GOG Prof. W.. B. Mortoia on some Cases of Propagation 



where R, L S are respectively the resistance, inductance, 

 leakage-conductance, aud capacity, per unit-length of the 

 leads. When the oscillations are not slow we may still 

 employ this formula, but R L S C will now be functions o£ p. 

 In the Annalen der Physik for June of the present year, 

 G. Mie* has given a very complete solution of this problem 

 of propagation along two similar parallel wires. He finds an 

 expression for the wave-length and attenuation involving a 

 series of ascending powers of the ratio of radius of wire to 

 distance of the wires apart, which is usually a small quantity. 

 He also determines completely the distribution of the electric 

 and magnetic vectors. 



§ 2. Scope of the present Note. 



Before this paper appeared I had been working at the 

 problem by a method of successive approximations. The 

 bulk of this work has been rendered nugatory by the publica- 

 tion of Mie's much more satisfactory analysis, which gives a 

 single formula from which the solution can be got to any 

 desired degree of accuracy. The object of the present note 

 is to point out how the first approximation to the complete 

 solution may be very simply deduced from the known single- 

 wire solution. This approximation, as Mie has shown, means 

 that the square of the small quantity, radius of wire divided 

 by distance apart, is neglected. The advantage of this way 

 of arriving at the approximate solution lies in the fact that 

 the method admits of application to more complicated cases 

 where an exact solution is not possible. In fact we can 

 obtain an approximate equation for m in the general case of 

 any number of parallel wires of any sizes and materials, and 

 any arrangement in space, provided that all the radii are 

 small compared with all the relative distances. The different 

 roots of this equation correspond to the different ways of 

 grouping the wires into two opposite sets, such as might per- 

 haps be realized by connecting them in different ways, each 

 wire to a separate secondary plate in a Lecher arrangement. 

 If Ave take corresponding points on the wires we shall have 

 positive charges and currents on all the wires of one set, 

 negative on those of the other set. We shall use " similar " 

 and " opposite " to indicate wires belonging to the same or 

 different groups. 



§ 3. TAst of Cases worked out. 



The equation in its general form is intractable. The 

 following special cases are treated : — 



* Mie,.-4ro». d. Phys. ii. p. 202 (1900). 



