SPHERICAL EARTH 



77 



Hence it follows that 



h = h 

 Since 



L\ 2kahJ di 



Thus, 



+ 



2kahi. 



s' S' 



-{L»„„ + ,,-i]^,4.„, 



ch (1 - q)d 1 - q 

 hi = hi 



(— ^ V 1 - p= + — ?P1 ) . (98) In terms of u and v, 

 M-g/V 1-9/ „ /, 



2 L d-/(2/fa/)i) J 



+ 



1 



2d'-/(2kahO 



i(D) 



.9 LO 



Figure 18. (1 - p-y/P as a function of p. (Radia- 

 tioa Laboratory.) 



5.5.8 



Generalized Coordinates 



The distance from the transmitter to the reflection 

 point di and the ratio p may be eliminated by using 

 the dimensionless coordinates 



hi 



d 



V = — . 



df 



(99) 



(100) 



The advantage of this substitution lies in the fact 

 that the coefficients of s = di/d in the cubic equation 

 (74) may be expressed as functions of u and v only. 



2 V V- I 2(>2 



(101) 



Figures 19 and 20 show contours of constant s 

 plotted in u, v coordinates. The curves are parab- 

 olas. 



Figure 19. s as a function of u and v. (See Figure 14 

 for definition of lengths.) 



Figure 20. s as a function of u and v. (See Figure 

 14 for definition of lengths.) 



