The motion of the stars 



77 



OAving to the larae mean errors in F and Ai I should have attached no im- 

 portance to these values, were it not that they are found to be in good accordance 

 with the theoretical considerations alluded to above. 



Let' indeed, and denote the coordinates of that point on the north hemi- 

 sphere, which is unaffected by the found motion of our system of coordinates. Then 

 we must have 



0 = r (cos s cos + sin s sin sin a^) — sin 8^ cos 

 0 = r cos «y sin £ -f M sin a^,. 



The latter equation gives: 



r sin £ 



tg «0 = - 



and, from the first equation, we then get 



sm a„ 



Using the values of F and M, found above, we obtain: 



186».7, 



Stars, having these coordinates, or coordinates little diverging from these values, 

 are only inconsiderably affected by this motion of the system of coordinates. Now 

 the pole of the Milky Way has, according to Hodzeau and Gould, the coordinates 



rj.= J 91 ".25, 



8=-\- 27" 43. 



Tailing into account the mean errors in V and A/, we may conclude that the 

 proper motions of the stars are consistent with a slow motion of the invariable plane 

 in such a manner that this plane maintains a constant inclination to the plane of 

 the Milky Way. 



17. What is the amount of the motion of the node of the invariable plane 

 on that plane? 



For deciding this question, let w be the angular mean motion of the system 

 of coordinates about the instantaneous axis of rotation (which may be assumed to 

 coincide nearly with the axis of the plane of the Milky Way). We may substitute 

 for (0 its components — io^, (Hy and co; — about the three axis of the coordinates, 

 putting 



(Or = (0 COS §0 cos ap , 

 (45) (.<),/ — w COS sin a^, , 



= w sin Sp. 



The variation — àx, At/ and Ae — in the spherical coordinates, caused by 

 these small rotations, is found from the formulae 



