147, 148] ELECTROMETERS. 283 



148. Symmetrical Electrometers. The last described 

 electrometer forms an intermediate type to the Kelvin absolute 

 electrometer and the class of symmetrical electrometers, of which 

 Lord Kelvin's quadrant electrometer is the commonest example. 



Suppose a conductor C, Fig. 60, in the form either of a thin 

 plate or a cylinder, to be surrounded by two conductors A and B, 



C 



FIG. 60. 



composed in part respectively of parallel planes or cylinders, and 

 together forming a box enclosing C. We must then consider the 

 coefficients 



where the suffixes 1, 2, 3, refer to A, B, C. As in the last 

 example, the distributions on the edges or ends of C will be un- 

 affected by a slight change in its position. Besides this there 

 will be charges on portions where the field is uniform, and pro- 



Sf ' 



portional to j ~ , where S is that part of the surface of C on which 



the field is uniform. If we displace C from the symmetrical 

 position by changing a coordinate 0, we shall change S by an 

 amount proportional to 6. 



Accordingly, if B and C are at potential 0, A at potential 

 unity has the charge 



qn = n + erf, 



where a u and d are positive constants. 



If A and C are at potential 0, B at potential unity has the 

 charge 



g 22 =a 22 - c 2 0. 



If A and B are at potential 0, the charge of C at potential 

 unity is 



q s s = 33 + (GI - c 2 ) B. 



If A is at potential unity, B at potential is not affected 

 by the position of C at potential whereas the negative charge 

 on C contains a part proportional to 0. Accordingly 



$12 = i2, <?i3 = i3 - erf, q 23 = a 23 + c 2 0. 



