622 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



We have therefore found the potential and lines of force due to a con- 

 ducting board infinitely long, two units wide, and charged with half a 

 unit of electricity per unit of length. Because of the shape of the equi- 

 potential lines, we may call this the elliptic element. 



Now to make if/ the potential, it must be made continuous. This is 

 done very simply by keeping the same distribution of values as before 



Figure 5. 



in the first and second quadrants, while changing the sign in the third 

 and fourth, xp now has the same value all along one branch of a 

 hyperbola and the supplementary value on the other branch. It in- 

 creases in value from zero on the positive piece of the X axis to ir on 

 the negative part. The discontinuity shows that there is a surface 

 charge on the interrupted X axis of 



± 1 



