322 Mr. Gr. A. Cam obeli on Loaded 



In cable circuits the inductance is quite negligible, and a 

 moderately loaded open wire circuit would have several times 

 more load than line inductance. 8 is the attenuation co- 

 efficient for a periodic interval, and will be small if the line 

 is to be efficient. 



Substituting (20) to {26) in (18) and (19), and expanding 



■»+ ^cosh-S (2^1)(l+ r )-2^ ( 4^y 



o (2/i + D ! VI + o/ v ; 



V 



V o (2n + l) ! \l+p. 



|" [2<2^+l)(2„HW>-rc)-4^^ 



(1^+1)! 



4 " J (S+IJ1 \T+- P ) ^ 



for all values of the variables. As the series converge 

 rapidly these formulae may be used for general computation 

 by noticing that 



cosh- 1 ^ +^0 = eosh-i^' r ±IZ±Z±y5^Z±? 



+ b cos -1 - 



2x 



(29) 



a = 



V(j; + v? + f + v(^-i) 2 +?/ 2 



In the limiting ease 8~0, the formulae become :— 



3 + 3/?-2o) 2 

 3(1+/,) v'l^S*"' ' ' • ' ( 30 ) 



G,Z1 J CO ,„ % 



»?= . _x , 31 



sin -to v ' 



^Vl-^ 2 , (32) 



/ Ad =2 cosh "V (33) 



i 



2co 

 a>71 *=— , (34) 



f "" 



#c = ft V® s -l (35) 



These simple formulae, which furnish the practical information 

 we require, are reduced to curves in diagrams IV., V., VI. 

 (PI. V.), which also give a few curves for 8 = 0*1, to show the 

 close approximation with which the (a, 77, k) curves for 8 = 

 will apply to any practical loaded line, for 8 would, perhaps, 

 never approach 0*1 in actual lines, but have a value nearer 



o-oi. 



