46 



Messrs. Boys, Briscoe, and Watson on the 



unit length at any part of the wire, the force of repulsion 

 upon an element at any moment will be 2 ^-, the average 



force on this element will be 2L an d the total repulsion 



between the wires will be %-=-. 



"la 



Now to find the relation between these it is necessary to 

 remember that the wires are resonators ; that is, the oscilla- 

 tions follow the natural period and are not forced. Also that 

 the total quantity of electricity on one half of the wire is the 

 integral of the current that' has passed the middle point. 

 Although there is no difficulty in finding the relation between 

 the attraction and repulsion, the following graphic method 

 may be worth giving. In order to simplify matters, the 

 resonator will at first be supposed of such a length that the 

 oscillations occur at the rate of one a second, i. e. it will be 

 supposed to be 1 of 3 x 10 10 centim. long ; also the maximum 

 current at the centre will be supposed unity. Now let the 

 vertical line in G (fig. 1) represent the wire, and the distance 

 of the harmonic curve from it at any point the strength of the 

 current at that point when it is at a maximum. 



Fig. 1. 



12 3 rv 



T CQ. 



In the same way, let the distance of the harmonic curve in 

 Q from the wire at any point represent the charge at that 

 point a quarter-period later, at which time it is at a maximum ; 

 then the total quantity on one end, represented by the shaded 

 area, is the integral of the current which has passed the middle 

 point p. Now this current varies harmonically with the time, 

 as shown in the time-diagram T. This is divided into four 

 equal parts. Thus the first represents (say) an upward 

 current rising from zero to its maximum ; this just neu- 

 tralizes the previously charged wire. Then, in the second 

 period, the continuation of the current produces an equal and 

 opposite charge, which is a maximum when the current has 

 become zero. In the third period, the current in the opposite 



