MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



13 



Similarly, for a counterclockwise rotation 4> about .V2 we have 



(cos 4> — sin <^\ 

 1 j :...(5.2) 



sin <i> cos 0/ 



and for a counterclockwise rotation </> about X3: 



/ cos sin 4> 0\ 



a = j — sin cos <^ 1 (5.3) 



\ 1/ 



Fig. 34 — The relationship between the components of a vector on one coordinate 

 system and on another. 



In the appendix we give the special transformations corresponding to the 

 symmetry operations of the 32 crystal classes. If we have three successive 

 rotations: 



the resultant rotation is 



or 

 where 



X = ax 

 x'" = a"x" 



x'" = a"a'ax 

 x'" = Rx . . 

 R = a"a'a. . 



(5.4) 

 (5.5) 



