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XXVIII. On the Acceleration of Secondary Electromagnetic 

 Waves. By Feed. T. Teouton*. 



[Plate VI.] 



IT is well known that if, after the manner of Huygens's 

 construction, the effect of a wave-surface at any point be 

 determined by summing up the individual effects of the 

 secondary waves obtained, by supposing the surface divided up 

 into elementary portions, each element of surface acting as an 

 independent source, it becomes necessary to assume that an 

 elementary portion produces its effect at the point with an 

 acceleration of phase of \ period in advance of the effect pro- 

 duced at the point by the general wave-surface, otherwise the 

 sum of the secondary effects would possess a phase J period 

 in error. 



As ordinarily considered f , it is somewhat surprising that 

 there should be this change of phase in a wave coming from 

 an element of surface. But the consideration of this question, 

 in the light of Hertz's investigations on the radiation emitted 

 from an electromagnetic "vibrator" or discharging con- 

 denser, seems to be particularly suggestive. 



At first the magnetic component of the wave will be taken, 

 as it can be more simply dealt with. Considering, for 

 the moment, points situated along a fine at right angles to, 

 and starting from, the centre of a "vibrator," Hertz's ex- 

 pression % for the magnetic component of the electromagnetic 

 wave at a distance r is 



p =?{"(K)-+£«*(£-7)}- 



At points near the "vibrator" the vibration is easily seen to 

 depend almost entirely on the latter term, or 



Mi-i)> 



2irr 



while at a distance it depends in like manner on the first 

 term, or, as it may be written, 



P = 



>HHi+l)} 



* Communicated by the Author. 



t The complete Elastic Solid Theory contains this acceleration. See 

 Enc. Brit., art. " Wave Motion," p. 453. 



% Wiedemann's Annalen, January 1889; also ' Nature,' February 21, 

 1889. 



