Middle of the Nineteenth Century. 255 



gutta-percha, " may be assimilated exactly to an immense 

 Leyden battery ; the glass of the jars represents the gutta- 

 percha ; the internal coating is the surface of the copper wire," 

 while the outer cgating corresponds to the sea-water. It 

 follows that in all calculations relating to the propagation of 

 electric disturbances along submarine cables, the electrostatic 

 capacity of the cable must be taken into account. 



The theory of signalling by cable originated in a corre- 

 spondence between Stokes and Thomson in 1854. In the case 

 of long submarine lines, the speed of signalling is so much 

 limited by the electrostatic factor that electro-magnetic induc- 

 tion has no sensible effect ; and it was accordingly neglected in 

 the investigation. In view of other applications of the analysis ; 

 however, we shall suppose that the cable has a self-induction L 

 per unit length, and that E denotes the ohmic resistance, and 

 C the capacity per unit length, Fthe electric potential at a 

 distance x from one terminal, and i the current at this place. 

 Ohm's law, as modified for inductance, is expressed by the 

 equation 



9^ T di _>. 



- -^- = L + Ri ; 



dx dt 



moreover, since the rate of accumulation of charge in unit 

 length at # is - di/dx, and since this increases the potential 

 at the rate - (l/C^difix, we have 



- 



'dt dx 



Eliminating i between these two equations, we have 

 1 8 2 F 



which is known as the equation of telegraphy* 



Thomson, in one of his letterst to Stokes in 1854, 

 obtained this equation in the form which applies to Atlantic 

 .cables, i.e., with the term in L neglected. In this form it is 



* "We have neglected leakage, which is beside our present purpose. 



t Proc. Roy. Soc., May, 1855 : Kelvin's Math, and Phys. Papers, ii, p. 61. 



