OF ARTS AND SCIENCES. 225 



Quadrant Electrometer. The other pole of the electrometer was con- 

 nected with the ground. The very One wire leading from the oppos- 

 lug section of the rod was so arranged that experiment showed no 

 ludnctive effect from the disc upon it. When the primary circuit was 

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

 circular plate. The insulated i.late was consequently charged to some 

 constant potential F^. 



According to Maxwell's Electricity, Vol. I. § 177, and Thomson's 

 I' Papers," 233, the surface density at any point on a thin circular 

 msulated plate is — 



6 = ; — ^ — , 



2 TT- \/ a- — nil 



where a^ is the radius of the plate, and m the distance of the point 

 from the centre. 



If the plate is in the co-ordinate plane x y, we have, — 



G = 



27r-v/«2 — j^t — ^2 



The potential at any point (x, y,z)m space due to this distribution is 



J J '^' '"'^^ ^^'^ P^^^^ ^« *^^"- The limits must be so chosen as 

 to comprehend the whole surface of the disc, and to avoid errors the 

 pomt {x,y,z) must be opposed to the disc. 



V ~ C C~° • I ^^ dy 



yi' 



At any fixed point {x^,y^, z^), therefore, the potential is proportional to 

 Fq. It was supposed necessary that the potential of the quadrants 

 attached to the short rod, which was at a great distance from the elec- 

 trometer,^ would be proportional to V^. The opposite quadrants were 

 at potential zero, being connected with the earth ; and since, when the 

 deflections are small they are proportional to the difference of poten- 

 tial of the two poles of the instrument, it was supposed that the 

 deflection of the electrometer needle would be a relative measure 

 of the potential of the plate. 



A great many observations were taken with this apparatus, and the 

 results agreed with the former ones, not only qualitatively, but very 

 nearly quantitatively. I select the following series of observations to 



VOL. XI. (n. S. III.) 15 



