498 REPORT — 1867. 



ductor, hung from one arm of a balance and kept in metallic communication 



■\Tith the earth, is attracted by a fixed insulated conductor, which is electrified, 



and, for the sake of keeping its electric potential constant, is connected with 



the inner coating of a Leyden battery. The first result which he announced 



is, that, when other circumstances remain the same, the attraction varies with 



the square of the quantity of electricity with which the insulated body is 



charged ; but '• it is readily seen that, in the case of ilr. Harris's cxperi- 



•' ments, it will be so slight on the unopposed portions that it could not be 



' perceived without experiments of a very refined nature, such as might 



' be made by the proof plane of Coulomb, which is, in fact, with a slight 



' modification, the instrument employed by Mr. Faraday in the investigation. 



' Now to the degree of approximation to which the intensity on the unop- 



' posed parts may be neglected, the laws observed by Mr. Harris when the 



' opposed surfaces are plane raay be readily deduced from the mathematical 



' theorv. Thus let v be the potential in the interior of A, the charged body, 



' a quantity which will depend solely on the state of the interior coating 



' of the battery with which, in Mr. Harris's experiments, A is connected, 



' and will therefore be sensibly constant for difl'erent positions of A relative 



' to the uninsulated opposed body B. Let a be the distance between the 



' plane opposed faces of A and B, and let S be the area of the opposed parts 



' of these faces, which will in general be the area of the smaller, if they be 



' unequal. When the distance a is so small that we may entirely neglect 



' the intensity on all the unopposed parts of the bodies, it is readily shown, 



' from the mathematical theory, that (since the difference of the potentials at 



' the surfaces of A and B is v) the intensity of the electricity produced by 



' induction at any point of the portion of the surface of B which is opposed 



' to A is - — , the intensity at anv point which is not so situated being 

 ■iira 



' insensible. Hence the attraction on any small element w, of the portion S 



' of the surface of B, will be in a direction perpendicular to the plane and 



' equal to 2it( - — | *. Hence the whole attraction on B is "^ 



STTrt-" 



" This formula expresses all the laws stated by Mr. Harris as results of his 



" experiments in the case when the opposed surfaces are plane " f. 



§ 18. After many trials to make an absolute electrometer founded on the 

 repulsion between two electrified spherical conductors for which I had given 

 a convenient mathematical formidain § 4 of the paper just qiioted, it occiu-red 

 to me to take advantage of the fact noticed by Harris, but easily seen as an 

 immediate consequence of Green's mathematical theory, that the mutual 

 attraction between two conductors used as in his experiments is but little 

 influenced by the form of the unopposed jiarts ; and in 1853, in a paper " On 

 transient Electric Currents " J, I described a method for measuring differences 

 of electric potential in absolute electrostatic measure founded on that idea. 

 The " absolute electrometer," which I exhibited to the British Association at 

 its Glasgow Meeting in 18-5.5, was constructed for the purpose of putting 

 these methods in practice. This instnmient consists of a plane metal disk 

 insulated in a fixed horizontal position with a somewhat smaller fixed metal 



* See Matbematieal Journal, vol. iii. p. 275. 



■|- •• On the Elementary La-svs of Statical Electricity," Cambridge and Dublin Mathema- 

 tical Journal, 184C; and Phil. IMag. July 1854. % Phil. Mag. June 1853. 



