186 PROFESSOR K. PEARSON AND MISS A. LEE ON THE VIBKATIONS 



negative value of the phase continues until - = Oc ; for the general case we may 

 take approximately 



For the special value of x used above, i.e., x 3 38' 33'5", we find 



Oc = '8664. 

 This is at a distance from the source of 



r= -1379A, 



or about T324 metres. Thus we see that the phase of this action does not, as HERTZ 

 states ('Electric Waves,' p. 154), "increase continuously from the origin itself." In 

 discussing the velocity we have seen that dj3 3 /dr = d(3 /dr, so that the velocity of 

 propagation is identical with that given by (xxi). Thus it becomes indefinitely great 

 when 27rr/X = sin 2^ = '1268 for the above values of the constants. The point, 

 therefore, of infinitely great velocity is much closer to the origin than that of zero 

 phase. We think HERTZ considered these two points to be identical. At any rate, 

 he held that the wave moved with infinite velocity up to the point of zero phase. 

 For he argues from his conclusion that the phase increases continuously from the 

 origin that : 



" The phenomena which point to a finite rate of propagation must in the case 

 of these interferences t make themselves felt even close to the oscillator. This was 

 indeed apparent in the experiments, and therein lay the advantage of this kind of 

 interference. But, contrary to the experiment, the apparent velocity near to the 

 oscillator comes out greater than at a distance from it . . ."j 



As a matter of fact, the alterations in the velocity of transmission of either magnetic 

 wave or transverse component electric wave are very complex in the neighbourhood 

 of the oscillator, and these variations do not bear a simple relation to the points of 

 zero phase, from which points HERTZ assumes the outward moving wave to start. 

 Something of the difficulties HERTZ met with in his experiments on " interferences of 

 the second kind " made close to the oscillator may well have been due to this com- 

 plexity of result arising from the use of a damped wave-train. 



IV. The Compound Electric Wave in the Equatorial Plane, and the Wave of 

 Total Transverse Electric Force (<, + < 2 ). S 4 = /3 4 . 



The formula is now (xl). 



For the special oscillator for which our curve is drawn, c = '995, 9635, c'f = '988,928, 

 o = '126,8098, and the asymptote is 8 = 3'2687. 



* This must only be taken as the basis to find a second approximation, as the series converges slowly. 

 t Interferences of the " second kind " : see ' Electric Waves,' p. 119. 

 } ' Electric Waves,' p. 154. 



