76 



STATIC ELECTRICITY 



the conductor is entirely surrounded by level surfaces lower in 

 the former case, higher in the latter, than the surface itself. 



If the surface is partly positively and partly negatively char 

 the surfaces are lower near the one part and higher near the other 

 part. 



We may illustrate these statements diagrammatic-ally by 

 Figs. 61 and 62, which are sections through systems showing iu each 

 case lines of force and level lines in the section. There is no 

 attempt to draw tu scale in these figures. 



Energy of an electrified system in terms of charges 

 and potentials. Let the charges be Q r Q r Q 3 , \r.. ropirti vi-ly on 

 conductors at potentials V r V 2 , V 8 , c., the /em-level bring any 

 conveniently chosen conductor. If all the charges be altered in 

 any given ratio the same for all, say to XQ X , XQ f , XQ 8 , \ 

 dently the intensity at every point will still remain the vun< in 

 direction, but will have X times the original magnitude. li- 

 the original level surfaces will still be leu -1, ;m<l the charges in 

 the new system will still be in equilibrium, The potentials \\ill 

 evidently be XV r XV 2 . XV 8 , &c. 



Let us represent the charges and potentials of the conductors 

 in the original system by points A, B, ('. 1). \c., on a charge- 

 potential diagram, Fig. (jtf, the abscissae representing charges, 

 the ordinat.es potentials. Thus AE = <<)., OK = V., BF = (J,, 

 OF = V 2 + C. 



Taking into account the whole .xvs|,-m, the sum of the charges, 

 i.e. the sum of the abscissae, must be zero. Now let u^ bring to t he 



FIG. 63. 



zero-level the same very small fraction of each charge. Then the 

 elementary charges will on their arrival exactly neutralise each 

 other. During the convection some small fraction of the energy 

 of the system will be given up. Repeating the operation a suffiY 

 number of times, we shall gradually exhaust the system, and it 

 is evident that as we remove the same fraction of each charge in 



