B6 Mr. 0. Heaviside on the 



reversals, or, for brevity, the proportional amplitude. If z — {, 



2 

 P 



A 2 2 



n 



Let n = 10, which would make the time t of a pair of contacts 

 T = ?_ ^ = 1*347«, where « is the unit previously used ; then 



= 1-82 nearly. 



' Vl-22 



Thus the fault increases the proportional amplitude for this 

 speed 82 per cent. If z = j^ and n =10> tnen P is ratner 

 more than 6; and a fault of infinitely small resistance makes 



n 



6. Now for condenser working. Let every thing be the 

 same as in the last paragraph, with the addition of a condenser 

 of capacity r x cl at the sending-end and another of capacity 

 r 2 cl at the receiving-end, r x and r 2 being extremely small. 

 We shall now have 



kl' ir 



r ^- n ( 1+ ^ + Snh) 



The fault-factor is the same as before ; and if the maximum 

 received current possible were also the same as before, we 

 should arrive at exactly the same conclusions as regards the 

 influence of the fault on the proportional amplitude of the re- 

 ceived current. But the comparison is here faulty, since 



E 



kl 



(-a 



is the maximum current possible with both ends to earth, and 

 the condensers do not allow the received current to reach such 

 a strength, except in the imaginary case of condensers of in- 

 finite capacity ; for a condenser of infinite capacity is mathe- 

 matically equivalent to a conductor of no resistance if there 

 is no difference of potential between the coatings to start with, 

 or to a battery of no resistance and electromotive force E if 

 there is a difference of potentials E. But, as is shown later 

 on, the maximum strength of the received current with con- 

 densers becomes proportional to 



E 



Id 



(»+£) 



