174 ADVANCED ELECTRICITY AND MAGNETISM. 



C = 



1-943 



io 8 X log 



( D ~*\ 



H~R~/ 



(i) 



where D is the distance of the wires apart center to center, and 

 R is the radius of each wire; D and R being both expressed 

 in terms of the same unit. This equation is only approximately 

 true as will appear in the following discussion.* 



Fig. 115. 

 The two circles represent sections of the two wires of a transmission line. 



Figure 115 is a sectional view of the two wires WW" of a 

 transmission line, and to find the capacity per mile it is necessary 

 to calculate the voltage between the wires due to an assumed 

 amount of charge, positive on one wire and negative on the 

 other wire. 



The diameter of the wires is small as compared with the dis- 

 tance between them, and therefore each wire may be thought of 

 approximately as a line charge as explained in Art. 94. There- 

 fore according to equation (2) of Art. 94 the electric field inten- 

 sity in volts per centimeter at the element Ax due to the posi- 

 tively charged wire on the left is : 



BQ I 

 2ir X 



(I) 



and the volts per centimeter at Ax due to the negatively charged 

 wire on the right is: 



e " = I ? ' D^~ X (2) 



* A rigorous discussion of the capacity of two parallel metal cylinders is given 

 on pages 273-277 of Franklin's Electric Waves, The Macmillan Co., 1909. 



