74 



C. V. L. Charlier 



= (Po) = ^> 



Hence we get: 



For stars of the 4*^ magnitude: 

 £(d^s) = + 0.0540, 

 s ( Z) ) = + 0.0540 : d-^S = ± 0.0516, 



e ( ^ ) = i 0.0540 : d'^s COS D = ± O.oô^e. 

 For stars of the ö*"^ magnitude: 



£(ô'j5) = + 0.0294, 



e( D ) = ± 0.0294 : ■9-^,9 = + 0.0308, 



£ ( ^ ) = + 0.0294 : d-^S cos Z) = ± 0.0360. 



The mean errors in D and Ä are expressed in radians. For having tiieir 

 values in degrees we have to multiply by 57". 2958. Thus we get: 



Position of Apex. 

 From stars of the 4'^ magnitude: 



A= 267 «.18 ±3«.59, 



D=-\- 34«.59 ± 2«.96, 

 d-^S = 4- 1.0472 ± 0.0540 = + 0".06236 ± 0".00270. 



From stars of the 5*'^ magnitude: 



A= 273°.i7 ±20.06, 



+ 310.15 ± 10.76, 

 è^S = + 0.9537 ± 0.0360 = + 0".04768 ± 0".00180. 



The agreement between the coordinates of the Apex from stars of the 4*'' and 

 from those of the ö''^ magnitude is tolerably good, taking into account the values 

 of the mean errors. With the usual formula for the mean error of compound 

 functions, we get from the mean errors in d-^s 



Xj = + 0.2030 ± 0.1467. 



It is, however, scarcely allowed to apply the elementary formula for the mean 

 errors of compound functions in this case and the mean error in Xj must be 'con- 

 sidered still greater than ± 0.15. In any case the value obtained for Xj must be 

 regarded as rather doubtful and I have preferred to use in the computations of the 

 characteristics the value Xj = 0.5 so much the more as we have found that a varia- 

 tion in the value of X^ to tlie amount of + 0.2 from this value is of little influence 

 on the resulting values of the characteristics. 



14. The value obtained for for stars of the 5'^ magnitude may be used 

 to determine the mean distance (or the mean parallax) of these stars, if a value is 

 assumed for the mean velocity (s) of the sun from spectroscopical observations. 



') Compare I S. 48. 



