Equipotential Curves and Surfaces, fyc. 5 



electrode at A, and two negative electrodes at B and B x on the edges of 

 the sheet. 



We may also regard the case with one positive electrode at the centre 

 and four negative electrodes at the corners of a square as equivalent to 

 two sets, each set consisting of one positive and two negative electrodes, 

 one on each side of it, at equal distances along the same straight line on 

 a sheet either unlimited or limited by that straight line. 



Case 5. The curves for this arrangement of electrodes are drawn in 

 Plate 1. fig. 5; the distance from the positive to each negative elec- 

 trode is 76 millims., or 3 inches, as in Cases 3 and 4, the electrodes being 

 near the centre of a very large sheet of tinfoil. 



Taking the curve which cuts the axis at a distance of 54 millims. from 

 the centre, and at distances of 1 millim. on either side, the distances 

 r v r x ' from the negative electrodes to the several points on the curve 

 differ by the quantities in the following Table. 





Values of (> 



\- r i)- 





53 millims. 



For 53'75 millims. 



For 54 millims. 



. For 55 millims 



106 



108 



109 



110 



105 



109 



109 



110 



104 



108 



110 



110 



104 



108 



109 



110j 



104 



108 



112 



110 



101 



108 



114 



111 



99 









97 









The curve drawn between those at 53 and 54 millimetres was drawn 

 as nearly as possible at a distance of 53|- millims. from the centre. 



The result of this case shows that in the case of one and four elec- 

 trodes (Plate 2. fig. 3) we may expect the curves which cut the axis 

 at a distance of about 54 millims. from the centre to be hyperbolas. 

 The fifth curve from the centre is in the position of the rectangular hy- 

 perbola, having its foci in the positions of the negative electrodes ; and 

 we find, on measuring this curve as well as the curve on the outside of 

 it, that near the vertex the curves are accurately hyperbolas. This is 

 also true of the corresponding curves in fig. 4. The curves first drawn 

 in fig. 5 were drawn at equal distances of 10 millims. apart along the 

 axis, reckoning from the centre ; and the differences of potential for these 

 curves, reckoned from the centre, are proportional to the numbers 



138, 85, 88, 100, 80, 



138 including the effect due to contact of the electrode. Other curves 

 were afterwards interpolated in the neighbourhood of the position of the 

 rectangular hyperbola and around the negative electrodes. 



The sheet of tinfoil in the last three eases was sufficiently large for 



