Prof. Thomson on the Electric Telegraph. 157 



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" — e"' + &c.), where e=(-\i ; 



a being half the side of one of the squares. 



li y=/(x) denote the equation of the principal wave, and if/(x) 

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

 rived curves are represented by the equations 



(1) . . . . yr^f(x)-f(x-a) 



(2) . . . . y =/(,,) -/(a. _2fl) 



(3) . . . . y=/(^)-/(^_3a) 



(7) . . . . y=/ix)-fix-7a) 



(II) .... y=a^. 



I think clearly the right way of making observations on telegraph 

 retardations would be to use either Weber's electro-dynamometer, 

 or any instrument of suitable sensibility constructed on the same 

 principle, that is, adapted to show deflections experienced by a 

 moveable part of a circuit, in virtue of the mutual electro-dynamic 

 force between it and the fixed part of the same circuit due to a 

 current flowing for a very short time through the circuit. Such an 

 instrument, and an ordinary galvanometer, (showing impulsive de- 

 flections of a steel needle,) both kept in the circuit at the remote end 

 of the telegraph-wire from that at which the signal is made, would 



give the values of I y'^dx, and I ydx (or the area), for any of the 



Jo Jo 



curves ; and the ratio of the time a of the diagrams to the time 

 during which the battery was held in communication with the 

 wire, might be deduced. The method will lose sensibility if the 

 battery be held too long in communication, but will be quite suffi- 

 ciently precise if this be not more than ten or twenty times a. I 

 believe there will be no difficulty in applying the method to tele- 

 graph-wires of only twenty or thirty miles long, where no retarda- 

 tion would be noticed by ordinary observation. Before, however, 

 planning any observations of this kind with a view to having them 

 executed, I wished to form some estimate of the probable value of a 

 certain element, — the number of electro-statical units in the electro- 

 magnetic unit of electrical quantity, — which I hoped to be able to 

 do from the observation of ^th of a second as the apparent retarda- 

 tion of signals between Greenwich and Brussels. I therefore applied 

 to the Astronomer Royal for some data regarding tlie mode of obser- 

 vation on the indications of the needle, and the dimensions and cir- 

 cumstances of insulation of the wire ; and he was so good as to send 

 me immediately all the information that was available for my pur- 



