214 Mr. 0. Heavisidc on the Speed of Signalling 



rate results by considering the cable's capacity as collected at 

 its centre. Then, by ihe theory of the condenser, when Aap- 



Ffe. 1. 



s\ 



y 



*3T 



i . '- k b 



plies his battery to the line, the current rises at B according 

 to the formula 



E ' 



C=|(l-*-T), 



where C is the current, E the electromotive force, R the total 

 resistance between A and B, t the time, and 



S 



*-4G+«#)(i+*t«). 



where S is the cable's capacity. Thus the magnitude of T 

 determines the slowness of the rise of the current, and we may 

 therefore call it the retardation. (In the time T, the current 

 reaches about 63 per cent, of its maximum.) Now when B 

 sends to A, /and g change places, producing the arrangement 

 shown in fig. 2. If C 7 is the current B produces at A, 



r — rff 



1 9 



Fig. 2. 

 a, r 





C'=g(l-e-4). 



where 



XV |.(| +«+*)(| +5+/)- 



Comparing the values of T and T', we shall find that if a = £>, 

 T = T' ; also if f=g, T = T' ; but if a<b, as in the figures, 

 T<T' iff<g, and T>T' if/>#. Or, in plain English, the 

 retardation is the same in both directions if the land-lines have 

 equal resistances, whatever may be the resistances of the bat- 

 tery and receiver ; it is also the same in both directions if the 

 battery and receiver have equal resistances, whatever may be 

 the resistances of the land-lines ; but if the resistances of the 

 land-lines are unequal, the retardation is greatest when the 

 station nearest the cable is receiving, if at the same time the 



