INFLUENCE OF AN INTERPOSED CIRCUIT ON THE QUANTITY TRANSMITTED. 227 



in an unit of space, or (supposing the electrical particles to repel each other) of the ten- 

 sion ; now the attractive force evinced by the electrometer, and which we have termed 

 intensity, is directly as the square of the quantity contained in a unit of space, and 

 cannot be taken as a measure of the tension, except under this condition. 



37. On reviewing these phenomena, as connected with the discharge of electricity 

 between conductors, we may trace an interesting and consistent relation between them. 

 If we call the force exerted between two points c c\ fig. 14, at the instant of a dis- 

 charge, unity, and we now suppose the balls to be placed with the same accumulation at 

 twice the previous distance, then, according to the general law of electrical attraction, 

 the force will be reduced to one fourth, since it varies in an inverse ratio of the squares 

 of the respective distances (67-), at three times the distance it would be one ninth, and 

 so on ; hence the discharge could not occur at these distances with the same quantity. 

 But since double, treble, &c., accumulations develop free quantities or intensities, 

 which are as the squares of the whole quantity accumulated (16.), we have with 

 double, treble, &c., quantities accumulated, attractive forces which exactly compen- 

 sate the decreased force due to the respective increases of distance ; and hence at the 

 instant of the discharge at double, treble, &c., distances, with double, treble, &c., ac- 

 cumulations, the force is precisely the same ; that is to say, it is in every case sufficient 

 to overcome the atmospheric pressure at each given distance. 



38. A similar result ensues when the same quantity is disposed on an increased 

 surface of similar dimensions, where the distance of discharge (35.) becomes reduced 

 in an inverse ratio of the surface : now in this case the intensity being as the square of 

 the quantity contained in a given space, it decreases in the inverse ratio of the square 

 of the surface (20. e.), whilst the attractive force increases in an inverse ratio of the 

 squares of the respective distances (670 ; hence in decreasing the distance between 

 the discharging points, whilst at the same time the extent of surface is proportionably 

 increased, we preserve the attractive force constant, and are thus enabled to overcome 

 the atmospheric pressure at any required distance, as before. 



39. It would seem to follow from this, that the resistance of the atmosphere to the 

 passage of electricity is not really greater through any one discharging distance than 

 through another, and is in no case greater than the existing pressure of the air ; an 

 induction which is found to correspond very completely with experiment. 



40. I have examined carefully the influence of an atmosphere of variable density 

 and temperature, in restraining electrical discharges, and have arrived at some inter- 

 esting results ; these are comprised in the following experiments. 



(z.) The electro-thermometer N, fig. 13, being placed in connexion with the dis- 

 charging electrometer/, the effects of given quantities of electricity discharged through 

 the wire d c were carefully observed, the circuit m hfr i den being varied, both as to 

 its extent and the nature of the substance, in the portion i d. A very few trials served 

 to shew, that the effect on the wire decreased in some inverse ratio of the resistance to 

 the transmission of the accumulated electricity ; thus, the effect was less with a long 



