Telephone Circuits. 683 



III. Isolated contrivances. When m is so great that 

 cosh mn and sinh mn are practically equal, calculations are 

 particularly easy. Thus, taking the case in which ^ = 5000, 



We have 



- = p= \/r//cqi=59'3 (-45°) = 419*3 (1-t) 

 c 



= a — ai = a— fiqi, say. 



(1) If in the middle of a very long line we merely insert an 



inductance leak to earth of L henry; L= - = /3= '11725 



gives the best effect. This multiplies the received current 

 by 1*414 and causes a lead of 45°. 



(2) An inductance of L = * 11725 henry in series with the 

 line and a leak to earth which is a condenser of capacity 

 1-f- fiq 2 farads (in the present case 0*532 microfarad) ; this 

 causes the current to be multiplied by 1*414 and to get a 

 lead of 225°. 



(3) An inductance of 0*11725 henry in series with the 

 line and no leak to earth. This multiplies the received 

 current by 1*414 and it creates a lag of 45°. 



IV. Returning to the contrivance consisting of two equal 

 condensers in series with the line and an inductance to earth 

 from the point between the condensers. For good telephonic 

 speech it is evident that the inductance ought to be small, 

 otherwise there is too much dependence on frequency; there 

 is some tuning. 



We want Jc'/l' to be small and nearly constant and k'V to 

 be small also. We cannot effect both these objects, but we 

 can obtain fairly good speaking by compromise. Thus, let 



k'= --05 x 10- 6 and /'= --128, so that K = .~ microfarad 



and L= 0*4 henry. Thus if m is 1 mile, r { — —'6'20 i and 

 r 8 =2000 i. 1 find that 



if g = 5000. C = 0*9704 (24° . 3'), 



if q = 4000, C = 0*9647 (35°). 



That is, with a frequency 800 there is an attenuation of 

 3 per cent, and a lag of 24° per mile, whereas with a fre- 

 quency of 640 there is an attenuation of 3f per cent, per 

 mile and a lag of 35°. We get practically the same results 

 by the continuous formulae. 



