Equipoteniial Curves and Surfaces, fyc. 



21 



and leaving a circular disk, the edge is in the position of a line of flow 

 for all the electrodes and their images in the unlimited sheet. At an 

 electrode and its image the currents are equal, and must be supposed to 

 be both entering or both leaving the sheet. 



In the case when the two equal sets of two unlike electrodes in the 

 unlimited sheet lie at the corners of a rectangle, then the straight lines 

 joining the like poles are bisected at right angles by a straight line, which 

 is a line of flow. 



Hence, if the sheet be cut along this straight line, no alteration is 

 made in the lines of flow on either side of it ; and the pair of unlike 

 electrodes on one side of it become the images of the electrodes on the 

 other side. 



In the case of a plane sheet limited by two lines at right angles, three 

 electrical images of each electrode will be formed by the two rectangular 

 intersecting sides ; and these images will be arranged in a circle about the 

 point of intersection, in the same positions as the optical images formed 

 by two plane mirrors at right angles to one another. 



The equipotential curves in this case will be the same as those in an 

 infinite sheet when there are four equal electrodes of each kind — the four 

 positive electrodes taking the positions of the one positive electrode and 

 its three images, and the four negative electrodes being similarly placed. 



A particular and an interesting case arises when one of the electrodes 

 is on the edge of the circular disk ; the electric image of this electrode 

 then coincides with the electrode itself ; and the case in an unlimited 

 sheet which corresponds to this is that where a current enters the sheet 

 at one point, and leaves it by equal currents at two other points, the 

 three points lying on a circle which touches the radius of the disk, i. e. 

 cuts the disk at right angles, at the point where the current enters the 

 sheet. 



Fig. 4. 



When a current enters a circular disk at one point on the edge, and 

 leaves it by equal currents at two other points, the corresponding case in 

 an unlimited sheet is that where a current enters the sheet at one point 

 and leaves by equal currents at four other points lying two and two on 



