40 BELL SYSTEM TECHNICAL JOURNAL 



If terms of third and higher order in 5 are dropped we have left 



pial—ikxx sin 9 



^Vl 



25 



5 + rVl - t2 + tH''12<T^t'' 

 [1 - 52(i + y^iV/2 - tV2(1 - t2) - i^iz/rVl - r^)], 



6= 



£, = gic-<-i*:i=r sin e 2 ( 1 - ^ \ 5 (' 1 - ^' ) ( 1 - yfeiV^ 



.3g2 

 2Vl - t2 



1 + ( rVl - t2 + , ,r"" ) ^^i2(l + ^i'2'5V3) 



/ 



(^^^ + ^+^vfb)' 



oiu<— iA:ix sin 



1 + rVl — T^^lZi 



25 



5 + tVI - t2 + 7352/2 Vl - t2 



The wave tilt is then 



£. 1 + ^vr^rv2^^2a "^ L2^wr^^2 2(1 - r^) 



_ • r^hzjl + r(l - T'')fei%V3 1 1 

 \l + rVl - rHhz)^\ - t2 J J 



The wave tilt in the Zenneck wave is just t. 



As a particular and probably typical case we may take e = 9, 

 (T = 2 X 10-1* and / = 60,000 and then r = kjki = 1/Ve - i2c\(T 

 = 1/V9 - ^600 = .04082 1 44.570° . If z = 30 ft. then 



kxz = 27r 30 X 30.48/5 X 10^ = .01149. 



If 5 = 10° = .1745 radian then 5= = .03045. The coefficient of r in 

 EJE^ then turns out to differ from unity by only about 1 per cent. 



