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 somewhat 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,
