1904.] Train of Waves emitted ~by a Hertzian Oscillator. 



77 



The second of these equations determines e and the first determines 

 A in terms of B. It appears that B (the moment of the initial 

 doublet) is the maximum moment of the vibrating doublet.* 



It has now been shown that the waves expressed by (2) in which ^ 

 is given by (3) can advance through the field expressed by (5), provided 

 the constants A, B, v, e, are connected by the equations (8). Incidentally 

 it has been shown that the waves expressed by (2) in which ^ is given 

 by (3) cannot advance through a region in which there is no electric 

 or magnetic force, and that the phase constant e cannot vanish. In 

 fact, the function ^ instead of vanishing at the front of the wave has 

 there its numerically greatest value. 



Expressions may be formed for the radial and transverse components 

 of the electric force and for the magnetic force. The lines of electric 

 force lie in planes through the axis of the doublet, and the lines of 

 magnetic force are circles about that axis. The radial component R of 

 the electric force is given by the equation 



2 cos 



...... (9), 



when ct > r, but when ct < r we have 



being the angle which a line drawn from the origin to a point at 

 distance r makes with the axis of the doublet. 



The transverse component of the electric force is given by the 

 equation 



sin (ct - 





when Ctf > r, but when ctf < r we have 

 ~ sin/9 



19 v 



(12). 





* The result that the maximum moment of the vibrating doublet ought to be 

 the same as the moment of the doublet existing at the instant when the vibrations 

 begin is noted by M. Brillouin, ' Propagation de 1'Electricite, Histoire et Theorie ' 

 (Paris, 1904), p. 313. 



