RADIO PROPAGATION OVER SPHERICAL EARTII 487 



Here the abscissa is chosen so that all of the Sommerfeld-Rolf curves 

 coincide. If the effect of imperfect conductivity were unimportant, 

 the curves for spherical earth would begin to depart from unity at the 

 points A, B, C, etc. The effect of imperfect conductivity is to move 

 these points to A\ B', C, etc., on the present Eckersley theory. The 

 horizontal motion was calculated by the approximate phase integral 

 method, while the vertical motion is the result of this recent assump- 

 tion. It can be seen that for the poorer conductivities the recent as- 

 sumption causes a greater change in the value of the field strength 

 than that calculated by the phase integral method. While this assump- 

 tion has removed the most obvious inconsistency in the results, the 

 writer believes that they still require experimental verification before 

 reliance should be placed in them. 



APPENDIX 



The rigorous solution for the perfect conductivity case, equation (1), 

 may be expressed in the form, 



£ = 2] ^"CosX„, (10) 



where An and X,, are functions of p„. By his approximate phase 

 integral method Eckersley was able to evaluate Xn in the above ex- 

 pression. He found the same relationship between X„ and p„ as 

 Watson. The p„'s he obtained, however, differed from those obtained 

 by W^atson. The values of p„ as determined by Eckersley may be 

 expressed 



Pn = 



(11) 



where rj depends upon the ground constants, being zero for perfect 

 conductivity, an is a constant independent of n whose value Eckersley 

 found by comparison with Watson's results to be 3/4. Herein is one 

 of the inaccuracies introduced by the approximate method, for to 

 obtain the correct values of p„, a„ must be allowed to vary with n. 

 While the necessary variation is small '^^ for the case of perfect con- 

 ductivity, without further proof we have no assurance that it is not 

 much larger for the more general case. 



Eckersley's method does not tell us anything about the magnitude 

 of .4 „ in equation (10). He tacitly assumed ^„ to be independent of 



=1 a, = 0.7819, a. = 0.7577, a, = 0.7544, a^ = 0.7530, a, = 0.7523, and a^ = 0.7519. 

 For larger values of n, u,, approaches 0.75 more closely. 



