IK THE HELD ROUND A THEORETICAL HERTZIAN o.M'ILLATOR. 183 



Now it is clear, both from this diagram and from that on p. 177, that we must go to 

 of 

 "- = 6 about to get fairly constant velocity of transmission. But X in HERTZ'S 



experiments was aljout 9'(> metres (see p. 162), or the experiments, supposing a constant 

 velocity of transmission desirable, ought to have been made at some 9 metres or 

 more from the oscillator. HEHT/'S first series are at less than 8, his third series at 

 less than 4, and his second, which do go up to 12, he states "required rather an 

 effort," 1 Within these limits the exact nature of the interference and the points at 

 which it may be expected to occur seem open to some criticism, even in addition to 

 the difficulties which have been raised by the problem of " multiple resonance."! The 

 views expressed above will be strengthened by an examination of the diagram giving 

 the phases of the waves, the velocities of which have been already discussed. 



(13.) The phasi-s have been plotted from the formula} given above, as follows : 



I. Transverse Component Electric Wave and Wave of Total Force perpendicular 

 to Axis (<,). 8, = $,. 



The formula is (xli). For the special oscillator for which our results are plotted, 



C, = sin 2x = '126,8098, c c = '995,964, 



X = '063,5760, c\ = 2'972,821. 



The asymptote is 8, = 3'2687 (i.e., 8, = (TT + 2 X )). 



We see from the diagram that the phase does not approach very rapidly to its 

 asymptotic value, being still about 5 per cent, of its value from it, when = 10. 



We notice that 8, starts from zero at the origin, and after high contact becomes 

 small and negative. This negative portion of the phase is too small to be seen on 

 the large diagram, but an enlarged inset figure is added. The curve cuts the axis 

 and becomes positive at about 1-165, or at about I '42 metres from the origin, a 

 distance within which some of HERTZ'S experiments on interference were made. The 

 range of negative phase could be considerably increased with a more rapidly damped 

 oscillator. 



The approximate value* of Oa for any value of x is 



20 2000 . /tan 1 y\l . 

 = (15 tan x) 1 + 7 tan x + jjjg tan x (~Y 5 ) + 



II. Axial Component Electric Wave and Wave of Total Radial Force 

 ,= -&. 



In this case the formula used was deduced from (xxiv). This may be altered to 



* ' Electric Waves,' pp. 118, 120, and 119 respectively. 



t PoiNCAR^, ' tflectricite et Optique,' vol. 2, p. 195 et seq., and p. 249 tl seq. 



I We owe this general solution to the kindness of Mr. L. N. G. FlLON, M . A. 



