346 The Followers of Maxwell. 



the strength of the current is varied according to the simple 

 periodic law. The circuit will be supposed to be ft circle of 

 small area S, whose centre is the origin and whose plane is the 

 plane of xy ; and the surrounding medium will be supposed 

 to be free aether. The current may be taken to be of strength 

 A cos (2ni?/jF), so that the moment of the equivalent magnet 

 is SA cos (2irt/T). Now in the older electrodynamics, the 

 vector-potential due to a magnetic molecule of (vector) moment 

 M at the origin is (l/47r) curl (M/r), where r denotes distance 

 from the origin. The vector-potential due to Fitz Gerald's 

 magnetic oscillator would therefore be (l/47r) curl K, where K 

 denotes a vector parallel to the axis of z, and of magnitude 

 (1/r) SA cos (2-n-t/ T). The change which is involved in replacing 

 the assumptions of the older electrodynamics by those of 

 Maxwell's theory is in the present case equivalent* to retarding 

 the potential ; so that the vector-potential a due to the oscillator 

 is (l/47r) curl K where K is still directed parallel to the axis of 

 z, and is of magnitude 



SA 27T/ r 

 K = - cos [ t 



The electric force E at any point of space is - a, and the 

 magnetic force H is curl a : so that these quantities may be 

 calculated without difficulty. The electric energy per unit 

 volume is E 2 /8?rc 2 : performing the calculations, it is found that 

 the value of this quantity averaged over a period of the 

 oscillation and also averaged over the surface of a sphere of 

 radius r is 



The part of this which is radiated is evidently that which 

 is proportional to the inverse square of the distance,! so the 



* Cf. pp. 298, 299. 



tThe other term, which is neglected, is very small compared to the term 

 retained, at great distances from the origin ; it is what would be obtained if the 

 effects of induction of the displacement-currents were neglected : i.e. it is the 

 energy of the forced displacement-currents which are produced directly by the 

 variation of the primary current, and which originate the radiating displacement- 

 currents. 



