188 ON THE VIBRATIONS ROUND A THEORETICAL HERTZIAN OSCILLATOR. 



The waves of magnetic force and of component axial electric force move outwards 

 each with the same velocity at all points, and this velocity is equal for all points at the 

 same distance from the oscillator. The intensity of the first force for points on the same 

 sphere varies as the cosine of the latitude, but that of the second force is constant. 

 The wave of component transverse electric force moves outwards with equal velocity 

 for all points at the same distance from the oscillator, and its amplitude varies as the 

 cosine of the latitude. Its velocity after it has reached a certain distance from the 

 origin, is always greater than that of the waves of component axial electric force, and 

 of magnetic force, and its excess over the velocity of light tends to become three 

 times the excess of the velocity of the wave of magnetic force over the velocity 

 of light. 



(iii.) The velocities of these waves undergo remarkable changes in .the neighbour- 

 hood of the oscillator, but still at distances such as HERTZ experimented at, and 

 which seem indeed to some extent within the field of possible physical investigation. 



(iv.) The point of zero phase for both transverse and axial component electric waves 

 does not coincide with the centre of the oscillator, so that these waves appear to start 

 from a sphere of small but finite radius round the oscillator. A fourth wave dealt with 

 by HERTZ, the wave of magnetic induction, does not, as he supposes, start from the 

 centre of the oscillator with zero phase, but in the case of a damped wave train with 

 a small but finite phase. 



(v.) Our analysis of these waves and of their singular points in the neighbourhood 

 of the oscillator appears to add something to HERTZ'S discussion ; it is possible that 

 it may throw light on the difficulties which arise in connecting with some of his 

 interference experiments. It would seem to us that all interference experiments 

 ought to be made at distances greater than 6 to 7 (V^) from the centre of the 

 oscillator, roughly about a wave-length from the oscillator, whereas HERTZ rather 

 terminated than started his experiments at this distance. At such distances the 

 phase curves are approximately parallel to their asymptotes. 



Finally, we are not unaware of the physical difficulties attending experiments, at 

 such distances, and wish in conclusion to again emphasise the fact that our analysis 

 only applies to a theoretical type of oscillator. It is, however, the type for which 

 HERTZ himself endeavoured to provide a mathematical investigation. 



