MATHEMATICAL NOTE 



17 



A special case of considerable importance arises when the 

 second set of axes of reference are the principal axes of the quad- 

 ric surface. In that case it is known that/', g', h' are each zero 

 and the equation of the surface has the form 



a'x'^ + by^ + c'z'^ = k. 



The results written above then become 



a' -\-b' + c' = a-^b -\- c, 



b'c' + c'a' + a'b' = be -\- ca + ab - f - g' - h\ 



a'b'c' = 



} (12) 



