98 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



4.626 Referred to its principal axes the equation of the quadric is, 



coi# 2 + (jj 2 y 2 4- co 3 s 2 = const. 



4.627 Applying the self -con jugate operator, co, successively, 



o?R = icoi^i 4- jcozRz 4- koj 3 ^3, 

 cocoR = co 2 R = coi 2 ^i + jco 2 2 ^ 2 + 

 = co 3 R = icOi 3 7?i + jco 2 3 ^2 4- 



4.628 Applying a number of self-conjugate operators, a, j8, . . . ., all with the 

 same axes but with different principal values (aid 2 a 3 ), (/3i/3 2 /3 3 ), .... 



aR = ia RI + ja 2 7? 2 + ka 3 7? 3 , 



a/5R = la^Ri + ja 2 /3 2 # 2 4- ka 3 /3 3 R 3 . 



4.629 



S.QcoR 



