324 Steady Currents in Linear Conductors [CH. ix 



We see that the current vanishes only when t = and when t = oo . 

 Thus even within an infinitesimal time of making contact, there will, accord- 

 ing to equation (306), be a current at all points along the wire. It must, 

 however, be remembered that equation (306) is only an approximation, 

 holding solely for slowly varying currents, so that we must not apply the 

 solution at the instant t = at which the currents, as given by equation 

 (306), vary with infinite rapidity. For larger values of t, however, we may 

 suppose the current given by equation (306). 



The maximum current at any point is found, on differentiating equation 

 (306), to occur at the instant given by 



t=*$KRa;* .............................. (307), 



so that the further along the wire we go, the longer it takes for the current 

 to attain its maximum value. The maximum value of this current, when it 

 occurs, is _ 



* ........................ (308)> 



and so is proportional to - . Thus the further we go from the end x 0, the 



CO 



smaller the maximum current will be. 



We notice that K occurs in expression (307) but not in (308). Thus the 

 electrostatic capacity of a cable will not interfere with the strength of signals 

 sent along a cable, but will interfere with the rapidity of their transmission. 



REFERENCES. 



On experimental knowledge of the Electric Current : 



WHETHAM. Experimental Electricity. (Camb. Univ. Press, 1905.) Chaps, v 



and x. 

 On currents in a network of linear conductors : 



MAXWELL. Electricity and Magnetism, Vol. I, Part n, Chap. vi. 

 On the transmission of signals : 



LORD KELVIN, "On the Theory of the Electric Telegraph," Proc. Roy. Soc., 

 1855; Math, and Phys. Papers, n, p. 61. 



EXAMPLES. 



1. A length 4a of uniform wire is bent into the form of a square, and the opposite 

 angular points are joined with straight pieces of the same wire, which are in contact 

 at their intersection. A given current enters at the intersection of the diagonals and 

 leaves at an angular point : find the current strength in the various parts of the network, 

 and shew that its whole resistance is equal to that of a length 



2\/2 + 1 

 of the wire. 



