G12 Prof. W. B. Morton on some Cases of Propagation 



see that, while the greater number of lines of force, starting 

 from a positive section of one wire, find their way to the 

 surface of the other wire, there will be also, close to the points o£ 

 zero surface-charge, some re-entrant lines, with their ends on 

 adjoining sections of the same wire. Our analysis shows that 

 the proportion of these latter lines is greater for the smaller 

 wire. It will help us to understand this result if we consider 

 that when the wires are isolated, as in Sommerfekfs case, the 

 scale is smaller -when the i-adius of the wire is smaller. The 

 loops formed by the lines of force, now all re-entrant, are 

 shorter; and so, when a second wire is brought up, the pro- 

 portion of these looped lines which lie close enough to the wire 

 to preserve their arrangement undisturbed, is greater. 



I have worked out, numerically, the case of two copper 

 wires of the dimensions and conductivity taken by Sommerfeld 

 in his first case, and found the effect of making the radius of 

 one wire 1 per cent, greater than the other, their distance 

 apart being 100, 200, and 300 times the radius. The numerical 

 data are: — 



a = 0-2 cm., P- = 10 9 , - = 5-83 x 10" 4 , e= ~. 



ITT p 100 



The ratio —r~ comes out :: — 



r h inn 99-5 + *M« . 



for - = 100* 1An r 



a 100 



b 99-3 + -llt 



--200, p- ; 



b _ ,99-2-t- 1-58?; 



- = 300, 



a 7 100 



So that the differences amount roughly to 5, 7, and 8 parts 

 in a thousand. The imaginary part indicates a small phase- 

 difference between corresponding points on the wires, the 

 larger wire being in advance. 



(b) When the two wires are similar we have, taking the 

 positive sign in equation (18), 



4=A + B + ie(A + B-l) 

 c 



A similar investigation shows that in this case the larger 

 wire carries more current than the other. We obtain results 

 of the same character when we suppose k 2 a small. 



