breaking a Circuit betiveen the Poles of a Magnet. 467 



found that a greater actual deflection was obtained when the 

 leaping-distance was as great as £ millim. than when it was 

 much smaller. May not Sir William Thomson's results be 

 partly accounted for by induction in the same manner ? 



Another method of experimenting upon the extra spark ob- 

 tained by breaking the circuit between the poles of an electro- 

 magnet gave excellent results. One of the poles of the induc- 

 tion-coil was connected with the outer coating of a very small 

 Leyden jar ; while the other pole was connected with the inside 

 coating through a small interval of air, to avoid the return cur- 

 rent. The inside coating of the jar was connected by a very 

 fine wire to a thin copper disk 261 millims. in diameter. Op- 

 posed to the copper disk ; at a perpendicular distance of 160 

 millims., was the end of a short rod 1 millim. in diameter. 

 Attached to the other end of the rod was a very fine wire con- 

 necting with one pole of the quadrant electrometer. The other 

 pole of the electrometer was connected with the ground. The 

 very fine wire leading from the opposing section of the rod 

 was so arranged that experiment showed no inductive effect 

 from the disk upon it. When the primary circuit was broken, 

 a spark passed, charging the Leyden jar, and consequently the 

 circular plate. The insulated plate was consequently charged 

 to some constant potential V . 



According to Maxwell's 'Electricity,' vol. i. § 177, and Thom- 

 son's ' Papers,' 233, the surface-density at any point on a thin 

 circular insulated plate is 



27rVa 2 -m 2 ' 



where a 2 is the radius of the plate, and m the distance of the 

 point from the centre. 



If the plate is in the coordinate plane xy, we have 



27rWa?-x 2 -f 

 The potential at any point (a, y, z) in space due to this dis- 

 tribution is 1 1 ^ f , since the plate is thin. The limits must 



be so chosen as to comprehend the whole surface of the disk ; 

 and, to avoid errors, the point (x, y, z) must be opposed to the 

 disk. 



v -fCXi 1 dxd y 



At any fixed point («#!, y 1} %), therefore, the potential is pro- 



2 12 



