38 PROCEEDINGS OF THE AMERICAN ACADEMY. 



where y" = 1/g" is the architrave conductance, and G g = 1/R g is the 

 conductance to ground of the line at one end, when grounded at the 

 other end. 



Thus, for the line considered, p" = 1000 sinh 2 = 3626.86 ohms, and 

 g " = 0.001 coth 2 — 2.757204 X 10~ 4 =*7.6159 X UP 4 mho. 



Single Line Corresponding to a Symmetrical T or n. 



Reciprocally, any star connection of three resistances AO, GO, BO 

 (Figure 2), having two equal line-branches AO and OB of p ohms, with a 

 leak to ground of R! = \/g' ohms, corresponds to some smooth uniform 

 line of angle, 



6 = 2 sinh" 1 \/-£g hyps, (21) 



and of surge-resistance, 



% = Vp (p + 2/0 ohms. (22) 



Likewise, any delta-connection ABG"G" (Figure 3) with two equal 

 grounded leaks of resistance R" = \/g" ohms, connected by an archi- 

 trave of p" ohms, corresponds to a smooth uniform line of angle, 



6 = 2 tanh" 1 Y %#? x ,, hyps, (23) 



and of surge-resistance, 



% = It" tanh - ohms. (24) 



It 



Equivalent Circuits of Single Line in Terms of Resistances of 

 Line Free and Grounded. 



If the line be first freed and then grounded at one end, say B (Figure 

 1), and the resistance of the line be measured correctly at the other end 

 in each case (R f and Ji g respectively), we have for the equivalent T of 

 the line, 



p =R f (\-\/ l-^A ohms, (25) 



R! = R f \/ 1-^2 ohms. (26) 



Similarly, we have for the equivalent fl of the line, 



= R I\/ 1 - h. ohms, (27) 



/ R f 



