376 Mr. 0. Heaviside on Electromagnetic Waves, and the 



But the frequency needed to bring about an approximation 

 towards the constant resistance is excessive; in copper, we 

 require trillions per second. This brings us to the third 

 reason mentioned ; we have no knowledge of the properties of 

 matter under such circumstances, or of aether either. The 

 net result is that although it is infinitely more probable that 

 the resistance should tend to constancy than to infinity _, yet 

 the real value is quite speculative*. Similar remarks apply to 

 sudden discharges, as of lightning along a conductor. The 

 above R', it should be remarked, is real resistance, in spite of 

 its ultimate forrn, suggestive of impedance without resistance f. 

 The present results are corroborative of those in Part I., and, 

 in fact, only amount to a special application of the same. 



44. Reflecting Barriers. — Let the medium be homogeneous 

 between r=a and r = a v where there is a change of some 

 kind, yet unstated. Let between them the surface r=abe & 

 sheet of vorticity of e of the first order. We already know 

 what will happen when/v is started, for a certain time, until 

 in fact the inward wave reaches the inner boundary, and, on 

 the other side, until the outward wave reaches the outer 

 boundary; though, unless the surface of/ is midway between 

 the boundaries, the reflected wave from the nearest barrier 

 will reach into a portion of the region beyond f 9 by the time 

 the further barrier is reached by the primary wave. The 



* The above was written before the publication of Professor Lodge's 

 highly interesting lectures before the Society of Arts. Some of the ex- 

 periments described in his second lecture are seemingly quite at variance 

 with the electromagnetic theory. I refer to the smaller impedance of a 

 short circuit of fine iron wire than of thick copper, as reckoned by the 

 potential-difference at its beginning needed to spark across the circuit be- 

 tween knobs. Should this be thoroughly verified, it has occurred to me 

 as a possible explanation that things may be sometimes so nicely balanced 

 that the occurrence of a discharge may be determined by the state of the 

 skin of the wire. A wire cannot be homogeneous right up to its boundary, 

 with then a perfectly abrupt transition to air ; and the electrical properties 

 of the transition-layer are unknown. In particular, the skin of an iron 

 wire may be nearly unmagnetizable, fi varying from 1 to its full value, in 

 the transition-layer. Consequently, in the above formula, resistance ^tt^v 

 per unit surface, we may have to take /z=l in the extreme, in the case of 

 an iron wire. But even then, the explanation of Professor Lodge's results 

 is capable of considerable elucidation. Perhaps resonance will do it. 



f There is a tendency at present amongst some writers to greatly extend 

 the meaning of resistance in electromagnetism ; to make it signify 

 cause/effect. This seems a pity, owing to the meaning of resistance having 

 been thoroughly specialized in electromagnetism already, in strict relation- 

 ship to " frictional " dissipation of energy. What the popular meaning of 

 " resistance " may be is beside the point. I would suggest that what is 

 now called the magnetic resistance be called the magnetic reluctance ; and 

 per unit volume, the reluctancy. 



