20 



Prof. W. G. Adams on the Forms of 



circle which passes through the two electrodes and cuts the circular disk 

 at right angles, we shall not alter the forms of the equipotential curves 

 within either of the separate disks bounded by the arcs of these two 

 circles. 



In all these cases the boundary-line will be made up of lines of flow, and 

 the equipotential curves will generally cut the edge of the disk at right 

 angles. Or if, in an unlimited sheet, each of two battery-electrodes be 

 divided into two, so that equal currents flow through each point, and if 

 these four electrodes be so arranged that they all lie on the circumfer- 

 ence of a circle, then the forms of the equipotential curves will be the 

 same as in the case of a circular disk which has its centre at the point of 

 intersection of the chords joining the two positive electrodes and the 

 two negative electrodes respectively, and whose radius is equal to the 

 tangent drawn from this point to the circle on which the electrodes lie. 

 In the case of the circular disk, the positive electrode outside the disk 

 becomes the virtual electric image of the other positive electrode, and the 

 outside negative electrode becomes the electric image of the other nega- 

 tive electrode. The edge of the disk cuts the other circle at right angles, 

 and is a line of flow for the four equal electrodes in the unlimited sheet. 

 Hence no alteration is made in the forms of the lines of flow by cutting 

 the sheet along this edge. 



This will apply to the case of any two unlike equal electrodes within 

 a circular disk when there are any number of electrodes connected with 

 the disk ; for if we take all these electrodes and their electric images, 

 and suppose them to be kept continually charged, each image like its 

 point, then in the unlimited sheet the line in the position of the edge of 

 the disk will be a line of flow for every set of two unlike electrodes and 

 their images, and therefore for all of them when taken together. 



Hence, by cutting along the edge of the circular disk to which such 

 images are due, no change is made in the lines of flow or in the equi- 

 potential curves. In fig. 3, A and C are like electrodes. 



"When the currents entering or leaving the disk at the several elec- 

 trodes are not all equal, since the sum of the currents entering the disk 

 must be equal to those leaving it, they may all be divided up into sets of 



rig. 3. 



two unlike equal currents ; and hence for all cases of currents entering 



