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PROCEEDINGS OP THE AMERICAN ACADEMY. 



that they would naturally assume when free from external forces. It 

 should he noted how, near the point of contact, one element dominates 

 the other, a line of force springing across from one to the other, although 

 the charges are of the same sign. This is because the surface density is 

 infinite at the free end of an element. 



Figure 2 is not a combination of any of the elements already described. 

 The heavy lines represent rods charged uniformly with electricity of the 



Figure 7. 



same sign, and the figure is a cross section through the plane of the rods 

 of a three-dimensional family of equipotential surfaces. The equipotential 

 surfaces of one of the rods singly are confocal ellipsoids of revolution, 

 and therefore a plane section of these surfaces through the rod is a family 

 of confocal ellipses of exactly the same shape as those of the elliptic 

 element. The potential varies from ellipse to ellipse in a different man- 

 ner, however; for the elliptic element it remains finite, while it becomes 

 infinite on approaching the rod. The figure was drawn to show how 



