ELECTRIC Clh'CL'll IIIIIORY 57 



affect the shape of the transmitted dot, which means that the cable 

 speed has reached its theoretical maximmn. These curves, it should 

 be obser\ed, can be interpreted in two wa>'s. First, we can regard the 

 length X of the cable as fixed and the duration of the impressed dot 

 as varied. On the other hand, we can regard the actual duration of 

 the impressed dot as constant and the length of the cable as varied. 

 From the latter standpoint the curves illustrate the progressive dis- 

 tortion of the signal as it is transmitted along the cable. 

 The dot signal of relative duration T can be written as 



D = I{t), r<T 



= I{t)-I{t-T), r<T 



and the second expression can be expanded in a Taylor's series, giving 



If T is sufficiently short this becomes 



D = T r{r). (173) 



Hence when the dot signal is of sufficiently short relative duration 

 T, the wave shape of the received signal is constant, I'{t), and its 

 amplitude is proportional to the relative duration of the dot. 



This can be generalized for any type of transmission system : 

 Let the dot signal be pi:oduced by an e.m.f. f{t) of actual duration T. 

 Then the received dot signal, by formula (31), is 



For t>T this becomes 



D = I\t) rf{T)dT-r'it) l''rf{r)dr+ . . . 

 Jo Jo 



and for sufficiently short duration T, we have approximately, 



D^r(t) rj\r)dT. (17-1) 



Ja 



Hence for a sufficiently short duration of the impressed e.m.f. the 

 received dot signal is of constant wave form, inde[)endent of the shape 

 of the impressed e.m.f., and its amplitude is proportional to the time 



