Wave-trains through a Conducting Dielectric. 313 

 If we write for brevity 



(8) 

 Ax - l+\' 



\ contains q, which is partly imaginary ; so we must separate 

 the real and imaginary quantities and rationalize. Let p x be 

 the real part ofp, andp 2 the imaginary part, so that 



p=— pi+p 2 i, 



and let us write 



Pi— 



^ 2 =^sm%. 

 In this notation then 



p — —7]e~ l x y 



t=»?cos%,T 

 ,=7? sin y.J 



period = — , 



f 2 



logarithmic decrement = 



y 



and using the value of q in (5), 



P2 



V /5 2 / 1 __«2. 



*X\§' 



The denominator of this expression is 



so if we put 



OCq 



p cos 6=1 ^-cosv 



* ^2 



/> sin 



in<9 = 



« 2 



?A 



siny. 



or 



[ 1 -ift** + '(s& ,fa *)T 



tan 0= 



«2 • Q 



P2&. 



-h^-^H 



pA 



(9) 



(10) 



