394 



of it). After the interval a, the current very rapidly rises, and after 

 about 4a more, attains to half its full strength. After 10a from the 

 commencement, it has attained so nearly its full strength, that the 

 farther increase would be probably insensible. The full strength is 

 theoretically reached only after an infinite time has passed. The 

 first (1) of the smaller curves represents the rise and fall of the 

 current in the remote instrument when the end operated on is put 

 in connexion with the ground after having been for a time a in 

 connexion with the battery ; the second (2) represents similarly 

 the effect of the battery for a time 2a ; the third (3) for a time 3 a 

 and so on. The curve (II) derived from the primary curve (I) by 

 differentiation (exhibiting in fact the steepness of the primary curve 

 at its different points, as regards the line of abscissas), represents 

 the strength of current at different times through the remote end of 

 the wire, consequent upon putting a very intense battery in com- 

 munication with the end from which the signal is sent, for a very 

 short time, and then instantly putting this end in communication 

 with the ground. Thus, relatively to one another, the curves (1) 

 and (II) may be considered as representing the relative effects of 

 putting a certain battery in communication for the time a, and a 



battery of ten or twenty times as many cells for a time a or a. 



If I were to guess what might be called " the retardation," which 

 in the observations between Greenwich and Brussels was found to 

 be about ^th of a second, I should say it corresponded to four or 

 five times a, but this must depend on the kind of instrument used, 

 and the mode of making and breaking contacts with the battery 

 which was followed. 



Equation of principal curve (I). 



y=10a-20a(e e* + e* <? 16 + &c.), where e~- 

 a being half the side of one of the squares. 



liy=f(x) denote the equation of the principal wave, and if/(.r) 

 be supposed to vanish for all negative values of x, the series of de- 

 rived curves are represented by the equations 



(1) .... y=f(x)-f(x-a) 



(2) .... y=/Gr)-/(*-2a) 



