REPORT ON ELECTRICITY, MAGNETISM, AND IIEAT. 7 
The Coulombian theory of electricity had thus a fair claim to 
be considered as satisfactorily proved; and it was further con¬ 
firmed, or countenanced at least, by the simultaneous and simi¬ 
lar establishment of a parallel theory of magnetism. Yet this 
theory of electricity made its way but slowly to general acquain¬ 
tance and acceptation. Here, as in physical astronomy, the 
length and complication of the mathematical calculations which 
the estimation of the theory presupposed, put it out of the reach 
of students in general; and the mathematical reasoning was not 
here, as in physical astronomy, invested with a kind of dignity 
by the grandeur of the cosmical views on which it bore. 
The AEpinian theory was hardly known in England, except 
by name, till the late Prof. Robison gave a view of it, at consi¬ 
derable length, in the article Electricity in the Encyclopaedia 
JBritannica. In an appendix to this article the memoirs of 
Coulomb inserted in the Acad. Par. for 1786 and 1787 are re¬ 
ferred to, but without any notice of the question of one or two 
fluids. The Trait4 de Physique of Haiiy, published in 1803, and 
that of Biot in 1816, made the theory more generally known ; but 
the latter date w^as subsequent to M. Poisson’s important labours 
upon it, of which we must now give some account. 
By using the methods invented by preceding analysts, in 
order to determine the figure of the planets, in the doctrine of 
universal gravitation, M. Poisson was enabled to solve ex¬ 
actly those problems respecting the distribution of the electric 
fluid on the surface of spheres which Coulomb, as we have seen, 
had been obliged to attack indirectly. The most material of 
the analytical improvements of which M. Poisson availed him¬ 
self was the use of certain functions, possessing very curious 
properties, which have by recent writers sometimes been termed 
Laplace's Coefficients . These functions play so important a 
part in all the sciences which I have here to review, that it will be 
proper to give some account of them. 
Suppose a thin stratum of variable thickness distributed upon 
a sphere symmetrically with regard to the axis,—thus, take, for 
instance, the protuberant part of the terrestrial spheroid,—and 
letitbe proposed to find the attraction of this stratum upon a point 
anyhow situated, the position of the point being given by means 
of its angular distance from the north pole of the sphere, and 
its linear distance from the centre. The attraction on this point 
will then depend upon the position of the point, and upon the law 
of thickness of the stratum, by certain complex integrations. But 
this attraction may be resolved into a series of terms, each of 
which is a particular solution of the problem. Each of these 
terms contains two factors, one depending on the position of the 
