ELECTRIC WAVES OVER THE SURFACE OF THE EARTH. 125 



This error seems to me to vitiate the whole of the work of MARCH and RYBCZYNSKI. 

 In particular, it seems to destroy the foundation for RYBCZYJSSKI'S solution of the 

 problem of the perfect conductor, and his extension of the solution to include the effect 

 of resistance. 



1 8. A result that should admit of being tested experimentally is the law of decrease 

 of amplitude of the electromagnetic waves with increasing distance. According to 

 what has been said in 12 and 15, this law must be very nearly the same for the 

 electric force in the field as for the magnetic, and it may be assumed that the amplitude 

 of the received antenna current at any place is proportional to the amplitude of the 

 magnetic force of the field at that place. The various diffraction theories lead to 

 approximate formulae for the law of decrease of the amplitude of the magnetic force. 

 Let H denote this amplitude at angular distance d, Hj the corresponding amplitude at 

 angular distance Q lt and X the wave-length, measured in kilometres. Then a result 

 given by MACDONALD( U ) leads to the formula 



H . _ COS ^ 



(4r 89 )X-Main'W,-ainV s ) 





a result given by NICHOLSON (") leads to the formula, 



H = A A' sin K\ e <*W *-'''<*,-*> , 

 H! V Isin ifl,/ 



and a result given by RYBCZYNSKi( 13 ) to the formula, 



H . //fl, sin 0A 



dr.-o^.-s) 



while ZENNECK( IS ) gives a formula equivalent to 



jH . //e, sin 6A <, ,-'/,(,,_ , } 



n V e sin 



e sin 9 



as the result of a correction of the work of MARCH ( 12 ). In the exponential factors of 

 the last three formulae and Q l are measured in radians. 



The discrepancies between these various formulas are sufficient to justify the 

 attempt to obtain an independent solution of the diffraction problem. The con- 

 firmation of MACDONALD'S result for a particular wave-length affords good reason for 

 accepting his formula as correct, and consequently rejecting the others as incorrect, 

 apart from the objections which have been brought against the analytical procedure 

 of their authors. 



MACDONALD has pointed out that the range of validity of such a formula as (54) is 

 restricted by the condition that neither 9 nor 9 1 must be too small. For X = 5 it 

 begins to be valid at about 7, for X = 2'56 at about 6 20', for X = 1'22 at about 6. 

 If it is desired to compare it with results of experiment, the distances to be considered 





