552 Royal Society : — 



site electrodes, is 



\r rj 



where r and r x are the distances of the point from the electrodes ; 

 so that for an equipotential surface 



= constant. 



r r 3 



These surfaces are cut at right angles by the curves cos 6 — cos = c, 

 which are also the magnetic lines of force, 6 and being the angles 

 which the distances from the electrodes make with the axis. That 

 the lines of force in a vessel of finite size should agree with the 

 lines of force in space, the form of the boundary of the vessel in a 

 plane through the axis should everywhere be a line of force ; but 

 the ends of a rectangular vessel coincide very closely with certain 

 lines of force, either when the electrodes are at the ends, or when 

 there are two electrodes within the vessel, and two supposed elec- 

 trodes at their electrical images at an equal distance outside the 

 ends of the vessel. 



The equipotential surfaces are given in this case by the equation 



1,111 , , 



-+-. — - — —7= constant, 

 r t r x ?y 



and the lines of force by the equation 



COS + COS 1 — COS0 — cos x = c. 



The curve for which c=2 coincides very closely with the ends of 



the box. 



The equipotential surfaces were traced out in sulphate of copper 

 and in sulphate of zinc by the following method : — 



A rectangular box was taken, and the battery-electrodes attached 

 to pieces of wood, which could be clamped at the centre of the end 

 of the box, and could be brought to any required point in the line 

 joining the middle points of the end of the box. The galvanometer- 

 electrodes were attached to "J" pieces which rest on the ends and 

 side of the box, and the position of the electrodes was read off by 

 a millimetre-scale placed on the ends and sides of the box. 



In the sulphate-of-copper experiments, covered wire with the end 

 exposed was immersed to half the depth of the liquid ; in the ex- 

 periments with sulphate of zinc, the zinc electrodes were just im- 

 mersed below the surface of the liquid. The close coincidence 

 between the experimental curves traced out and the theoretical 

 curves and surfaces in space is shown by a comparison of the 

 numbers given in the paper for several of the curves which have 

 been traced out ; it also shows that, by reversing currents alter- 

 nately, it is easy to keep the polarization very small, and of constant 

 amount, on the galvanometer-electrodes. 



"When the electrodes are parallel lines extending throughout the 

 depth of the liquid, the equipotential surfaces are cylindrical, and 

 their sections are given by the equation 



log(/V . . .)— (log vV • • -) = lo g c . 



