[ IU!7 ] 



LXXXIII. Tlte I})ipossih'dki/ of Lndaitiped ]^iffraflo7is in a)i 



Unbounded Dielectric. By Prof. W. M^F. Orr, M.A.^ 

 1. 7N his recent important Avork on ''Electric Waves/^ 

 J. Maodonald claims that there is an essential difference 

 between a simply-connected and a multiply-connected space 

 in respect of the propagation of electric effects, in that an in- 

 detinitelv extended space of the latter description possesses 

 modes oi: free oscillation which do not involve loss of energy 

 by radiation, and are therefore absolutely permanent. As 

 I believe this view to be erroneous, and as such authorities as 

 Larinorf and Pocklington J have commented on it without 

 definitely rejecting it, no serious apology seems necessary for 

 endea'S'ouring to point out objections which may be urged 

 against such a conclusion and against the arguments on which 

 it is based. 



2. Macdonald discusses in detail § those modes of free oscil- 

 lation of the unlimited doubly-connected region bounded in- 

 ternallv bv a conductor in the form of an infinitely thin anchor- 

 ring in which the wave-fronts intersect the surface orthogonally 

 in circles whose planes contain the axis of revolution, and 

 obtains wholly real values for the periods, in agreement with 

 a result previously obtained by Pocklington || in much the 

 same way. The fact, however, that these periods are real, 

 in itself proACS nothing as to the absence of radiation. If we 

 take a ring whose circular axis is in a fixed position and 

 trace the effect of continually diminishing its thickness on 

 the free vibrations of any of the types considered, making 

 the supposition that the maximum electric force has an as- 

 signed value at a given point, as the thickness diminishes 

 indefinitely the energy inside any given closed surface which 

 incloses the ring at a finite distance increases indefinitelv, 

 since the normal electric force at the surface contains a terin 

 which varies inversely as the thickness. The reality of the 

 free period accordingly implies merely that energy is not 

 being radiated at an infinite rate. It may plausibly be con- 

 jectured, indeed, that when the ring is infinitely thin, if 

 the surrounding space be made simply-connected by cutting 

 away a portion of the ring, in this case also there will be 

 modes of free vibration having real periods. 



3. Macdonald gives an independent proof that there is no 



* Communicated by the Author. 



t ' Nature," Feb. 19, 1903. X Ibid. Mar. 26, 1903. 



§ ' Electric Waves/ p. 05. 



II Proc. Cauib. Phil. Soc. 1897. A complex value is there obtained 

 for the fundamental period when the thickness is finite ; I make no 

 further reference to this, through inability to understand Ai-t. 4 of the 

 paper. Of course if the correct value is complex, Macdonald's view is 

 wron<_'. for such a conductor at all events. 



