(229 ) 
5. The difference between the two considerations may also be 
put thus: 
let A, and D, be the co-ordinates of a given point at the heavens; 
(if there is a parallactic solar motion, that point may be the assumed 
Antapex). 
1°, If there existed only a parallactic solar motion, the proper 
motion for each separate star would be represented exactly by the 
formulae : 
By : he 
Ty = — sinAsine; vy =—sindeose; 
Q Q 
hence: 
OF h 0de h 0 
9 —— sind cos e Se Den doo ete. 
d4g e@ A,’ AD @ ID, 
2°. Even if the proper motions are distributed arbitrarily, without 
being influenced by any parallactic motion 
Ty = HSIN Po, Vy = M COS Poy 
OF __ 0X0 Or) _ 0X0 
tc. 
Den Ce 
hold for each star separately. 
Airy starts from the first set, KAPTEYN from the second. 
6. If we substitute in the conditions (C) 
ES Fy sin a} — (54) dA — (54): aD) 
ee a). vies Gp), a and 4 (84) + 
(EE) + Ga Rn 
and ueglect the small quantities, we obtain, the equations found 
before (B). 
The equations which Kaprryn (l.c.p.360) deduces from the same 
two conditions (C) differ from ours, because also in this case he 
uses the development 
15* 
