86 C. V. L. Charlier 



and put , 



18 ' 



70) r = Y^^-\s,,, 



7 I / ^' 1 



— y -fj. — i =33- 

 Taking into regard the relation (70), we thus get 



|/ ^ — 1 cos 'Ss = 3y^^ + Ty^i + Zy3i> 

 (70*) ^ 



1/4^-1 sill 'h = ^7^2 + TYja + Zy32. 



These relations allow to determine with the method of least squares S, Ï and Z 

 and thus the parameters of the velocity ellipsoid. 



24. It remains to evaluate the value of the left member of these relations. 



P^'or deducing (68) from (67) with the help of the substitution (66), the angle cp 

 must be determined from the equation 



(71) tg2cp,-- 



The values of and are then found from : 



yly = cos^ (p.s -|- A^ sin^ 'f., + 2F-^ cos cp..- sin 'i\ 



= A^ sin^ -f cos^ tp, — 2F^ cos a;« sin 



or 



" 111 cos 2'rs 



(72) ' 



" 111 cos 



The values of A^, B^ and F^, for every square, are found from the moments j 

 Nij of the linear velocities by the formulae 



1 



^1 = 



(73) 5, = 



1 



(l->-')^' 



(1 - r') N,, N,, 

 We thus get 



2iVii 



(74) tg 2f,= 



AT M ■ 



