328 Astronomical and Nautical Collections. 
centres of magnetic action, must produce a perfect equilibrium: 
in this case, the two fluids may be in different quantities in each 
of the thin strata, provided that they be always in equal quantities 
in the two surfaces taken together. In this manner the theory of 
magnetic attractions and repulsions is reduced to the same princi- 
ples, and is made to depend on the same formulas with the theory 
of electric forces in conducting bodies; being only a particular case 
of these problems. But in the case of electricity the proposition 
here laid down is the original foundation of the theory, while in 
magnetism, on the contrary, it is a consequence deduced from 
the equations of equilibrium obtained by means of other consi- 
derations. 
It may also be remarked that, according to this general propo- 
sition, if we had a collection of small masses of metal, or of any 
conductor of electricity, of dimensions so small that they might be 
neglected in comparison with those of the whole collection or ag- 
gregate, and each being surrounded by a substance capable of 
restraining the passage of the electricity from one to the other, but 
not sensibly adding to their volumes; and supposing the aggregate 
thus constituted to be brought near any electrified body; it would 
then become electrical by induction, and in this state, the attractions 
and repulsions, which it would exert externally, would be the same 
with those of a simple conducting body of the same form, subjected 
to the same external forces, although in the one case the two elec- 
tric fluids would be transferred to opposite extremities of the body, 
and in the other they would be obliged to remain in the constituent 
masses to which they originally belonged. This supposed consti- 
tution of an electrical body is well calculated to give us a distinct 
idea of the disposition of the two magnetic fluids in a magnetized 
body. 
Upon applying the general formulas of this memoir to the case 
of a hollow sphere, of which the solid part is of an uniform thickness, 
‘a remarkable theorem is deduced from them, which is applicable 
both to magnetism and to electricity. Suppose such a sphere to 
be formed of a conductor of electricity, and suppose electrified 
