324 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25, 



(1) Electrical Oscillations in Wires. By Mr H. C. Pockling- 

 ton, St John's College. 



1. In this paper are discussed some problems relating to 

 the propagation of electrical oscillations along wires. The wire is 

 always supposed to be a perfect conductor, and to have a circular 

 cross-section, the diameter of which is small compared with the 

 other dimensions of the system. We have therefore to solve the 



equations V 2 (P, Q, R) = F 2 -^(P, Q, P), conv. (P, Q, R) = 0, with 



the further condition that at the surface of the wire the vector 

 (P, Q, R) is perpendicular to the surface. The method of solution 

 used is to start with the simplest solution of the general equations 

 and by adding an infinite number of such solutions together to 

 obtain one of sufficient generality. The arbitrary function which 

 represents the infinite number of arbitrary constants introduced 

 into this last solution is then found from an equation deduced 

 from the surface condition. This last part of the work is con- 

 ducted by means of approximations. 



2. The simplest solution of the general equations, that 

 corresponding to the solution $ = 1/r of the equation V 2 <£ = 0, is 

 given by the formulae* 



„ d 2 U _ d 2 H _ d 2 U oTT , _ ,. 



P = -y— r , Q = -^—r , R = —j-- + a 2 U, where II = e lo » '&** r, 

 dxdz dydz dz 2 . 



in which 2ir\p is the period of the disturbance, and 27r/a(= 27rV/p) 

 the wave-length corresponding in free ether to this period. This 

 result can be expressed in words as follows. The electric force 

 due to an elementary Hertzian oscillation with the element of 

 length ds as axis, is compounded of two forces ; the first of these 



is derived from a potential function — -j- , and the second is a 



force a 2 II parallel to ds. This system of forces satisfies the equa- 

 tions of propagation of electric force everywhere excepting at the 

 element ds. If we place an infinite number of such elements 

 consecutively so as to form a curve, of which ds will then be an 

 elementary arc, and attribute varying strengths A, to them, we 

 shall obtain a system of forces Avhich satisfies the equations of 

 propagation everywhere except on the curve. The resulting 

 system of forces is 



(*'.&*>—(£' Ty> -^}Jd^ d § + a 'fd S (l, m ,n)xn. 



* Hertz, Wied. Ann. 1889, vol. 36, p. 4 ; Electrical Waves (tr. Jones), p. 140. 



