246 Prof. Karl Pearson and Miss Alice Lee. 



" On the Vibrations in the Field round a Theoretical Hertzian 

 Oscillator." By KARL PEARSON, F.K.S., and ALICE LEE, B.A., 

 B.Sc., University College, London. Received January 2, 

 Bead January 19, 1899. 



(Abstract.) 



(1) The object of this paper is to investigate the types of wave motion 

 in the neighbourhood of a theoretical Hertzian oscillator. By a theo- 

 retical Hertzian oscillator the writers understand a Maxwellian " double 

 point " of initial maximum moment E/. But as the actual oscillator 

 has been shewn by Bjerknes and others to give a damped wave train, we 

 take the maximum moment to run down with the time, and to oscillate 

 between the limits Efe~^ f . This gives a wave train corresponding 

 to that observed by Bjerknes and represented at a given distance by 



Ce-PJ sin (p 2 t + y). 



The investigation for a " double point " with a steady wave train was 

 originally made by Hertz himself, and has found its way into most of 

 the current text-books of electro-magnetism. The theory thus given, 

 is insufficient for two reasons, both of which were recognised by Hertz 

 himself, namely, because (i) the actual oscillator has sensible extension, 

 and (ii) the wave train it gives forth is not steady. 



The present paper only attempts to remove the latter objection to 

 Hertz's original theory ; like that theory it becomes less accurate as 

 we approach nearer to an actual oscillator. Still the range within which 

 the damping produces a very sensible divergence from Hertz's theory, 

 seems sufficiently large to allow of experiment being made at a 

 considerable distance from the oscillator; certainly the chief diver- 

 gences between the present and Hertz's original theory actually fall in 

 the portion of the field, wherein his chief interference experiments 

 were made. Besides therefore the difficulties arising from the 

 phenomena of "multiple resonance," it seems necessary to measure 

 the influence of damping in modifying the mathematical results for a 

 steady wave train, which results are what Hertz made use of in 

 interpreting his interference experiments. The four sources of diver- 

 gence between theory and experiment in Hertz's case, i.e. : 



(i) the damping of the wave train, 



(ii) the size of the oscillator, 



(iii) multiple resonance, 



(iv) defect of electro-magnetic theory, 



may one or all be effective, but the object of the present paper is 

 confined entirely to a theoretical investigation of the first. 





