TIr' motion of the sshiis 85 



We now turu the axes of coordinates UV through an angle cc., and put 



U = X cos — // sin cps 

 F = a; sin ©s + // cos «p« 



and call the new system of coordinates the system (with the axes x, y and s). 

 hi K.^ the projection of the velocity ellipsoid has the equation 



(67) f=A^U''^B,V^^2F^UV. 



The angle tp,, may be chosen in such a manner that in K^ this equation takes 

 the form 



(68) f==A,x'-^B,y\ 



One of the axes of the coordinates — say the new y axis — is then })er- 

 pendicular to the axis Z', as is found from the expression (65) for F^. 

 Let p be the angle between s and W so that 



cos Z'z = cos 



then 



cos Z'x = sin p 

 cos Z'y = 0, 



and 



^ ' C=B' — [B' — C) cos' p, 



= C' + [B'— C')sm'p. 



These equations give the relation of Schwa rzsohild 

 (70) -^--i=^l^-l]sm^p 



"-0 



Further we get 



cos XZ =^ sin p cos 'f s 

 cos YZ' = sin p sin (p^. 



Observing that, according to (55), 



cos XZ' = + + £33 73,, 



COS YZ' = s,3 + Ï22 + ^33 T32. 



we have 



sin p COS tp, = £,3 Tn + £23 Ï21 + hs Ï31 ' 

 sin^J sin 9, = £^3 + £^3 + £33 Y32 . 



These equations we multiply by 



