STANDARDS OF CAPACITY. 453 



determined from the geometrical dimensions of the bodies em- 

 ployed. 



The problem is easily solved in certain cases for example, a 

 sphere at an infinite distance from any conductor; the capacity is 

 then equal to the radius (73). But these conditions are impossible 

 to realise, and external objects for instance, the sides of the room 

 greatly increase the real capacity. 



This difficulty is avoided with a condenser formed of two con- 

 centric spheres* (77). If R and R x are the internal and external 

 radii, the value of the capacity is 



RR R 



R,-R R 



Sir W. Thomson has used a standard of this kind. The radii 

 were deduced from the weight of water contained in the external 

 sphere alone, and in the interval between the two spheres when they 

 were placed concentrically. Allowance must also be made for the 

 insulating wedges which support the inner sphere, and which do not 

 act like the air which they displace ; allowance must further be made 

 for the orifice which must be made in the outer armature, to allow 

 passage to the rod which communicates with this internal sphere, 

 as well as the influence of this rod. These corrections can only 

 be made approximately. In the apparatus of Sir W. Thomson, for 

 which R 1 = 5'857 cm., R = 4*511 cm., and therefore = 63*264 cm., 

 the corrections amounted to 0*255 cm., and raised the capacity to 

 63*519 cm. 



Concentric cylinders (80) might also be used, but in this case a 

 correction for the ends must be introduced into the formula. 



Condensers formed of two parallel planes are to be preferred ; it 

 is comparatively easy to ascertain if the two surfaces are truly plane, 

 and to measure accurately the distance between them. It is to be 

 observed, however, that the density of the electric layer is greater at 

 the edge than in the centre, and that therefore the true capacity is 

 greater than that deduced from the dimensions. Further, we do not 

 consider the electricity which exists on the external surface of the 

 disc, and which, in fact, would not exist if the system were infinitely 



* This formula holds particularly for an insulated sphere in the centre of a 

 hall of mean radius R. 



