706] 
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706. 
ON THE DISTRIBUTION OF ELECTRICITY ON TWO SPHERICAL 
SURFACES. 
[From the Philosophical Magazine, vol. v. (1878), pp. 54—60.] 
In the two memoirs “ Sur la distribution de Fdlectricite a la surface des corps 
conducteurs,” Mem. de VInst. 1811, Poisson considers the question of the distribution 
of electricity upon two spheres: viz. if the radii be a, b, and the distance of the 
centres be c (where c > a + b, the spheres being exterior to each other), and the 
potentials within the two spheres respectively have the constant values h and g, then— 
for Poisson’s f ^ writing cf> (x), and for his F (^j writing <f> (#)—the question depends 
on the solution of the functional equations 
where of course the x of either equation may be replaced by a different variable. 
It is proper to consider the meaning of these equations : for a point on the axis, 
at the distance x from the centre of the first sphere, or say from the point A, the 
potential of the electricity on this spherical surface 
the point is interior or exterior; and, similarly, if x now denote the distance from 
the centre of the second sphere (or, say, from the point B), then the potential of 
the electricity on this spherical surface 
interior or exterior; <£ (x) is thus the same function of (x, a, b) that <£> (x) is of 
C. XI. 
1