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

 The magnetic force H is given by the equation 



sin Ae - J-*-r) r/I _ rjl*?y} sin ^ (ct - r + e) 



II = 5- Ae * \ \ \ X2 / A x ' 



when C/ > r, but when C* < r it vanishes. 



The radial electric force is continuous at the front of the wave, i.e., 

 at the surface r = Ct. The discontinuity of the transverse component 

 of the electric force at the front of the wave is 



... .................. (H), 



and this is equal, as it should be, to the magnetic force at the front of 

 the wave. 



The lines of electric force are the intersections of the planes through 

 the axis of the doublet with a certain family of surfaces Q = constant.* 

 If we denote by p the distance of a point from the axis, so that 



p = r sin 0, the quantity Q is p ( ), and the components of electric 



op Vf/ 



force parallel to the axis and at right angles to it are respectively 

 1 ?O 1 }O 



- - \2 and - 2-S. The flux of electric force through any circle 



p Op p OZ 



with its centre on the axis of the doublet may be expressed as 



- 2rQ. The form of Q is given by the equations 



QOJIl V . __ (ct- 

 ~~7~ Ae A 



when c/ > r, and 



when ct < r. At the separating surface Q is continuous, just as the 

 radial component R of electric force is continuous, and in fact we 

 have 



Q= y 2 R (17) 



throughout the field. 



The particular case where there fa no damping by radiation is 

 included in the foregoing by putting v-0, 2/X = ^ * and then we 



-r), B = A. 

 Th. w of th. function Q in te.e problem, w initiated by Hertz, loo, cit. 



