CHAPTERS ON THE STABS. 451 



parallactic motion of a star lying at right angles to the direction of the 

 solar motion during the time that the sun, by its proper motion, is pass- 

 ing over a space equal to the radius of the earth's orbit, is equal to 

 the parallax of the star. For this parallax is simply the angle sub- 

 tended by that radius as seen from the star; and the same angle is 

 the difference in direction of the star as seen from the two ends of 

 the radius. 



As yet, the actual amount of the sun's motion has not been well 

 determined. Kapteyn's estimate is 16.7km. per second, which may be 

 called 10 miles. But the results of additional determinations of radial 

 motions make it likely that this result should be increased to perhaps 

 19 or 20km. per second, or 4 radii of the earth's orbit per year. Ac- 

 cepting this speed we shall have the following rule: 



The parallax of a star lying in a direction nearly at right angles to 

 that of the solar motion is equal to one-fourth of its parallactic mo- 

 tion in a year. 



In the case of stars in other directions, the parallax would be greater 

 in proportion to the cosecant of the angle between the direction of 

 the star and the solar apex. 



If the stars were at rest this rule would enable us immediately to 

 determine the distance of any star by its proper motion, which would 

 then be simply the parallactic motion itself. Unfortunately, in the 

 case of any one star considered individually, there is no way of de- 

 ciding how much of its motion is proper to itself and how much is 

 the parallactic motion. But when we consider the great mass of 

 stars, it is possible in a rough way to make a distinction between the 

 two motions in a general average. 



The direction or motion of any particular star having no reference 

 to that of the sun is as likely to be in the direction of one of the three 

 components we have described as of any other. Hence, in the average 

 of a great number of stars we may conclude that these components are 

 equal. 



One of the simplest applications of this law will enable us to 

 compute the mean parallax of the stars whose radial motions have 

 been determined. As this application is, in the present connection, 

 made only for the purpose of illustration, I shall confine myself to the 

 47 stars of which the radial motions have been measured by Vogel. 

 The mean annual proper motions of these stars, taken without any 

 regard to their signs, are: 



Including Arcturus. Omitting Arcturus. 



n tt 



In right ascension 0.163 0.144 



In declination 0.155 0.168 



The difference of the mean motions in right ascension and 



