140 Mr. 0. Heaviside on Electromagnetic Waves, and the 



tailing. This subject is, however, far better studied in the 

 telegraphic application, owing to the physical reality then 

 existent, than in the present problem, and also then by 

 elementary methods*. 



8. Owing to the presence of d/tlz in (45) and (47) we are 

 enabled to give some integral solutions in a finite form. 

 Thus, let H = H constant and E=0 initially on the whole of 

 the negative side of the origin, with no E or H on the posi- 

 tive side. The E at time t later is got by integrating (45), 

 giving 



*=&•{&-***}**> • ■ • (4< *° 



which holds between the limits ~= ±rt, there being no dis- 

 turbance beyond, except the H on the left side. When g = 

 and z/vt is small, it reduces to 



B = £?(£)*'"**" (50) 



This is the pure diffusion- solution, suitable for good con- 

 ductors. 



If initially E=E , constant, on the left side of the origin, 

 and zero on the right side, then at time t the H due to it is, 

 by (48), 



H =|r J «{^- A2 } ! H < 51 > 



The result of taking c = 0, <? = 0, in this formula is zero, as 

 we may see by observing that c in (49) becomes /j, in (51). 

 It is of course obvious that, as the given initial electric field 

 has no energy if c = 0, it can produce no effect later. 



The H solution corresponding to (49) cannot be finitely 

 expressed. It is 



which, integrated, gives 



1,3/«V ! / T, <T n 1.3.5 /^ 1 „ T T , i 



* " Electro-magnetic Induction and its Propagation." Electrician. \rt* 

 xlii. to ]. (1887). 



