Polarization in Biaxial Crystals. 363 



reduces to 



/A+V.XV\(^/A + fi)/)cVToAA)=0, ... (2) 



or, writing />ct = 7 and expanding, 



/jl 4- X 2 (</>//. 4- (oVyu) = \SX(0/a + coYyfJ,) . 



The scalar differential equation satisfied by <r reduces to 

 S\/x = 0. Writing 



a perfectly general form of the self-conjugate function (j>, we 

 have 



*IIU« + g)/i + uSPfi, + pSafi + aYyp. . . (3) 

 Operating by V. X( ) this becomes 



(J- + ^\ yx/* + Y\*$P/i 4- YXpSap + a>VxV 7 ^ = 0, 

 or, remembering that SX//< = 0, 



(\ + <j)\fi + YX*$l3fi + Y\0SafL + G>fiSy\ = O, 



Now we have identically 



/aS«£A.= V£\S*/a 4- VX«S/3/<, 4- Va/3S\fi, 



where in our case the last term vanishes. 



Eliminating the term VA/3Sa//, by means of this equation 

 the previous one becomes on rearrangement 



2VaXS/fy=(- 2 +^W-A'S*/3\ + o¥'S7X. 

 Multiplying by VaX and into /i, this gives 



f II V«A • [(p +/jA-S*/3A-r-o>S 7 x], 



|| V. xj~(i + <A Va\-aSa£X + ao>S7\]. (4) 



From the symmetry of (3) in a, and ft we can at once write 



