474 Prof. A. Gray on Relations of 



of two coplanar concentric circles, would therefore seem to- 

 be as follows. Imagine the circle AEB (fig. 1) replaced 

 by a uniformly charged disk and calculate the repulsion of 

 the disk on a unit charge placed at P. This will be most 

 easily done by dividing the disk into narrow strips all at 

 right angles to the diameter through A. Then the repulsion 

 exerted on unit charge at P, by one of these strips at 

 distance d' from P, of breadth das, and having D, F for 

 its extremities, is equal to the repulsion of the incomplete 

 circular strip of radius a?, breadth dx, and intercepted between 

 the lines PD and PF. 



3. A distribution of electricity on a plane conductor bounded 

 bij two close, similar, and similarly situated ellipses, and 

 a uniform current in the confocal ellipse through the point 

 considered. 



To generalize the theorem of § 1 consider the space 

 between the ellipses of which the equations are 



9 9 9 9 



~2 + 72—*' "o+'j7 2 =/C-d/C. . . . (3) 



ar tr or Ir 



One of these is shown by the heavy curve in fig. 3. We 

 take an element of elliptic arc at E of length ds, and suppose 



FW. 3. 



that over the area of this length, which lies at E between 

 the two curves, electricity is distributed with uniform sur- 

 face density a. If the length of the perpendicular from the 



