176 PROFESSOR K. PEARSON AND MISS A. LEE ON TI1K YIIWATJONS 



points of infinite negative velocity, we should have the radius = J (r -\- qr } ) 



(5 

 -f '5 ) Hence, the point of minimum velocity is more than half-way 



towards the outer point of infinite velocity. For the particular oscillator referred to on 

 p. 162, q~ = '17556, and the radius of the sphere of minimum velocity = 4*21 ? nearly, 

 while the sphere of infinite negative velocity has 6'70r for radius nearly (see p. 174). 

 At a distance from the centre of the oscillator we have very approximately 



V, v 3 cos s % 

 ~~v~ = (iVr/X) ! ' 



or, 



V, - v = 3 (V, - v). 



Thus at some distance from the centre of the oscillator, the excess of the velocity 

 of this component transverse electric wave (or of the total electric wave perpendicular 

 to the axis) over the velocity of light is three times the excess of the velocity of the 

 magnetic wave. 



In order to find the distance from the centre at which this component transverse 

 electric and the magnetic waves have equal negative velocities we must make 



1 



r (r r a ) r { (r r u ) s - r rf} 

 or, putting r r u, solve the cubic 



2tt 8 + Sr-u + ?y1 = 0. 

 Take u = - 7)r = 779'?', ; hence 



Thus, 



T] = \ -g-f q 6 , nearly (xxxiv). 



We conclude accordingly that the two velocities are negatively equal at a distance 

 from the centre equal to f ?* (1 -f- -faq") = fr , nearly. 



This equ.il negative velocity is v ( 1 r-^ j , nearly. Similarly, the minimum 



negative velocity of the electric transverse wave may be shown to be 



242601^} . . . . (xxxv), 



where ,= 



For the special oscillator discussed above it equals 59'545, or is slightly less 

 than 60 times the velocity of light. The minimum negative velocity of the trans- 





