1897.] Mr Pocklington, Electrical Oscillations in Wires. 325 



If the curve is either closed or has its extremities at infinity, this 

 is equivalent to 



^«- iJ ) = (s.- 1- $/*£n + *J&ft«,.)xn...<i). 



This is a general solution containing an arbitrary function X. 



3. It now remains to consider the equation derived from the 

 surface conditions. At a point at a small distance e from the 

 curve we have, neglecting all terms that are not large, 



and similarly for JdsIX II, etc., so that, to this order of approxima- 

 tion, 



P = - 



2 !s io ^- 2 ^ io ^H' 



tt.pt 



and similarly for Q and B. 



The component of force along the wire therefore is, to this 

 order, 



_ /d' 2 \ „\, 



~ 2 U^ +aX J loge,e 



The force tangential to the cross-section of the wire = to 

 this order. Hence the system of forces given by (1) is a solution 

 of the problem (to this order) provided that 



— - + a °\ = or X = e ias , 

 as- 



and the disturbance is propagated along the wire with velocity V 

 and without diminution of amplitude. This is only what might 

 have been expected from a knowledge of what happens in the 

 case of a straight wire ; for if in our case we take the electrical 

 forces to be finite near the wire, at a finite distance they are zero. 



4. It is clear that in order to obtain results of much interest 

 we must approximate more closely. We will now consider the 

 equations obtained by neglecting only small quantities of the 

 first and higher orders. 



As given by (1) the force at any point on the wire tangential 

 to the axis is the same for all points on the same cross-section, 

 and contains two terms, one containing log e, the other finite. 

 The force tangential to the cross-section is finite and varies for 

 a given value of s as the cosine of some azimuth angle. 



■ 27—2 



