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



of the same diameter of the pin cuts the radius drawn to the singular 

 point at a distance of more than one third of the radius from the sin- 

 gular point. 



In order to draw the curves near the singular point correctly, both 

 galvanometer-electrodes must be placed in contact with the disk in the 

 neighbourhood of the singular point. 



Electrical Distribution in Space of three dimensions. 



To consider the laws of distribution of electricity in space of three 

 dimensions, let a point or small sphere be charged with electricity ; then, 

 by Laplace's equation, the potential at any point at distance r from it 



is of the form — . 

 r 



If there be two points with charges of electricity proportional to 



A B 



A and B, then the potential at any point is of the form — +— -, where 



r r 



r, r' are the distances from the point to the two charged spheres. 



When the charges on the two spheres are equal, but of opposite kinds, 



the expression for the potential becomes A / - — - ). 



The equipotential surfaces will then be surfaces of revolution about 

 the straight line joining the two charged spheres. For an equipotential 



curve we shall have -—— = _. 

 r r. L c 



On referring to the experiments with battery-electrodes immersed to 

 a considerable depth in a conducting liquid, so as not to be near the 

 boundary of the liquid, we see that the same equation is true for the 

 equipotential surfaces when a steady current flows in at one electrode 

 and out at the other. 



The equation to an equipotential surface will be of the form 



111 



Take a section of the surface through the axis, and refer the section to 

 rectangular coordinates. 



Let the axis of revolution be the axis of so, and a line equidistant from 

 the electrodes be the axis of y, then the equation to the curve is 



{(x-af+f}-i-{(x+ a y+f }-$=!, 



c 

 where 2a is the distance between the electrodes. 

 For a consecutive point in the same curve, we get 



(x — ayx-{-y$y _ (x + a)$x + y? y __ 

 \ x — a x-\-a) * , * /l 1\ '- 



