72 



C. V. L. Charlier 



These results are expressed in class-breadths, used as unit in the correlation 

 tables (Tab. I). For obtaining the values in seconds of arc we have to multiply 

 hy w — 0".06. Let s denote the linear velocity of the sun and B and A the de- 

 clination and right ascension of the Apex, we thus get 



Q\ s cos D COS A = — 0".00212 -|- 0". 00226 



(41) d-^ s cos D sin A = — 0".04305 — 0".04076 



s sm D = + 0".02973 -j- 0".02460 



Solving these equations we get: 

 For stars of the fourth magnitude: 



A = 267".18, 



Z) = + 340.59, 



xi-^S = + 1 0472. 



For stars of the ffth magnitude: 



A=^ 273".i7, 

 J)^+ 31«.15, 

 {>,.v=^ 0 9.=.37, 



From the values of d-^s we may derive the value of the coefficient by means 

 of the formula I (75*), which gives 



(42) = 5 [log ^^,(4'") — log ^'>i(ô"')]. 

 Hence we get 



Xj ^ + 0.2030. 



The uncertainty in this value is however very large, owing, above all, to the 

 large mean errors of and for stars of the 4*^^ magnitude. For evaluating these 

 mean errors we may proceed in the following way. 



12. We have given in § 5 the mean values of the dispersions in Xq and 

 for stars of the 4**^ and the ö*'' magnitude separately. With these values we are 

 able to deduce the mean errors in and «/^ through the formulée (denoting by s{x) 

 the mean error in x): 



where N is the mean number of observations in a square. 



We have, according to Tab. I, for stars of the 4*** magnitude 



iV-= 19.21 



and, for stars of the 5*^^ magnitude, 



N= 56.15. 



Hence we get: 



4™ : £{Xq) = ± 0.3254; s(«/y) = ± 0.2850 



5"' : £{xq) = ± 0.1714; 5(^0) = ± 0.1614. 



