The motion of the stars 



93 



28. The values obtained for the skewness and the excess for every square, 

 h. e. in the system of coordinates ffj, vary from one square to another. If the 

 corresponding vahies of the coefficients in the system of coordinates — which 

 has the Z'-axis directed against the vertex — were calculated, we ought to have 

 identical values for these coefficients, presuming that the accidental errors of the 

 coefficients are neglected. I have not, yet, had apportunity to carry out this 

 reduction. 



29. As soon as a frequency curve, or a correlation surface, is characterised 

 by a sensible value of the skewness and of the excess, it is generally reason to 

 examine, if the frequency curve — or the correlation surface — can be dissected 

 into two, er eventually more, normal components. Such a dissection correspond in 

 our present problem to the decomposition of the stellar system into two indepen- 

 dent star-streams (Hypothesis of Kaptetn). I shall show in the following paragraphs 

 how such a decomposition can be mathematically performed with the help of the 

 values — Nij — of the moments of the linear velocities given in tab. IV. 



30. Let us denote by a sphœrical stream a group of stars, where the (internal) 

 velocities are distributed according to the simple law of Maxwell. Then the problem 

 is to dissect a given correlation surface into two sphœrical streams, supposing such 

 a dissection to be possible. As the projection of a sphserical stream is itself a 

 sphserical stream, it must be possible to dissect, for every square, the correlation 

 surface into two sphserical streams in two dimensions. Let 



F{x,y) 



be the correlation function of the linear velocities, perpendicular to the line of sight, 

 for a certain square and let 



'2 «,3 



(x-m,)2 + (y-n,)2 



(86) 



be the projection of the sphserical streams in the system of coordinates K^. 



Let iVj^ and denote the number of stars in the two star streams, then we 

 ought to have 



(87) N F(x, y) = NJ, [x, y] + NJ, [x, y), 



where iV(=iVj +^2) ^^^^^ number of stars. 



The moments Nij of the correlation function F{x, y) are supposed to be known. 

 The quantities to be determined are 



(88) ' ' ' 



Fui- determining the values of these 8 characteristics we ought to know 8 

 moments, say 



