Self-induction of Wires. 287 



choose the resistances &c. properly. The following will show 

 how the above apply practically. Remember that 1 ohm per 

 kilom. = 10 4 per cm. Then, if l x = length of line in kilom., 



If E/=10 3 , and 1/= 1, .;. ^=10 3 , and Z 1 = 856, 



„ R'=10 3 , 



)) 



L'= 10, 5 



>i=10 2 , 



)> 



Z 1 = 8568, 



„ B'=10*, 



V 



L' = 1, „ 



7l = 10 4 , 



V 



^ = 85, 



„ R'=10*, 



5) 



L' = 10, „ 



^ = 10 3 , 



?? 



^ = 856, 



„ Bf=10*, 



J? 



17 = 100, „ 



rc = 10 2 , 



53 



^ = 8568, 



„ R'=10 6 , 



?J 



L'= 1, „ 



?i = 10 5 , 



J? 



Z 1= 8-5, 



„ R'=10 5 , 



» 



L'= 10, „ 



7i= 10 4 , 



V 



^ = 85, 



„ R'=10 5 , 



J) 



L' = 100, „ 



7l=10 3 , 



?> 



Zi = 856, 



„ R'=10 6 , 



J) 



L'= 10, „ 



71= 10 5 , 



» 



^ = 8-5. 



The resistances vary from ^ to 100 ohms per kilom., the 

 inductances from 1 to 100 per cm., the frequencies from 

 10 2 /27r to 10 5 /27r, and the lengths from 8'5 to 8568 kilom. 

 In all cases § is the ratio of the distant end impedance to the 

 resistance. The common value of nl x is 856800. 



In the other case, nl/v ! has one fourth of the value just used, 

 so that, with the same B! and L/, l x has values one fourth of 

 those in the above series. 



Telephonic currents are so rapidly undulatory (it is the 

 upper tones that go to make good articulation, and convert 

 mumblings and murmurs into something like human speech) 

 that it is evident there must be a considerable amount of this 

 dielectric resonance, if a tone last through the time of several 

 wave periods. 



Having got the solution for C, the wire current, we may 

 obtain those for H, T, and <y from it. Thus, H r being the 

 same as (2/r)C r , where G r is the longitudinal current through 

 the circle of radius r, we may first derive C r or H r from C, 

 and then derive T and y from either by (11). Thus, make 

 use of (49) and (50), and the value of A x there given. Then 

 we shall obtain 



q _ r Ji(V) — (Ji/Ki)(gia )K 1 (g 1 r) ^ 

 r a 1 J 1 (8 1 a 1 ) — {J 1 IK 1 )(8 1 a )'K 1 (8 1 d 1 ) ' 



where, in the s h p and m 2 are to be d/dt and —d 2 /dz 2 . 

 Similarly for the return tube. 



In a comprehensive investigation, the C solution would be 

 only a special result ; as this special result is more easily got 

 by itself, it might appear that there would be some saving of 

 labour by first getting the C solution and then deriving from 



