(4*) 



The general Characteristics of the frequencyfunction of stellar movements 

 Hence we have for a -j- ß -j- 7 = 3 or 4 



Vr=Vr+ M) a+P+T Ifl Ii li 



2. Before proceeding further we first write the exponent / in the form * 

 (5) / = Ax- + By* -f Ce* + D t yz + D^sy + E x zx + E 2 xe + J>«/ + /•:,//./• 



where D 1 = I), = D E i = E., = E F t = E, = F 



and define the determinants 



(6) 



A, F lt E 1 

 F 2 , B, D 1 

 D„ C 



M 



^110' ^1 

 '"010' ^0 



Making a linear orthogonal transformation of the variables thus 



x = a n 4 + a lt -q + a n C 

 (7) // = a 21 £ + « 22 rj + ffl 23 C 



* = «31 É + «32 T l + «33 C, 



we may chose the coefficients a# so that 



and the coefficients .9 are the roots of the equation 



(8) 



A— 



B- t 



Do, 



= 0. 



Consequently we find 



and as now the variables may be separated we find from the condition (2) 



(9) 



(Ws)" _ 

 (2*)" 



(2«) 



3. To find the parameters of the functions F(x, y, e) expressed through the 

 moments we first remark that for a -f- ß -j- y = 2 we have \ rx Q., = v a ß„ and con- 

 sequently 



'110' '101 



^020' V 011 



101' y 011' '002 



Now we write the equation (2) in the form 



" Ml 



d.r dy dz e 



* For a part of the developments of this and the following paragraph compare Greiner: 

 Zeitschrift für Mathematik und Physik Bd 57 P. 227, ff. 



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



