Forced Vibrations of Electromagnetic Systems. 155 



force as a basis, and ignore the imaginary fluid behind it as being 

 a positive hindrance to progress, as soon as one leaves the elemen- 

 tary field of steady currents and has to deal with variable states. 



The remarks in the text on the subject of the speed of waves in 

 conductors relates to a speed that is not considered in Sir W. 

 Thomson's article. It is the speed of transmission of magnetic 

 disturbances into the wire, in cylindrical waves, which begins at 

 any part of a wire as soon as the primary wave through the dielec- 

 tric reaches that part. It would be no use trying to make signals 

 through a wire if we had not the outer dielectric to carry the mag- 

 netizing and electrizing force to its boundary. The slowness of 

 diffusion in large masses is surprising. Thus a sheet of copper 

 covering the earth, only 1 centim. in thickness, supporting a cur- 

 rent whose external field imitates that of the earth, has a time- 

 constant of about a fortnight. If the copper extended to the centre 

 of the earth, the time-constant of the slowest subsiding normal 

 system would be millions of years. 



In the article referred to, Sir W. Thomson mentions that Kirch- 

 hoff's investigation, introducing electromagnetic induction, led to 

 a velocity of electricity considerably greater than * that of light, 

 which is so far in accordance with Wheatstone's observation. 

 Now it seems to me that we have here a suggestion of a probable 



* [Note by Sir William Thomson.] In this statement 1 inadvertently 

 did injustice to Kirchhoff. In the unpublished investigation referred to 

 in the article Electricity, Velocity of [Nichols's Cyclopcedia, second edition, 

 1860 ; or my ' Collected Papers,' vol. ii. page 135 (3)J, I had found that 

 the ultimate velocity of propagation of electricity in a long insulated wire 

 in air is equal to the number of electrostatic units in the electromagnetic 

 unit; and I had correctly assumed that Kirchhoff s investigation led to 

 the same result. But, owing to the misunderstanding of two electricities 

 or one, referred to in § 317 of my 'Electrostatics and Magnetism,' I 

 imagined Weber's measurement of the number of electrostatic units in 

 the electromagnetic to be 2x3-lxl0 10 centimetres per second, which 

 would give for the ultimate velocity of electricity through a long wire in 

 air twice the velocity of light. In my own investigation, for the sub- 

 maiine cable, I had found the ultimate velocity of electricity to be equal 

 to the number of electrostatic units in the electromagnetic unit divided 

 by s/k ; k denoting the specific inductive capacity of the gutta-percha. 

 But at that time no one in Germany (scarcely any one out of England) 

 believed, in Faraday's " specific inductive capacity of a dielectric." 



Kirchhoff himself was perfectly clear on the velocity of electricity in a 

 long insulated wire in air. In his original paper, " Ueber die Bewegung 

 der Electricitat in Drahten" (Pogg. Ann. Bd. c. 1857 ; see pages 146 and 

 147 of Kirchhoff 's Volume of Collected Papers, Leipzig, 1882), he gives 

 it as el \/2, which is what I then called the number of electrostatic units 

 in the electromagnetic unit ; and immediately after this he says, " ihr 

 Werth ist der von 41950 Meilen in einer Sekunde, also sehr nahe gleich 

 der Geschwindigkeit des Lichtes im leeren Baume." 



Thus clearly to Kirchhoff belongs the priority of the discovery that the 

 velocity of electricity in a wire insulated in air is very approximately 

 equal to the velocity of light. 



