28 C. V. L. Charlier 



The left-hand members of (59) and (59*) can be considered to be known (to 

 a certain extent: a{m) to w = 9.5 and somewhat vaguely for some higher values, 

 My,(2:)) to m = 6. b). It is hence possible to determine (and D) and *). This 

 can indeed be done with the help of the general solution of Schwa kzschild in § 7. 

 But the matter can be treated more easily. 



Suppose indeed that the unknown functions and are frequency functions 

 of type A), so that 



_ iy—nipf iy~nhf 

 (60) A,(^)==— '^^^ ; x,(^) = — ^ . 



and hence 



(60*) 'fo(»l^y)= 



then according to (51), (52), (59) and (59*): 



(m — — m^f 



(60**) ■ nim) =. — P. 2(V+^^') , 



K27r(a,^+^/) 



1 ~ ' 2V 



(60***) M,n[p) = M[P)e + V 2(Gj^+V). 



From these formulée we immediately draw the following important conclusions. 

 Let us suppose that the observations show tha,t the functions a[m) and Mm{p) are 

 represented by the following formulée 



(61) a{,u) = --^e ; MM^K^e^-^'' 



then the values of Aq(«/) and cp(,(«/) are given by (60) and the parameters , m^, 

 a , , 0^ and C are given by the formulae 



(61*) 0,^ + 0,^ = 7.^ l'^' =\ = h\, 



(61**) — m, =m^; M{P) e + ^^^i' + "^'^ 



(61***) C^=C/j 



From (61*) we get and o^, from (61**) and mg, from (61***) G. Solving 

 the equations (61*) we obtain 



(62) o,' = Jc'{l — \). 



The relations (61**) may be written in the form 



(32*) } '"'^'^ ~ + ^1=5 log -^b\,{l- \) , 



— - — nif^. 



*) We may suppose that M{p) can be determined from (58***) with the help of the existing 

 direct parallax-rleterminations. 



