534 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



in free space however shows us that in all cases we must have the 



coefficient of ? equal to epA\ 

 ot 



If accordingly the resistance of the wires is negligible, the 

 disturbances are propagated with the speed l/A^/e/j, or in air 

 with the velocity l/A=v. The determination of this velocity 

 and the comparison of it with the results of determinations of 

 the ratio of the two units v is thus a matter of great importance. 

 Determinations of the velocity have been made by Blondlot*, by 

 Trowbridge and Duane^, and by SaundersJ, under the direction 

 of the author. These have given a satisfactory agreement with 

 theory, and are the only direct experimental verifications, for it is 

 to be noticed that in the determinations of Hertz, based upon 

 measurements of wave-lengths, the frequency was not observed, 

 but calculated, thus virtually begging the question. 



The result just announced, and the statement that the velocity 

 of the waves should be approximately that of light, were contained 

 in a paper published by Kirchhoff in 1857, and were afterwards 

 rediscovered by Heaviside||. The equations (i) and (2) were given 

 by Heaviside|| in 1876, and both researches remained singularly 

 unnoticed until recently. 



254. Particular Case. Submarine cable. The first case 

 of the telegraphic equation to be treated was that in which the 

 self-inductance of the circuit is negligible in comparison with its 

 resistance. This is the case in a submarine cable, in which the 

 wire is surrounded by a concentric tube of water, separated from 

 it by a thin layer of dielectric. We may then neglect the first 

 term of (5), making use of the equation 



* Blondlot. Comptes Rend. 117, p. 543, 1893. 



t Trowbridge and Duane. " The Velocity of Electric Waves." Phil. Mag. (5), 

 40, p. 211, 1895. 



J Saunders. " On the Velocity of Electrical Waves." Physical Review, (4), 2, 

 p. 81, 1896. 



Kirchhoff. "Ueber die Bewegung der Electricitat in Drahten." Pogg. Ann. 

 Bd. 100, 1857 ; Ges. Abh. p. 131. 



II Heaviside. "On the Extra Current." Phil. Mag. Aug. 1876; Papers, Vol. i. 

 p. 53. 



