PHYSICAL REALITY OF ZEN NECK'S SURFACE WAVE 41 



These figures show that if we retain only the principal terms in our 

 formulae we have 



77 __ p'.at—ik\x sin 



5 + t4\ 



=,'^V-^i\-'^) 



E^ = g"-'-'*!^ sm 9 — J _^ -25[1 - §6-], 



As a rule the wave tilt is so nearly equal to the value t predicted 

 by Zenneck that present day wave tilt measurements do not dis- 

 tinguish between the two. 



Part Three — The Wave Tilt of the (2o-^^'AVE 



It would be but natural for a reader to ask what wave tilt would 

 be observed at the surface of a flat earth if there were no Heaviside 

 layer. It was shown in Part One that the asymptotic expansion of 

 the complete wave function is Qo + Q^, of which Q2 is negligible. 

 The function Qo there considered is the surface value of a detached 

 wave that carries energy to infinity in all directions. One would 

 therefore expect that at the surface of the earth the ^o-wave would 

 act like the detached plane wave employed in Part Two. It will 

 now be shown that it does. 



It was shown in paper 8 that in the air 



goi(c) = 



where 



c — ta/I — T^ + tV 



c 



+ rVl - t2 + tV 



fo(n+i)(c) = — 2 — ^O"^'^) ~«^""'^^^ + 2n ^""''^^^' 



c = COS d and ti and 6 are shown in Fig. 2, 

 r-i = Vp^ + w^, c = w/rz, w = z + a. 



We need to compute (elm. units are employed, /i = : 



Ea = 



k^ dpdz ' 



