STELLAR ASTRONOMY 



415 



less extended area, the centre of gravity of which might be taken as 

 the most probable position of the Apex. 



The position of the Apex being once determined, if we draw the 

 great circles Apex II; Apex III (see Fig. 3), and take these as 



FIG. 3. 



the axes of the x for the points II, III, . . . then if our fundamental 

 hypothesis is approximately true, we must find the condition of 

 symmetry ly = satisfied, with a certain degree of approximation 

 for all the points II, III . . . 



Not only that, but we shall have further to expect that any other 

 condition of symmetry will be also approximately fulfilled for every 

 point. Such another condition will be, for instance, that on both 

 sides of the great circles through the Apex the total quantity of proper 

 motion shall be the same ; or again that Ix shall be the same on both 

 sides of these circles. How the first of these conditions is satisfied is 

 shown in Fig. 3. 



This figure summarizes the more important points in regard to 

 the question in hand, furnished by a treatment of the stars observed 



