- 

 scribed on the lower side of the boxes corresponding to that magni- 

 tude in figure 4. 



