is 



Walter Gyllenberg 



The same relation must also be valid for each star, if its motion is only due 

 to the velocity of the sun. 



If, however, there exists a systematic displacement K, that may be caused by 

 errors in the measurement, by atmospheric conditions of the stars or by a real basis, 

 the equation (2) takes the form 



(3) T« U 0 " + 7 23 V 0 " + Ï33 W 0 " -e 0 + K=0. 



The equation thus contains an additional unknown quantity. 



13. Consider the following relations: 



cos 8 cos a, 

 cos S sin a , 

 sin S, 



where a and 3 denote the coordinates of the centre of a square. Assume further 

 A and J) to be the angular coordinates of the apex, then we evidently have 



U 0 " = S cos D cos A, 



(4) V 0 " = £ cos D sin A, 

 W 0 " = S sin D. 



Introducing these values into the equation (2) we find this quite identical 

 with the equation deduced by Campbell x . 



14. Regarding the displacements in the different squares as the observed 

 quantities, we have to solve from 48 equations of condition of the form (2) viz. (3) 

 only three viz. four unknown quantities. Applying the method of least squares we 

 get from (2) the following normal equations: 



[Tis Vis] ^o" — fris %l = °- 



(5) [T 23 T 23 ] V-[Y23*o] = <>> 

 [Y33Ï33] W 0 " — [y S3 * 0 ] = °. 



or, when the numerical values of the direction cosines are introduced: 



16.2344 U 0 " — [i u 0 o ] =0, 

 (5*) 16.3552 F 0 "-[ Ï2S * 0 ]==0, 



15.4132 W 0 "-[ hs * 0 ]=0. 



All other coefficients vanish owing to the symmetrical distribution of the squares. 



Introducing the fourth unknown quantity K the expressions (5) will not change 

 their form. A new equation independent of the others will be added, namely 



(6) 482T=|>J, 



where the coefficient of the left membrum is the number of the squares. 



Yl3 = 



Ï23 = 

 Ï33 = 



Astropl). Journal. XIII. page 80. 



