THE PROPAGATION OF LONG ELECTRIC WAVES 

 ALONG WIRES. 



By E. p. ADAMS. 

 (Read December 2, igio.) 



In the usual deduction of the equations of propagation of electric 

 waves along wires the notion of the electric constants per unit length 

 is introduced. While there is no difficulty involved in this as far as 

 resistance and leakage are concerned, the legitimacy of the extension 

 of this notion to self-induction and capacity is not obvious. In order 

 to determine the exact meaning to be attached to these terms it is 

 convenient to consider a line in which the electric properties are 

 localized in a finite number of coils, condensers and leaks, joined 

 by ideal conductors of no resistance, self-induction and capacity. 

 For the special case of long electric waves the solution can readily 

 be obtained by means of the calculus of finite dififerences. On pass- 

 ing to the limit, by letting the number of coils, etc., increase indefi- 

 nitely while their electric constants decrease indefinitely, the equa- 

 tions of propagation and their solution for a uniform line are at once 

 obtained. There appears to be a considerable advantage in the use 

 of this method in respect to its simplicity, particularly where the 

 terminal conditions are at all complicated. Two problems are 

 worked out in this paper ; the first that of the free vibrations of a 

 line earthed at both ends, and the second that of the forced vibra- 

 tions when a periodic impressed electromotive force is applied to the 

 circuit. 



Consider a line of length /, in which are inserted at equal inter- 

 vals n coils each of resistance R' and self-induction L. At points 

 between each pair of coils one plate of a condenser of capacity .S is 

 connected, the other plate being earthed ; and at the same points 

 leaks to earth, each of conductance K', are introduced. The cur- 

 rent in the ^th coil is C;,, and the potential at a point between the 



