300 



vanic batteTy to give, during a limited time, a definite variation of 

 electric potential determined by theory, so as to fulfil the condition 

 of producing an electric effect at the other extremity, which, after 

 first becoming sensible, rises very rapidly to a maximum, then sinks 

 as rapidly till it becomes again, and continues, insensible. 



The principle followed is that pointed out by Fourier, by which 

 we see, that, when the wire is left with both ends uninsulated after 

 any electrical operations whatever have been performed upon it, the 

 distribution of electric potential through it will very quickly be 

 reduced to a harmonic law, with an amplitude falling in equal pro- 

 portions during equal intervals of time. Unless the electric opera- 

 tions fulfil a certain condition, this ulterior distribution is according 

 to the simple harmonic law (that is, is proportional to the sine of the 

 distance from either extremity, the whole length being reckoned as 

 1 80). The condition which I propose to fulfil is, that the coefficient 

 of the simple harmonic term in the expression for the electrical 

 potential shall vanish. Then, according to Fourier, the distribution 

 will very much more quickly wear into one following a double har- 

 monic law (that is, the sine of the distance from one extremity, the 

 whole length being reckoned as 360). In this state of electrifica- 

 tion the two halves of the wire on each side of its middle point, 

 being symmetrically and oppositely electrified, will discharge into 

 one another, as well as into the earth at their remote extremities ; 

 each will be like a single wire of half-length, with the simple har- 

 monic distribution ; and the wire will, on the whole, be discharged 

 as fast as a wire of half the length, or four times as fast as a wire of 

 the whole length, after an ordinary electrification. There is con- 

 siderable latitude as to the mode of operating so as to fulfil this con- 

 dition, but the theoretical investigation is readily available for finding 

 the best way of fulfilling it in practice. The result, as I have tested 

 by actual calculation of the electric pulse at the remote end, is most 

 satisfactory. The calculations, and curves exhibiting the electric 

 pulse in a variety of cases, will, I trust, very soon be laid before the 

 Royal Society. 



The time and law of operations being once fixed upon, a mecha- 

 nical contrivance of the simplest kind will give the means of direct- 

 ing a regulated galvanic battery to perform it with exactness, and to 

 any stated degree (positive or negative) of strength. Complete 



