268 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



Calculation of velocity of progression of the electromagnetic 

 wave. The intensities of the mutually dependent electric and 

 magnetic fields which constitute a pure electromagnetic wave must 

 satisfy two conditions, namely, (a) the magnetic energy per unit 

 volume in the wave must be equal to the electric energy per unit 

 volume in the wave,* and (b] the velocity of the wave must be 

 such as to satisfy equation (78), so that the electric field may be 

 wholly sustained by the inducing action of the moving magnetic 

 field. 



The magnetic energy in ergs per cubic centimeter in a wave is 

 equal to //" 2 /8?r according to equation (27), the intensity H of 

 the magnetic field being expressed in gausses. The electric 

 energy per unit volume in a wave is given by equation (75), in 

 which equation the energy is expressed in joules per cubic centi- 

 meter and the electric field intensity is expressed in volts per 

 centimeter. Reducing to c.g.s. units (energy in ergs per cubic 

 centimeter and electric field intensity in abvolts per centimeter) 

 we have 



I0 9 ) 



as the expression for the electric energy in ergs per cubic centi- 

 meter. Therefore the first condition above mentioned gives the 



equation 



H 2 f 2 



_ J _ ( 7Q \ 



STT 2B x io 9 

 Therefore solving equations (78) and (79) for V, we have 



TD * 



F 2 -- x io 9 (80) 



47T 



but the factor B is equal to 1.131 X io 13 , according to Arts. 

 91 and 98. Therefore we have 



cm 



V= 2.996 x io 10 - (81) 



oCC, 



The velocity of an electric wave thus calculated is identically 



* See footnote to Art. 144. 



