CHAPTERS ON THE STARS. 459 



6ite regions of the heavens, so as to eliminate any constant error de- 

 pending 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 per- 

 centage 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 oppo- 

 site direction with a greater speed than that of the sun. We con- 

 clude, 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. Mul- 

 tiplying 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 prob- 

 lem, that of the distribution of the stars in space. While we cannot 



