On Systems ivith Propagated Coupling. 433 



to the creation of such waves. Experimentally it was found 

 easy to follow the variations for separations of over twelve 

 yards, whilst diffraction effects could be illustrated using a 

 plane edge (a door) or by reflexion from, or transmission 

 through suitable zone plates. 



The system used was too complicated to deal with satisfac- 

 torily when treated mathematically, but other simpler cases^ 

 can be considered in illustration. Case (i.) below is given 

 merely as an illustration of the propagation of mutual induc- 

 tion ; but no importance in practice can be attributed to it. 



(i.) Electrical transformer allowing for propagation. 



Assuming the two circuits to be separated by a distance 

 x and an alternating e.m.f . in the primary, using the ordinary 

 notation, we have 



M ^f+( L 4 +B 0° 2=o - 



The variation of the phase of the mutual action with x is 

 adequately expressed by the introduction of the factor- 

 exp( — Iqoc). 



Hence 



Let 



T> ' _ t> M 2 p 2 [R 2 cos 2qx — L 9 /> sin 2qx~] 



±1 - Kl+ " ' R 2 2 +L 2 y 



T , _ T M 2 /) 2 [R 2 sm 29a? + Lc, p cos 2qx] 



L ~ Ll E 2 VL 2 y 



tan ^ 2= B7 . tan.^^, tan .= 5^. 

 Then C 1= E ^ 



R'+.L'tp 



_ E cos (pt — ot) 



The denominator passes through maxima and minima as 

 x increases. The value of M itself decreases with increase 

 of distance. At near points the change through the distance 

 of a wave-length is very great, but at distant points its 

 variation produces a small effect compared with that due to 



