52 



BELL SYSTEM TECHNICAL JOURNAL 



Examination of (17.1) suggests that we might consider the ^'s as being 

 lineraly modified by the field. Writing ^ as a single column matrix: 



K = 



we may write 



K = K° + hE. 



(17.2) 



where K° is the dielectric matrix for vanishingly small fields. 



We can develop the modified reciprocal matrix in the same manner: 



k-' = 



K-'^ 



where 



= K~'° + zE 



(17.3) 



It is to be noted that K"^ is not the reciprocal of K but merely a symbol 

 for the single column matrix formed from k~ in the usual way. Taking 

 reciprocals of both sides of k' = akac we find ik~ )' = ak Cc. That is, 

 k"^ transforms exactly as did k. Whence, K~ transforms exactly as A' 

 does, i. e. 



A = a K 



We can rewrite (17.3) as 



a K~ = a K -\- {a zac) aE 



or 



K' 



= (A"' )' + z'E' 



= a zac (17.4) 



In case a ^ = ac the z's transform as do the conjugates of the piezo- 

 electric constants, d. Of the transformations permitted by the symmetry 



