of Equipotential Curves and Surfaces. 551 



This is an interesting case, as showing that the equipotential curves 

 do not always cut the edge of the disk at right angles. The curves 

 around the centre of the disk are nearly ellipses of small eccentri- 

 city, with one focus in the centre; but on placing one tracing 

 electrode at a distance from the centre 



between the electrodes, where a is the radius, there is great uncer- 

 tainty in determining the form of the curve on the opposite side 

 of the centre of the disk. 



This is explained by the fact that the electrodes were 1 millim. 

 in diameter, and a difference of distance of 1 millim. between the 

 electrodes near this point corresponds to a large portion of the 

 disk on the other side of the centre — this portion including an 

 area of about 500 square millims. in a circle 36 millims. in radius, 

 i. e. about one eighth of the whole area of the circle. On placing 

 one of the galvanometer-electrodes at the extremity of the diameter 

 through the battery-electrodes and tracing with the other, it is 

 found that the equipotential curve through that point cuts the 

 edge of the disk at an angle of 45°, and that there are two branches 

 cutting one another at right angles. 



These peculiarities are explained on tracing the curve 

 r 2 =4ar 1 



corresponding to this case. The extremity of the diameter is a 

 point through which two branches of the curve pass at right 

 angles to one another. 



The forms of the equipotential surfaces and lines of force in space 

 may be determined experimentally by taking a large vessel contain- 

 ing a conducting liquid and placing two points, the ends of two 

 covered wires, for battery-electrodes, at a given depth in the liquid 

 and away from the sides and ends of the vessel, taking similar 

 covered wires, immersed to the same depth, for galvanometer- 

 electrodes. 



For two electrodes, the equipotential surfaces will be surfaces of 

 revolution around the straight line joining them, and so will cut 

 any plane, drawn through this straight line or axis, everywhere at 

 right angles. 



Hence we may suppose sections of the liquid made along such 

 planes without altering the forms of the equipotential surfaces. 

 This shows that we may place our battery-electrodes at the side of 

 a rectangular box containing the liquid, and with the points only 

 just immersed below the surface of the liquid; and the equipotential 

 surfaces will be the same as if the liquid were of unlimited extent 

 in every direction about the electrodes. 



We shall obtain the section of the equipotential surface by taking 

 for galvanometer-electrodes two points in the surface of the liquid, 

 keeping one fixed and tracing out points of equal potential with 

 the other. 



The potential at any point in space, due to two equal and oppo- 



