Self-induction of Wires. 279 



current, R the resistance per unit length, and V is a quantity 

 whose meaning is rather indistinct in Ohm's memoir, but which 

 would be now called the potential. The second equation is of 

 continuity. Misled by an entirely erroneous analogy, Ohm 

 supposed electricity could accumulate in the wire in a manner 

 expressed by the second of (70), wherein S therefore depends 

 upon a specific quality of the conductor. The third equation 

 results from the two previous, and shows thatV, or C, or Q = SV 

 diffuse themselves through the wire .as heat does by differences 

 of temperature when there is no surface loss. This system 

 has at present only historical interest. The most remarkable 

 thing about it is the getting of equations correct in form, at 

 least approximately, by entirely erroneous reasoning. 



The matter was not set straight till a generation later, when 

 SirW. Thomson arrived at a system which is formally the 

 same as (70), but in which V is precisely defined, whilst S 

 changes its meaning entirely. V is now to be the electro- 

 static potential, and S is the electrostatic capacity of the con- 

 denser formed by the opposed surfaces of the wire and return 

 with dielectric between. The continuity of the current in the 

 wire is asserted ; but it can be discontinuous at its surface, 

 where electricity accumulates and charges the condenser. In 

 short, we simply unite Ohm's law (with continuity of current 

 in the conductor) and the similar condenser law. The return 

 is supposed to be of no resistance, and V = Oat its boundary. 



The next obvious step is to bring the electric force of inertia 

 into the Ohm's law equation, and make the corresponding 

 change in that of V ; that is, if we decide to accept the law of 

 quasi-incompressibility of electricity in the conductor, which is 

 implied by the second of (70), when Sir W. Thomson's mean- 

 ings of S and V are accepted. Kirchhoff seems to have been 

 the first to take inertia into account, arriving at an equation 

 of the form d 2 V/^ 2 = (R + Lp)SpV. 



I am, unfortunately, not acquainted with his views regarding 

 the continuity of the current, so that, translated into physical 

 ideas, his equation may not be conformable to Maxwell's ideas, 

 even as regards the conductor. Also, as his estimation of the 

 quantity L was founded upon Weber's hypothesis, it may 

 possibly turn out to be different in value from that in the next 

 following system. In ignorance of KirchhofPs investigation, 

 I made the necessary change of bringing in the electric force 

 of inertia in a paper " On the Extra Current" (Phil. Mag. 

 August 1876), getting this system, 



-g=(K+L^)0, -J = Si>V, g=(R+L^)S P V, (71) 



