5 2 ELECTRICAL EQUILIBRIUM. 



important of which we shall afterwards investigate; but we may 

 deduce from the general enunciation a certain number of remarkable 

 properties. 



66. GENERAL OBSERVATIONS. Let us first suppose that among 

 all the conductors which are in presence of each other, A v A 2 . . . A n , 

 one of them, A 1? has received a charge M, and that all the others 

 are in connection with the earth. 



When equilibrium has been established, the potential has a 

 constant value V x on A 15 and it is zero on all other conductors. Let 

 us suppose V l > 0. 



Within the whole dielectric the potential can neither be higher 

 than Vj nor lower than zero, and it lies between V l and (55). 

 It follows from this, that those conductors connected with the 

 earth only possess negative electricity; for if there were positive 

 spaces on their surface, lines of force would start from them towards 

 the points where the potential was lower, that is to say negative, and 

 these points do not exist. 



All the lines of force of the field start then exclusively from the 

 conductor A l ; one set terminates in the conductors in connection 

 with the earth, the others proceed towards an infinite distance. 



It follows from this that the negative charge on these conductors 

 is only a fraction of that upon A l ; the two charges would only be 

 equal, provided one of the conductors in connection with the earth 

 completely surrounded A r 



67. Let us now suppose that in the vicinity of Aj there are 



other insulated conductors A 2 , A 3 , , at first in the neutral state, 



and whose total charge therefore is zero. 



The potential is still positive and is less than V a within the 

 whole dielectric. It has a constant value on each of the other 

 conductors ; this value is positive, since part of the surface of each 

 of the conductors is charged with positive electricity, and therefore 

 lines of force start from them, and these lines of force proceed 

 towards spaces where the potential is everywhere positive. 



Let A 2 be that insulated conductor whose potential V 2 is 

 highest ; part of its surface is negative, it therefore receives lines of 

 force. None of these lines of force come to it from the earth, nor, by 

 hypothesis, from the other conductors whose potential is lower ; they 

 all proceed then from the conductor A p and therefore V 2 is less than 

 V r As, moreover, the lines of force received by A 2 do not form the 

 whole of those proceeding from A v each of the positive and negative 

 layers which make up the zero charge of A 2 is smaller than the total 

 charge of A r 



