CHAPTER II. 



The frequency function of the linear motions. 



7. We denote by U, F, W the components of the linear motion of a star 

 along any three rectangular axes. Then we write the frequency function according 

 to (1) in the following way 



(33) F( Ü, F, W) = ?( U, V, W) + S Biß ^J^^l 



where as before 



» = I 



VM(2k) s ' 2 



(33*) /= 4t/ 2 + BV' 2 + CW-f WVW +2EUW + 2FUV. 



We here denote the moments by jV^ thus having 



CO 



j\r ;M . = jfjfjf cr< J7j jp* ^ jr W) dUdV d W 



CO 



or as it will be in practice 



N ijk = Mean of ( ü* F' W k ) = M{ IP Vi W k ). 



The characteristics A, B, C, D, E, F, B,-j k are given in terms of the moments 

 Nij k by the equations (11) (16) (17) when the v (>7 , are changed against the N ijk . 

 The equation 



/= constant 



is the equation of the correlation ellipsoid or as it here is called the velocity 

 ellipsoid. 



By the way, we will here remark, that the correlation ellipsoid is not identical 

 with the ellipsoid of Schwartzschild even when the latter is taken three axial, except 

 in the case when the higher characteristics all vanish. Generally they are both 

 approximations to the surfaces of equal frequency, but not the same approximations. 

 This circumstance is intimately connected with the fact hinted at in the introduction 



Lunds Universitets Årsskrift. N. F. Aid. 2. Bd U. 3 



