site regions of the heavens, so as to eliminate any constant error depending on the right ascension. The result of a count of 733 stars is:
| Number | of | positive | motions | 530 | |
| " | " | zero | " | 50 | |
| " | " | negative | " | 153 |
If we proceed as before, dividing the zero motions equally between the positive and negative ones, we shall find the respective numbers to be 555 and 178. The percentage of negative motions is, therefore, 24. This will still be slightly too large, owing to the obliquity under which many of the stars were seen. We may estimate the most likely percentage as 23.
We conclude, therefore, that when the motions of all the stars are so resolved that one component shall be that in the direction of the apex, 23 per cent, of the stars will be found moving toward the apex with a greater speed than that of the sun. It may, therefore, be assumed that in the general average an equal number are moving in the opposite direction with a greater speed than that of the sun. We conclude, therefore, that the resolved motion of 46 of the stars is greater than of the sun, leaving 54 per cent. less.
In the absence of an exact knowledge of the relation between the magnitude and the number of motions, we shall not be far wrong in assuming that one-half the stars move to or from the apex with more than the average speed, and one-half with less. Comparing this with the percentage found, we may conclude that the average motion of a star is less than that of the sun, in the ratio 46:50; or that it is found by multiplying the motion of the sun by the factor 0.92. This is almost exactly the number which we have quoted from Kapteyn.
We have already stated that the actual speed of the solar motion, still somewhat uncertain, may be estimated at 20 kilometers per second, or 4 radii of the earth's orbit in a year. For our present purposes the latter method of expressing the velocity is the more convenient. Multiplying this speed by the factors already found, we have the following results for the average proper motions of a star in space expressed in kilometers per second, and radii of the earth's orbit in a year:
| Straight-ahead motion | 37km. | = | 7.4r. |
| Projected motion | 29km. | = | 5.8r. |
| Motion in one component | 19km. | = | 3.7r. |
The motion of 20km. or 4r. assigned to the sun is its straight-ahead motion. This is little more than half the average. It follows that our sun is a star of quite small proper motion.
THE DISTRIBUTION OF THE STARS IN SPACE.
We shall now bring the lines of thought which we have set forth in the preceding chapters to converge on our main and concluding problem, that of the distribution of the stars in space. While we cannot
