516 THE ELECTROMAGNETIC FIELD. [FT. m. CH. XIII. 



Of this a solution is 



(24) 



as has been shown (12). Accordingly for all points and times for 

 which at r has the same particular value we have the same 

 value of r^, or a particular value of <f> travels outwards with the 

 velocity a. The value of <f> is inversely proportional to the distance 

 r traversed. The solution makes the value of <f> infinite at the 

 point from which it is propagated. This is only an apparent 

 difficulty, for just as the potential due to a single mass-point is 

 infinite at the point, but is never infinite when the mass is 

 continuously distributed with finite density, BO here if we consider 

 a finite region in which <f> is not zero, the infinite value will not 

 occur, as is shown by our general solution (22). 



We see, accordingly, that a state of electric or magnetic field 

 existing in any region of space has its action propagated with the 

 finite velocity a = 1[A V/i in all directions, and inasmuch as by 

 the equations (A), (B), the time-variation of one field is propor- 

 tional to the curl of the other, the second term of (22) shows that 

 a curl of one field in any part of space causes a propagation of a 

 field of the other kind. 



The conclusion that electrical and magnetic actions are pro- 

 pagated with a finite velocity is the great and remarkable 

 consequence of Maxwell's theory, and was enunciated by him in 

 1864 in his celebrated paper on the Dynamical Theory t>f the 

 Electromagnetic Field. From this, and the other consequences 

 of the equations, he was led to enunciate the theory that light 

 was an electromagnetic phenomenon. In feet, the equation (3) 

 is, as we have shown, the equation of wave motion, and is the 

 basis of any undulatory theory, whether of light or of sound. 

 The manner in which the equations give us a theory suitable for 

 light and not for sound will be discussed in 249. 



Since the velocity of propagation is I/ A Vep, in air the velocity 

 should be I/ A v, or the velocity which corresponds to the ratio 

 of the two electrical units of quantity. Determinations of this 

 purely electrical quantity, as refinements in measurement in- 

 creased, gave results showing a surprising agreement with the 



