Measurement of Electromagnetic Radiation. 45 



known method, the two wires will act as resonators, and 

 induced oscillations will occur in them, not necessarily in 

 absolutely the opposite phase to the oscillations in the pri- 

 mary, but at any rate in the same phase in the two wires, 

 so that the electricity in each will surge up and down at 

 the same time. It", then, the ordinary theories of electro- 

 dynamic and electrostatic action apply in the present case, 

 which may be true or may not, then the currents going up 

 together and down together will attract one another, while 

 the charges resting chiefly at the two ends, being at one 

 moment -f- above and — below, and at the next moment 

 reversed, will repel one another. Owing to the harmonic 

 distributions of the current and the charges, the electro- 

 dynamic attraction will be mainly in the middle parts, while 

 the electrostatic repulsion will be mainly at the two ends. 

 Further, both these distributions vary harmonically with 

 the time, and are a quarter-period removed from one 

 another ; but the integral effect of each is equivalent to 

 a steady force, and the quarter-period difference of phase 

 has no influence as far as forces are concerned. 



In order to realize what these forces are, and what are the 

 relations between them, it will be necessary to consider them 

 separately. 



(1) Electrodynamic Attraction. — Let the wires be supposed 



to be very close together, so that the force felt by any element 



is almost entirely due to those elements of the other wire 



which are so close to it that the variation of the current strength 



in those elements along the wire is inconsiderable. Now, if the 



distance apart is e?, if c is the strength of the current at any 



moment (measured electrodynamically), and if / is the langth 



of the element, the force exerted by the other wire on this 



cH 

 element will be 2—r dynes. But as the current at any point 



varies harmonically with the time, the average force will be 



necessarily half the maximum force ; therefore the average 



cH 

 force on the centre elements will be — j , if c is the maximum 



a 



current at the centre. 



Since, also, the current varies harmonically along the wire, 



the average force per unit length over the whole wire will be 



half that at the centre ; so that the attraction between the 



wires will be ^-r, where L is the whole length of the wire. 



(2) Electrostatic Repulsion. — In the same way, if q is 

 the quantity of electricity (measured electrostatically) on 



