The general Characteristics of the freqnencyfunction of stellar movements 65 



As by q — 0.75 the distribution is not far from normal we may use the 

 equations (71), (75) and (75*), and obtain for the order of magnitude of the mean 

 error in a (/-square 



V s (Ay = 0.19; & 1 *e{N 11 ) = 0.ni V s (#m) = 012 > 



» 1 8 t(B S0 ) = 0.n; V e ( J5 2i) = °-l 2 ; ^ 3 £(^ 12 ) = Oio ; ù 1 3 e{B Q3 ) = 0m, 



ü 1 U{B i0 ) = 0.0b; l> 1 4 £(2? 31 ) = 0.07; & 1 i s{B S2 ) = 0.QT, V s (^i 3 ) = 0.05; V e(BJ = 0.02. 



As adequate values we now take 



|t» = 0.15 



jj. l8) = O.io 



jj.' 41 = 0.05 



and have from (82*) 



1 7 K p »ii»] 



where for [a 1P we have to take the coefficient of the characteristic £W in the 

 normal equations of Chapter VI. 



26. Of far greater importance than the mean errors are the systematic errors 

 that may come forth by a systematic variation of the parameters q and i> l in the 

 several squares. As to the parameter q we have at present no means to ascertain 

 its variation. By & t the matter is more ripe and we shall in the next paragraph 

 try to determine its probable variation with galactic latitude. First we shall, howe- 

 ver, deduce the formulas of correction to be applied after having found the amount 

 of the variation. This we are in a position to do by the equations of the preced- 

 ing paragraph. 



We denote by ^(ß) the value of ■9 , 1 in regions of the galactic latitude ß. The 

 «/-squares now form rings of equal galactic latitude, in which 0- x (ß) is assumed to 

 be constant. By index ß denoting that only the ring of squares having the latitude 

 ß is used we obtain from each ring normal equations of the approximate form 



Taking the sum for all the rings we obtain normal equations of the form 



^s^)H5«g]ß = [«g^]. 



Putting 



we come back to our old form 



[«g^](*i)p^ = K^)], 



save for the circumstance that we here have the »mean» values {&\) p instead of 9i. 

 By & t denoting the mean parallax of the whole heavens as deduced by comparing 



Lunds Universitets Årsskrift. N. F. Afd. 2. Bd 11. 9 



