Forced Vibrations of Electromagnetic Systems. 497 



front. The subsidence to the steady state in the cylinder and 

 outside is very rapid when the front of E 4 has moved well out. 

 Thus, when vt = Sa, we have E 3 =V022e at r = a, and of 

 course, just outside, we have E 4 = *022£ ; and when vt~—10a, 

 we have E 3 = l'005e, E 4 =-005e, at r = a. 



As regards H, starting when t = with the value e/2fiv at 

 r = a only, at the front of the inward or outward wave it is 

 E= +/atH as usual. It is positive in the cylinder at first 

 and then changes to negative. Outside, it is first positive for 

 a short time and then negative for ever after. 



74. We can now see fully why the solution for a filament 

 e of e can not be employed to build up more complex solu- 

 tions in general, whilst that for a filament / of curl e can be 

 so employed. For, in the latter case, the disturbances come, 

 ab initio, from the axis, because the lines of curl e are the 

 sources of disturbance, and they become a single line at the 

 axis. But in the former case it is not the body of the fila- 

 ment, but its surface only, that is the real source, however 

 small the filament may be, producing first E negative (or 

 against e) just outside the filament, and immediately after E 

 positive. Now when the diameter of the filament is in- 

 definitely reduced, we lose sight altogether of the preliminary 

 negative electric and positive magnetic force, because their 

 duration becomes infinitely small, and our solutions (372) 

 show only the subsequent state of positive electric and nega- 

 tive magnetic force during the settling down to the final 

 state, but not its real commencement, viz. at the front of the 

 wave. 



75. The occurrence of momentary infinite values of E or of 

 H, in problems concerning spherical and cylindrical electro- 

 magnetic waves, is physically suggestive. By means of a 

 proper convergence to a point or an axis, we should be able 

 to disrupt the strongest dielectric, starting with a weak field, 

 and then discharging it. Although it is impossible to realize 

 the particular arrangements of our solutions, yet it might be 

 practicable to obtain similar results in other ways*. 



* If we wish the solution for an infinitely long cylinder to be quite 

 unaltered, when of finite length /,let at 2 = and z= £ infinitely conducting 

 barriers be placed. Owing to the displacement terminating upon them 

 perpendicularly, and the magnetic force being tangential, no alteration is 

 required. Then, on taking off the impressed force, we obtain the result of 

 the discharge of a condenser consisting of two parallel plates of no resist- 

 ance, charged in a certain portion only ; or, by integration, charged in any 

 manner. 



To abolish the momentary infinity at the axis, in the text, substitute 

 for the surface distribution of curl of e a distribution in a thin layer. 

 The infinity will be replaced by a large finite value, without other 



