ELECTRIC CIRCUrr 'II/EORV 55 



(170). From these formulas he announced the hivv that the "speed" 

 of the cable, i.e., the number of signals transmissible per unit time, 

 is inversely proportional to the product of the total capacity and total 

 resistance of the cable (KR in the English notation). To see just 

 what this means requires a little digression into the elementary 

 theory of telegraph transmission. 



Telegraph signals are transmitted in code by means of "dots" 

 and "dashes." The "dot" is the signal which results when a battery 

 is impressed on the cable for a definite interval of time, after which 

 the cable is short circuited. A "dash" is the same except that the 

 time interval during which the battery is connected to the cable is 

 increased. The "dots" and "dashes" are separated by intervals, 

 called "spaces", during which the cable is short circuited. Now when 

 the cable is short-circuited we may imagine a negative battery im- 

 pressed on the cable in series with the original battery. Conse- 

 quently the current in the cable, corresponding to a signal composed 

 of a series of dots, dashes and spaces, will be represented by a series 

 of the form 



I{t)-I{t-h)+I{t-h)-I{t-h)-\-I{t-U)- . . . (171) 



where, in the cable under consideration, /(/) is given by (168). /i is 

 the duration of the first impulse, h — ti of the first space, h — h of the 

 second impulse, etc. 

 Now by (168) 



m = -—-7= -7= = ^-7=<^w- 



XAV TT V T XK\/ IT 



T is, of course, 4t/x~CR = 4:t/KR (in the English notation). Now 

 suppose that 



4/1 



Tl = 



T2- 



x'CR 



'CR 



, etc. 



Then the signal can be written as 

 2 



cRVtt 



<^(r)-(A(r-rO+0(r-r,)- ... \ (172) 



Now if the relative time intervals ti, 72 . . . are kept constant (as the 

 length of the cable is varied), the actual time intervals ti, to . . . are 

 proportional to X'CR or to KR, and the wave form of the total signal 

 is independent of KR, when referred to the relative time scale r. 



