82 Prof. A. E. H. Love. The Advancing Front of the [May 9, 



the vibrations. These parts lie within the circles obtained from (19) 

 by riving to a the values |, f, ... V, * the corresponding instants 

 I -(0-26, 0-385, 0-51, 0-635, 0-T6, ... I'l 35) x (period) The 

 corresponding lines of force outside these circles are given by the 



equation 



sm " = - 1 (6-99403)6 (20), 



r X 



in which b has the values T ^, T V> A i- These are the 

 curves drawn in fig. A above. The remaining figures (1256) of 

 Plates 27 are unaffected by the conditions that hold at the front of 

 the waves. The figures by which Pearson and Lee's figs. 411 of 

 their Plates 1 and 2 should be replaced are the figures numbered 411 

 on Plates 2 5 accompanying this paper. 



In these figures the fine continuous circle represents the wave-front 

 at the time*[ = f-(0-24)2r]. The discontinuity of the electric field 

 at the wave-front is shown by the change of direction of the lines of 

 force at this circle 1 . Those lines of force which are determined by 



putting j^gj equal to T ^, T V, A, and J, are shown by the 



heavy dotted, heavy continuous, fine dotted, and fine continuous lines 

 respectively. The dotted circles that lie within the fine continuous 

 circle are curves at which Q vanishes, or the electric force has no 

 radial component. A surface Q = travels outwards at a varying 

 rate so as to lie within the wave-front r = Ct and to tend to overtake 

 it as / increases. This is shown by the inner dotted circles in 

 figs. 5 8, and by the outer dotted circles which in figs. 9 11 lie 

 within the fine continuous circle. It appears that no spherical surface 

 of the set given by Q = is the front of the advancing wave-train, but 

 that one of these surfaces tends to coincidence with this front as the 

 wave-train advances. 



The discontinuity of the electromagnetic field may also be shown in 

 a striking manner by tracing curves to represent at particular instants 

 the values of the transverse component of the electric force, which 

 correspond with all values of ?, the distance of a point from the 

 oscillator. Consider points in the equatorial plane of the oscillator, 

 for which = TT. The form of as a function of r is determined by 

 the equations 



when ct > r, and 



