12 Prof. W. G. Adams on the Forms of 



These electrodes are 100 milliins. apart. The galvanometer-electrodes 

 in these experiments could not be brought within less than 5 millims. of 

 the axis of the curves. 



The curves drawn represent the sections of equip otential cylindrical 

 surfaces which are at distances of 10 millims. apart, measured along a 

 line which is parallel to and 5 millims. distant from the axis. 



The case of a circular cylinder containing sulphate of copper, with the 

 battery-electrodes at the two ends of a diameter, has also been worked 

 out experimentally ; and the equipotential surfaces are circular cylinders 

 cutting the sides of the vessel at right angles. Mercury was tried for 

 these experiments ; but from its almost perfect conducting-power it was 

 very difficult to determine two vertical lines in it which were precisely of 

 the same potential. 



Case 11. Another case was worked out experimentally with line-elec- 

 trodes in sulphate of zinc. One positive electrode was placed at the middle 

 point of one side of the rectangular box, and two negative electrodes were 

 placed symmetrically at the same distance from the positive electrode ; so 

 that the lines joining the positive to the two negative electrodes were at 

 right angles to one another. This corresponds to the case drawn in 

 Plate 2. fig. 4 ; and the sections of the surfaces at points which are not 

 near the side of the box are the same as the curves in figs. 3 or 4 of 

 Plate 2. Having previously determined the forms of these curves in the 

 tinfoil experiments, it was very easy to move the tracing-electrode from 

 one point to another on the same equipotential curve, by making use of 

 the curves previously drawn as guides for the electrode. 



Comparison of Experimental results with the Theory of Electrical Distribution. 



To examine the forms of the equipotential curves and surfaces with a 

 view to determine how far the results of experiment agree with and are 

 accounted for by the theory of distribution of electricity in a plane and 

 in space of three dimensions, take first the case of a plane of unlimited 

 extent in every direction, when two battery-electrodes are joined to two 

 points in the plane, so that there are equal and opposite currents at 

 those points. The potential at any point P of the plane is equal to 

 C — A (log r — log r ), where r, r x are the distances of the point P from 

 the two battery-electrodes A and B. Hence the condition for an equi- 

 potential curve is log r — log r^logc, ovr = c?\, where c is some constant. 

 This equation indicates that the bisector of the angle at any point P 

 between the lines r andr a cuts the line joining the two battery-electrodes 

 in the same point, which is a point on the equipotential curve. 



If 2a is the distance between the electrodes, the distances from A and B 



2ac 2a 



to this intermediate point are and . The locus of the point P 



* 1+c 1+c r 



4ac 

 is a circle whose diameter is - , and whose centre is on AB produced. 



1— c 2 r 



