16 



Prof. W. G. Adams on the Forms of 



currents at the several electrodes are all equal, then for an equipotential 

 curve we shall have 



If the current enters at one point and leaves by four currents equal 

 to one another, then 



r 1 — c r x r^ r " r "'. 



We have an instance of this case (Plate 2. fig. 3) when a current enters 

 a very large sheet of tinfoil at the centre, and leaves by the four corners 

 of a square round this electrode as a centre. 



When a current enters a conducting-sheet by one point and leaves in 

 equal currents by two others, the equation to an equipotential curve 

 becomes 



r 2 =c r L r x ', 



where r is the distance from the positive electrode, and r v r 1 ' the dis- 

 tances from the negative electrodes to any point of the curve. 



In the particular case when c=l, and when the electrodes are all in 

 the same straight line, this becomes a rectangular hyperbola, the foci of 

 which are the positions of the negative electrodes, and the positive elec- 

 trode is at the centre of the hyperbola. 



This is the case which is given in fig. 5, as worked out experimentally, 

 where the focal distance of the hyperbola is 76 millims., and its vertex is 



at a distance from the centre equal to 53 # 75 millims., i. e. very nearly — j=, 



X 76 millims. The measured values of r — r*, starting from the axis for 

 six successive points some millims. apart from one another, are 108, 109, 

 108, 108, 108, 108 millims. The theoretical value for this difference is 

 107-5 millims. 



The Theory of Electrical Images. 



When there are four equal electrodes with currents entering the sheet 

 by two of them and leaving by the other two, we have 



rr' = c r y r l '. 

 Consider the case when these four electrodes lie on the circumference of 

 a circle. Join each pair of like electrodes by straight lines, and produce 

 the chords of the circle so joined to meet one another. 



Let AA l5 BB, be these chords meeting in C. Then the potential at the 

 point C is 



c + A{log (CA . CA X ) -log (CB . CB,)} =c. 



Pig. 1. 



