Prof. Thomson on the Electric Telegraph. 155 



The accompanying set of curves represents the strength of the 

 current through the instrument at the remote end of a wire as it 

 gradually rises, or gradually rises and falls, after the end operated 

 on is put in connexion with one pole of a battery, and either kept 

 so permanently, or detached and put in connexion with the ground 

 after various short intervals of time. 



The abscissas, measured on OX, represent the time reckoned 

 from the first application of the battery, and the ordinates, mea- 

 sured parallel to OY, the strength of the current. 



The time corresponding to a is equal to —^ loge ( o ). if I be the 



length of the wire in feet, k its " resistance" per foot, in electro- 

 statical units, and c its electro- statical capacity per foot (which is 



equal to ~"rT» if ^ ^e the electro-statical inductive power of the 



21og^ 



gutta percha, probably about 2, and R, R' the radii of its outer and 

 inner surfaces). The principal curve (I.) represents the rise of the 

 current in the remote instrument, when the end operated on is kept 

 permanently in connexion with the battery. It so nearly coincides 

 with the line of abscissas at first as to indicate no sensible current 

 until the interval of time corresponding to a has elapsed ; although, 

 strictly speaking, the effect at the remote end is instantaneous (i. e. 

 according to data limited as regards knowledge of electricity, to such 

 as those assumed in hydrodynamics when water is treated as if in- 

 compressible, or the velocity of sound in it considered infinitely great, 

 which requires instantaneous effects to be propagated through the 

 whole mass of the water, on a disturbance being made in any part 

 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 3a 

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

 difi'erentiation (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 



M 2 



