Method of treating Electrostatic Theorems. 23 



centric sphere of radius a! is evidently 



2 '4<7rAa a')' 



6. We may define the " capacity " of a conductor to be 



such a quantity C that if Q be the charge on it and V the 



resultant pressure, either the pressures or the charges on all 



neighbouring conductors being zero, then Q= VC ; or energy 



of system =i tt* 



^ 4w 



Hence the capacity of the sphere in § 5 = ^- . a. 



Again, the capacity of a sphere surrounded by a concen- 

 tric spherical conductor which is connected to the earth is, 



b y § 5 > 4tt/ oaf \ 



E \a'-ah 



a' being the radius of the concentric conductor. For of 

 course the effect of the extra conductor is simply to relieve 

 all the strain external to it. The encroachment upon the 

 interior wall of the conductor simply causes aether to flow 

 away to the earth, for there is no opposition to this move- 

 ment ; whilst force would be required to enlarge the outer 

 boundary of the conductor (fig. 3). 



Fig. 3. 



7. Next consider the case of two spheres containing charges 

 Q l and Q 2 , the distance between the centres being d, and 



Fig, 4. 



a 



o 



the radii r 2 and r 2 being small compared with d (fig. 4). 



