The motion of the stars 



H7 



and, after some reductions, 



^02 



(7Ô) 



Putting 



(76) 



|/fnrT3in,.=K 



AT AT 



A Q f ^02 cotg-'f, — 



M M 



■^'20 -^-'02 



V 



N — - N 



^02 COtg - iV,o ' 



the equations for determining the parameters of the velocity ellipsoid accept the 

 form 



^ ^ ^Tii + Ï'T2i + 7^T3i , 



'^1 ~ •^Tl2 ~^ ^T22 '^T32- 



Comparing these relations with those for determining the position of the apex 

 (§ 9, formula (41)) we find the form of both relations to be the same. The equa- 

 tions (77) for determining the true vertex differ, indeed, from those for the apex 

 only regarding the left members. The quantities i and 7) are proportional to the 

 projections in of the excentricity of the velocity ellipsoid, whereas, in (41), 

 and «/g denote the projections in the same system of coordinates of the relative 

 motion of the sun. 



The values of i and t] for our 48 squares are given in the adjacent table VIII. 

 Treating the equations according to the method of least squares, we get the following 

 normal-equations : 



From the 



26.0000 S = f 10.3097, 

 22.0008 1' = — 35.6812, 



and from the 



5.7680 3 = + 1.0717, 

 g.6460 Ï = — 14.0209, 

 32.5888 Z = — 18.4302. 



Adding these equations together, we get: 



31.7680 3 = + 11.3814, 

 (76) 31.6468 Ï = — 49.7021 , 



32.5888 Z = — 18.4302. 



From these equations we deduce: 



3 =3 -f 0.36827, 



(76*) r=— 1.57053, 



Z= — 0.56564. 



