324 Mr. G. A. Campbell on Loaded 



ferring resistance from the coil to the line, and that the 

 loaded line attenuation may be less than that* for a uniform 

 line of the same total resistance, inductance, and capacity. 

 Inspection of the formulae shows that this applies to any line 

 of hi oh inductance for which 



,<i 



33 



and that the maximum reduction is for 



p=0, 



1 



when it amounts to 5" 7 per cent. 



1Y. 



To determine the loading for maximum efficiency., the total 

 weight of copper in cable and load being given, we may make 

 use of the following formulae for the weights of loading coils 

 and cable conductors per unit length of line, the formulae 

 applying to coils of similar proportions! and cables of similar 

 cross-section : — 



<'/w=»-'(t;y, (s?) 



(l-/)W=^ (38) 



where W is the total weight of copper per unit length ; w, iv r 

 are constants made a minimum by suitable proportions of 

 coils and cables, respectively : d is the spacing of the coils ; 

 and / is the proportion of the total copper in the coils. We 

 will assume that the line is to be of high efficiency so that 

 formulae (30), (SI), (32) apply, and suitable terminal 

 apparatus or terminal transformers will be employed to 

 practically annul terminal reflexion. The problem reduces 

 to securing minimum attenuation at the frequency of trans- 

 mission. Taking the product of equations indicated bv (20), 

 (23)£, (30). (37)i, (38)1, and substituting R' = pR. we'obtain 

 for the attenuation 



. o-rop — 2co- ivhcipi 



A ~G-2ia)^l/i(1^7)l(l-^)?-" Wt ' ' ( ° tj 



