322 POPULAR SCIENCE MONTHLY. 



Each of these zones cuts the galaxy at a considerable angle. Each 

 zone, as a matter of course, has a far larger richness of stars per unit 

 of surface in the galactic region than in the remaining region. We, 

 therefore, divide each zone in four strips, two including the galactic 

 regions and two the intermediate region. The boundaries are some- 

 what indefinite: we have fixed them by the richness of the total number 

 of stars. For the galactic strips we take in Boss's zone the strip between 

 5h. and 8h. of B. A. and that between 17h. and 20h. Each of these 

 strips being 3h. in length, the two together comprise one-quarter the 

 total surface of the zone. If the proper motion stars crowd towards the 

 galaxy like others do, then the numbers in the galactic region should be 

 proportional to the total number observed in the region. But if they are 

 equally distributed then there should be only one-quarter as many in the 

 galactic region as in the other regions. 



In the case of Boss's zone, the total number of stars observed and 

 of those having a proper motion found in the four regions described are 

 as follows: 



Total Number Proper Motions. 

 Observed. Actual. Prop. 



Galactic strip, 5h. to 8h 1,614 24 37 



Galactic strip, 17h. to 20h 1,340 36 37 



Intermediate strip, 8h. to 17h 2,458 124 111 



Intermediate strip, 20h. to 5h 2,831 111 111 



The last column contains the number of proper motions we should 

 find if the whole 295 were distributed proportionally to the areas of 

 the several strips. There is evidently no excess of richness in the 

 galactic strips, but rather a deficiency in the strip near 6h., which is 

 accidental. 



In the case of Auwers's zone, the galactic strips are those between 

 5h. and 8h., and again between 18h. and 21h. Here, as in the other 

 case, the galactic strips include one-quarter of the whole area. But, 

 owing to the greater richness of the sky, they include nearly 40 per cent, 

 of the whole number of stars. Then, if the proper motion stars are 

 equally distributed, one-quarter should be found in the region, and if 

 they are proportional to the number of stars observed, 40 per cent, 

 should be within this region. Grouping the regions outside the galaxy 

 together, as we need not distinguish between them, the result is as 

 follows: 



Stars Proper Motions. 



Observed. Actual. Prop. 



Galactic strip, 5" to 8" 1,797 155 157 



Galactic strip, 18" to 21" 1,984 202 157 



Outside the galaxy 6,008 901 944 



We see that in the strip from 5h. to 8h. there is contained almost 

 exactly one-eighth the whole number of proper motion stars. That is, 



