Advancing Front of Waves emitted "by Hertzian, Oscillator. 



" The Advancing Front of the Train of Waves emitted by a 

 Theoretical Hertzian Oscillator." By A. E. H. LOVE, F.R.S., 

 Sedleian Professor of Natural Philosophy in the University 

 of Oxford. Received May 9, Read June 2, 1904 



[PLATES 26.] 



The waves emitted hy Hertz's oscillator have been identified with 

 those due to a vibrating electric doublet, that is to say, to a singular 

 point (of a certain type) of the electromagnetic equations. In air or 

 in free aether 1 these equations may be written in the forms 



i a 



2) 



in which c is the velocity of radiation, (X, Y, Z) denotes the electric 

 force measured in electrostatic units, (a, /3, y) denotes the magnetic 

 force measured in electromagnetic units. These equations are nearly 

 identical with those which have been used by Hertz.* They differ 

 from the latter in that C is here written for the quantity which Hertz 

 wrote I/A, and they differ also in the signs of the right-hand members. 

 The reason for the latter difference is that Hertz used a left-handed 

 system of axes of x, y, z ; but it is on many grounds more convenient 

 to use a right-handed system, as will be done here. The field due to a 

 variable doublet at the origin, with its axis parallel to the axis of 2, is 

 expressed by equations of the form 



(X, Y, Z) = (, 



\8zc 



c \3yct am 



(2), 



in which r denotes the distance of any point (x, y, z) from the origin, 

 and ^ (vt) is the moment of the doublet at time t. In Hertz's work 

 the function-^ is taken to be a simple harmonic function of its 

 argument, and written in a form equivalent to E/ sin n (t - r/c). 

 This supposition would be adequate if the vibrations were maintained, 



* " Die Krafte elefctrischer Schwingungen, behandelt nacli der Maxwell'schen 

 Theorie," 'Ann. Phys. Chem.' (Wiedemann), vol. 36 (1888). Keprinted in Hertz, 

 ' Tint ersuchun gen ii. d. Ausbreitung d. elektrischen Kraft ' (Leipzig, 1892), p. 147, 

 and in 'Electric Waves' (English edition), p. 137. The detailed references in 

 the text are to the pages of the English edition. 



