DURATION OF PROPAGATION OF AN ELECTRICAL WAVE. 223 



This time T l corresponds to the point of inflexion of the curve 



W 2 2 V 



A (Fig. 56), for the condition = 0, is equivalent to ^7 = ; it is 



a third of the time T, required to attain maximum current at this 

 point, with a constant potential at the end of the wire. 



The time T, may therefore be considered as expressing the 

 duration of propagation of an electrical wave. 



232. We may, in like manner, determine either graphically or by 

 calculation, the wave which would result when the origin of the wire 

 is put alternately in contact with sources at potentials + V and - V 

 during equal or unequal times. The curves in Fig. 58 correspond 

 thus to alternating contacts which may be collated in the following 

 table : 



Curves. Duration of Contacts. 



I a a 



II a a a 



III 2.a 2a 



IV 2.a a 

 V 30 2a 



VI 30 a 



VII 3# 2a a 



It will be seen that, by choosing the duration of these contacts, 

 we may obtain a far shorter wave than by a single contact. The 

 wire is then quickly restored to the neutral state after the passage 

 of the wave ; this is the problem which it has been attempted to 

 solve in certain cases of telegraphic communication. 



The curve of contact T may be simply constructed by adding 

 algebraically the ordinates of the curve A, and of another curve 

 - AT, the origin of which has been displaced through T. The curve 

 corresponding to the succeeding contact r of the opposite sign, is 

 obtained in like manner by the ordinates of the curves AT and 

 + AT+T/. The curves corresponding to the contacts r and r' of 

 opposite signs will therefore be obtained by the sum of the ordinates 

 of the three curves A-2A T + A T+T /; we thus avoid the separate 

 construction of curves relative to the different contacts. 



233. In the most general case, the potential V at the origin of 

 the wire does not pass suddenly from zero to a constant value ; it is a 

 continuous function F (9) of the time 6, counted from the moment 



