452 POPULAR SCIENCE MONTHLY. 



declension is to be regarded as accidental. The velocity of Arcturus 

 is so exceptionally great that we ought, perhaps, to leave it out in 

 taking the mean. 



Now, the mean of the radial motions as found by Vogel is 

 16 kilometers per second. By hypothesis the actual motion in the 

 radial line is in the general average the same as in the other two 

 directions. We have, therefore, to acquire what must be the parallax 

 of a star in order that, moving with a velocity of 16 kilometers per 

 second, its angular proper motion may have one of the above values. 

 This result is by a simple computation found to be: 



From the mean motion in R. A 0.049 or 0.043 



From the mean motion in Dec 0.064 or 0.035 



The difference of these results shows the amount of uncertainty of 

 the method. Our general conclusion, therefore, is that the mean par- 

 allax of the Vogel stars, which may be regarded as corresponding 

 approximately to the mean parallax of all the stars of the second 

 magnitude, is about 0".04. 



We have spoken of the two components of the apparent motion 

 as those in right ascension and declination, respectively. But there 

 is no particular significance in the direction of these coordinates, 

 which have no relation to the heavens at large. For some pur- 

 poses it will be better to take as the two directions in which the 

 motions are to be resolved that of the parallactic motion and that 

 of right angles to it. That is to say, taking the solar apex as a 

 pole, we conceive a line drawn from it to the star, and resolve the 

 apparent motion upon the celestial sphere into two components, the 

 one in the direction of this line, the other at right angles to it. 

 The former, which we may call the apical motion, is affected by the 

 parallactic motion; the latter, which we call the cross-motion, is not, 

 and therefore shows the true component of the motion of the star itself 

 in the direction indicated. 



Kapteyn has gone through the labor of resolving all the proper mo- 

 tions of the Bradley stars given by Auwers, in this way. His assumed 

 position of the solar apex was: 



Eight ascension 276°=18h. 24m. 



Declination* -(-34° 



The radically new treatment found in this paper embraces three 

 points. The first consists in the distinction between the spectral types 



*This work of Kapteyn is yet unpublished. The author is indebted to his 

 courtesy for the manuscript copy, with permission to use it. Kapteyn's researches 

 based on this material are contained in a paper on the 'Distribution of the Stars 

 in Space,' communicated to the Amsterdam Academy of Science, January 28, 

 1893. An abstract in English is found in 'Knowledge' for June 1, 1893. 



