86 STATIC ELECTRICITY 



this plane at right angles and it will be a level surface. Now 

 consider a unit tube passing as in Fig. 65c from one cylinder to the 

 other and cutting the plane in the area a. If a be made into an 

 infinitely thin conductor, it then has charges 1 induced on it, but 

 these will not disturb the course of the lines of force, since a 

 is infinitely thin. We may imagine each unit tube treated in the 

 same way and the corresponding units formed on the two sides 

 of the median plane. The charges thus imagined are all at one 



FIG. 65o. 



potential and will not tend to move, so that the system thus fonm <1 

 is in equilibrium. We shall then have two systems really inde- 

 pendent of each other, since there is a conducting screen entirely 

 separating one from the other. The upper cylinder po.sitively * K < -tri- 

 fled will have the corresponding negative on the upper face of tl it- 

 median plane, and the lower cylinder negatively electrified will have 

 the corresponding positive on the lower face of the median plane. 

 Either gives the case of a cylinder with axis running parallel to a 

 plane. Evidently the difference of potential between the plane 

 and the cylinder is half that between the two cylinders, and we 

 have approximately, if we put d = 2A, 



and 



The result shows that wires used in laboratory experiment* 

 may have quite considerable capacities. If, for instance, a \siie 



