Telephone Circuits. 679 



so that e" A = "97513, or there is an attenuation of 2*55 per 

 cent, per mile. The approximation to this is by an induct- 

 ance to earth of L henries per mile, where 



•055 x 10- 6 - -~ 9 = -01375 x 10~ 6 , 

 Lq- 



or L = *972 henry. When I use an inductance to earth I 

 generally prefer to put it in series with a condenser. Thus, 

 instead o£ an inductance of 0*972 henry, I would use an 

 inductance of 1*012 henrie* in series with a condenser of 

 1 microfarad. This enables the line to be tested more 

 easily. 



Instead of an inductance leak of 0*972 henry per mile 

 we may insert 0'972/m henry every m miles. As m gets 

 greater ihe discrepance from the continuous conditions gets 

 greater. The problem to be solved, later, is in all cases, to 

 find the discrepance for a particular value of m and what 

 therefore is the most convenient distance by which con- 

 trivances ought to be separated. 



3. Suppose Z / = — -09112 and k' = --0125 X 10~ 6 . These 

 values will cause c to be a maximum if the distance is 

 300 miles. It will be found that they mean, a capacity of 

 0139 x 10 -6 farad per mile in series with the line and an 

 inductance leak of 0*5925 henry per mile. Here ^ = 0*16775 

 and h = ±\/h / /l / =z 0*00333. This means an attenuation of 

 0'333 per cent, per mile when q is 5000. 



Now when q is taken as 3000 or 4000 the attenuation is 

 064 or 0*53 per cent, per mile. 



The approximation to these conditions is (a) a contrivance 

 every m miles consisting of a capacity of 0'439/m microfarad 

 in series with the line and an inductance leak of 0'5925/m 

 henry ; or (b) a contrivance every m miles consisting of 

 a capacity of 0'439/m microfarad in series with the line 

 between two inductauce leaks each of 1185/in henries ; or 

 (c) a contrivance every ?7i miles consisting of two condensers 

 in series, each of the capacity 0'878/m microfarad, the 

 point of junction being put to earth by an inductance of 

 5925/ra henry. It will be found that as m is smaller and 

 smaller the line with detached contrivances approximates 

 more and more to the line with continuous properties. 



Detached Contrivances. 



Suppose we have contrivances at the equidistant places 

 A, B, &c, m miles apart. There is a contrivance whose 

 terminals are A and A , another whose terminals are B and 



