28(i Professor Thomsox on Transient Electric Currents. 



which will imply that the strength of the current at each instant must 

 be sensibly uniform through the whole length of the discbarg,;r. 



(2.) That there is no sensible resistance to conduction over the princi- 

 pal conductor, so that the amount of charge left in it at any instant of the 

 discharge will be distributed on it in sensibly the same way as if there 

 was complete electrical equilibrium. 



The theorems demonstrated in the first and third parts of the previous 

 communication give expressions for the mechanical values of the charge 

 left in the principal conductor, and the electrical motion in the discharger, 

 at any instant, in terms of the amount of that charge, and the rate at 

 which it is diminishing. The sum of these two quantities, constitutes the 

 whole electro-statical and electro-dynamical energy in the apparatus, and the 

 diminution which it experiences in any time, must be mechanically com- 

 pensated by heat generated in the same time. We have thus an equa- 

 tion between the diminution of the electrical energy in any infinitely small 

 time, and the expression according to Joule's law for the heat generated 

 in the same time in the discharger multiplied by the mechanical equiva- 

 lent of the thermal unit. The equation so obtained is in the form of a 

 well-known differential equation, of which the integral gives the quantity 

 of electricity left at any instant in the principal conductor, and conse- 

 quently expresses the complete solution of the problem. Precisely the 

 same equation and solution are applicable to the circumstances of a pen. 

 dulum, drawn through a small angle from the vertical, and let go in a 

 viscous fluid, which exercises a resistance simply proportional to the velocity 

 of the body moving through it. 



The interpretation of the solution indicates two kinds of discharge, 

 presenting very remarkable distinguishing characteristics ; a continued 

 discharge, and au oscillatory discharge; one or otherof which will take place 

 in any particular case. In the continued discharge the quantity of elec- 

 tricity on the principal conductor diminishes continuously, and the dis- 

 charging current first increases to a maximum, and then diminishes con- 

 tinuously until after an infinite time equilibiium is established. In the 

 oscillatory discharge, the principal conductor first loses its charge, becomes 

 charged with a less amount of the contrary kind of electricity, becomes 

 again discharged, and again charged with a still smaller amount of elec- 

 tricity, but of the same kind as the initial charge, and so on for an infi- 

 nite number of times, until equilibrium is established ; the strength of the 

 current and its direction, in the discharger, has corresponding variations ; 

 and the instants when the charge of either kind of electricity on the prin- 

 cipal conductor is at the greatest, being also those where the current in 

 the discharger is on the turn, follow one another at equal intervals 

 of time. The continued or the oscillatory discharge takes place in 

 any particular case, according to the electrical capacity of the principal 

 conductor, the electro-dynamical capacity of the discharger, and the resis- 

 tance of the discharger to the conduction of electricity. Thus, if the dis- 

 charger be given, it will effect a continued or an oscillatory discharge, ac- 



