288 Prof. Thomson on the Mutttal Attraction or Repulsion 



according to the two methods. They are reproduced here in 

 terms of the same notation, and with the same numbers affixed. 

 The first-mentioned method is expressed by the formulae (16), 



(17), (18), and the other by (8) (15). The formula) 



marked with letters (a), {b), &c. in the present paper express 

 details of which I had not preserved exact memoranda. 



Let A and B designate the two spherical conductors ; let a 

 and b be their radii, respectively ; and let c be the distance 

 between their centres. Let them be charged with such quanti- 

 ties of electricity, that, when no other conductors and no excited 

 electrics are near them, the values of the potential* within them 

 may be u and v respectively. 



The distribution of electricity on each surface may be deter- 

 mined with great facility by applying the ''principle of suc- 

 cessive influences'' suggested by Murphy (Murphy's Electri- 

 city, Cambridge, 1833, p. 93), and determining the efi*ect of 

 each influence by the method of "electrical images," given in a 

 paper entitled " Geometrical Investigations regarding Spherical 

 Conductors t-^' The following statement shows as much as is 

 required of the results of this investigation for our present 

 purpose. 



Let us imagine an electrical point containing a quantity of 

 electricity equal to ua to be placed at the centre of A, and an- 

 other vb at the centre of B. The image of the former in B will be 



b ...... . Z>2 



.wfl, at a point in the line joining the centres, and distant by — 



c c 



from the centre of B. The image of this in A will be jo-ua, 



c 



a^ ^ 



in the same line, at a distance j^ from the centre of A ; the 



c 



c __i 



image of this point in B will be g" ^^^ ^* * distance 



h^ 



c 



c 



c— 



a2 



from the centre of B ; and so on : and in a similar 



62 



c 



c 



manner we may derive a series of imaginary points from vb at 



* The potential at any point in the neighbourhood of, or within, an elec- 

 trified body, is the quantity of work that would be required to bring a unit 

 of positive electricity from an infinite distance to that point, if the given 

 distribution of electricity were maintained unaltered. Since the electrical 

 force vanishes at every point within a conductor, the potential is constant 

 throughout its interior. 



t Cambridge and DubUn Mathematical Journal, Feb. 1850, vol. v. p. 9. 



