ELECTRIC WAVES OVER THE SURFACE OF THE EARTH. 



117 



This equation (39) may be expressed in a real form. Corresponding to primary 

 waves given by 



n _ cos k(Ct-'R) , 



~ir~ 



we find 



H = - 



sn 



-z0)-(S 21 -S 22 ) cos (kCt-z6) 



A/ ?-s [(S' U -S' 12 ) sin (kCt-ze) + (S' 21 + S' 22 ) 

 v TT sin u 



cos 



where m = i/(<ir<rkC), and 



Q _ V ( H + 



z r 



-.Jt^cos Xn cos g,,tf- - 



7T 



T/' 



/ 2 



V " ~ 



it/ 



cos-x.smlg.e- 

 cos 2 v- tan Y,, cos 



and 



S' n = 2 

 S' 18 = 2 

 S' ai = 2 - 



M 2 roq 4 v Cl tin 2 v ^ ^in n ft 



. -*-Vfi L/U& V H \ J. tdll Xtt/ ^m '/ ?i v7j 



A/ -- . R,, 2 cos 4 x 2 tan Xn cos q n 6, 

 /Y/-- . R n 3 cos 1 Xn (1-tan 2 Xn ) cos q n O, 



V- . R n 2 cos 4 x n 2 tan Xn sin q n 6. 

 Iti 



(42) 



(43) 



(44) 



n 



12. It may be observed here that similar expressions can be obtained for the values 

 of E r and E 9 , the radial and tangential components of electric force at a point on the 

 surface. With the formula (39) for H we should find E = kH/k', where the second 

 line of the expression for H may be omitted. This form gives the amplitude of E fl at 

 any distance as k/m times the amplitude of H at the same distance. In the case of 

 primary waves given by (41) the value of E r can be obtained from the formula (42) 

 for H by changing the signs of the coefficients of sin (kCt z6) and cos*(kGt z6), and 

 in the sums such as S u and S' n replacing (w+^) 2 /i~ v 'z~ s/I by (n + ^) (n+ 1) n' /2 z~ >; '. Since 

 z is a large number, and, in the relevant terms, n differs but little from z, it is manifest 

 that the terms of E r which contain the sine or cosine of (kCtzQ), are nearly the same, 



