255] ELECTROMAGNETIC WAVES. 547 



the velocity of electric waves by means of telegraph lines, what 

 was generally observed being more probably the maximum dis- 

 turbance than the front of the wave. 



In order to give a concrete idea of the nature of the propagation, 

 and to afford a means of comparison with the electrostatic theory, 

 we shall suppose that the function V is constant and equal to F , 

 from a^ to x. 2 . We shall also change our units of time and length, 

 by taking the relaxation-time r = 1/6 for the unit of time, and the 

 relaxation distance, d ar = ajb, as the unit of length. Accordingly 

 putting 



., t , , , x # 2 b (x # 2 ) b\ 

 =- = &, * 2= ^_ = _A__' ( __^ 



we have 



(35 ) F 



for a point on the right while the wave is passing over. This 

 equation was given by Heaviside in 1888, who carefully refrained 

 from giving his method of deduction, remarking " since, although 

 they were very laboriously worked out by myself, yet as mathe- 

 matical solutions, are more likely to have been given before in 

 some other physical problem than to be new*." 



Inasmuch as not only Heaviside's results but any others were 

 overlooked by the three French mathematicians quoted, who 

 published results six years later, we may conclude that in the 

 English writer modesty and original productiveness were more 

 strongly developed than historical research. (This modesty is not 

 maintained on the same plane throughout.) 



Inserting in the value of V the series for / (dropping accents), 



_ O=oo//2 I/2V7 



(36) 



and developing each term by the binomial theorem, we obtain 



* "Electromagnetic Waves." Phil. Mag. 1888; Papers, Vol. n. p. 373, 

 eq. (52). 



352 



