70 BELL SYSTEM TECHNICAL JOURNAL 



Conclusions 



For transmission over plane earth with antennas on the ground the 

 received field strength in volts per meter is given by the formula, 



£=i2^f(,)=3V|V?^(^)_ (34) 



where HI is the transmitting ampere-meters, P is the radiated power 

 in watts exclusive of ground losses, d the distance in meters, X the 

 wave-length in meters and F(x) is the factor plotted in Fig. 2. 

 When the Q of the ground is large compared with unity, the factor 

 plotted in Fig. 3 is to be preferred to that plotted in Fig. 2. 



When the antennas are not on the ground the received field strength 

 may be calculated by means of equation (27) or its equivalent, 



I- + 



^ + ^"^ aJ^^'^ L-4.iA,A,/x<i^ (35) 



where the reflection coefficient, 



R = - Ke^'l' = - 1 -\- (a - ib) sin ^2 -\- '■ -. (36) 



The quantities K and ^ are plotted in Figs. 5-12. 



When the antennas are sufficiently removed from the ground that 

 the second term within the bracket of equation (35) may be neglected 

 the simpler expression given in equation (21) applies. 



EJEo = V(l - Ky-^AKsin^i-y/l). (21) 



When the distance between antennas is sufficiently great that the 

 exponential factor in equation (35) may be replaced by the first two 

 terms in its series expansion, the received field strength may be cal- 

 culated by eqtiation (30) and Table I. Four special cases are given 

 by equations (32) and (33) and Fig. 13. 



Appendix I 

 The values of the components of 



W = A-\-D^A-B/2+F^C-\-F 

 are: 



4= 1 



1 - 



iTrifd/Xy 

 „=: V 1 -f r2 / l-3-5---{2n 



1 + S Tt^ ) . . c ;. TV, (37) 



■J]' 



B =^-l—J2T^ll -f r2 J^^^e<2«./XKi-i/Vi+.^)^ 



(38) 



