253] ELECTROMAGNETIC WAVES. 533 



Differentiating (i) by x and (2) by t we eliminate F, obtaining 



Consequently both the current and the potential are propagated 

 in accordance with the equation 



which, as it will be observed, is of the same form as the equation 

 250 (2), the resistance of the wires here taking the place of the 

 conductivity of the medium. We shall, with Poincare, refer to 

 the equation (5) as the Telegraphic Equation. If the wire is sur- 

 rounded by a concentric tube, we have ( 144), inserting the factor 

 J. 2 for electromagnetic measure, 



K= 



while if the currents be supposed concentrated in the adjacent 

 surfaces of the tubes, we have by 234 (21), since r 12 = r n , 



Consequently the coefficient of the first term is 



KL 



If we have two wires of the same diameter, which is small with 

 respect to their distance apart, the formula 159 (29) becomes 



2 " 



while the formula of 234 (22) gives 



so that we have the same relation as before. This relation is of 

 course not accidental, depending upon the similar equations 

 satisfied by the electric and magnetic fields between the conductors, 

 relations which are brought out in 234. The only reason for 

 any deviation from the above relation is that in obtaining L the 

 current density was supposed uniform, while in obtaining K the 

 surface density was not. The theory of electromagnetic waves 



L 'sS2^ 



