Conductors conveying Steady or Transient Currents. 239 



proportion holds between the current and the potential, as 

 already calculated. 



But if by reflexion at distant unjoined ends of an open 

 circuit the pulses be turned from progressive into stationary 

 waves, then localities can be found on the wires at which 

 attraction or repulsion permanently occurs ; for X and C are 

 no longer companions, the sinuous distribution of current lags 

 a quarter period behind the sinuous distribution of charge. 

 Hence at a given instant there will be places where the cur- 

 rent force is a maximum and the static force zero ; while at 

 a quarter wave-length on either side the current force is zero 

 and the static force a maximum. Halfway between these 

 places only will the two forces be equal, but with alternate 

 agreement and disagreement of sign. A readjustment of 

 phnse between the conductors will now make all the difference; 

 a shift of a quarter wave-length changing from maximum to 

 zero, and a shift of half a wave-length bringing about reversal 

 of sign. 



According to all this therefore (if it be correct) it follows 

 that the simple ideas on which Mr. Boys set to work are right 

 after all, and that he will detect the forces in the way he 

 expects. 



Variation with Distance. 



A few words as to the magnitude of the effect to be ex- 

 pected. Hertz has shown (see ' Nature/ vol. xxxix. p. 404) 

 that at a reasonable distance from a rectilinear oscillator, one 

 or two wave-lengths being practically sufficient, the electric 

 force (or electromotive intensity) is perpendicular to the 

 radius vector from middle of oscillator, and is of magnitude 



E = ^! . sin (qp-pt) . sin 6 ; . . . (8) 



where p and 6 are the polar coordinates of the place, and 

 q = 27rj\. 



Calling the length of the oscillator the axis, and the normal 

 plane through its middle the equator, this means that the 

 electric force is a maximum at the equator, diminishes towards 

 the poles, and varies along any radius with the inverse distance 

 from the centre. 



At smaller distances the law is not so simple, but at any dis- 

 tance in the equatorial plane the electric oscillation is parallel 

 to the oscillator, and of amplitude 



g^V-jV + l), ■ 



showing that close to the oscillator the electric force varies as 

 the inverse cube of the distance, at intermediate distances 



8 2 



