30 BELL SYSTEM TECHNICAL JOURNAL 



we may write: 



hii = C°jTc,, (8.34) 



Hii^ S°,Ts,, (8.35) 



Multiplying (5) by (6) we get: 



SC = I ^ S°C° = S°C° + i(S°h + HC°) + t\S°/i + Hh + h'C°) + • • • 



whence, for this relation to hold for all values of /: 



S°h + IIC° = (8.36) 



whence 



h = -C°HC° 



(8.37) 



H = -S°hS° 



also 



S°h' + Hh + H'C° = (8.38) 



so that 



h' = hS°h - C°H'C° 



, (8.39) 



H' = HC°H - S°h'S° 



From these we can compute the h's given the H's and vice versa. 



SECTION 9 

 Temperature Expansion 



The change in the dimensions of a crystal caused by a temperature change 

 can be considered as a strain. The shift of the terminus of a vector / 

 relative to its origin is given from the strain matrix e by the equation Al = 

 iel 



Since e is symmetric a proper choice of axes makes it possible to make the 

 strain per degree a diagonal matrix, 



/A, 0\ 



Al = tAl where ^=10 A2 ) (9.1) 



\0 As/ 



As / and Al both transform as vectors, a transformation a causes A to 

 transform as 



A' = aAa~' (9.2) 



