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FIFTH REPORT* —1835. 
elements to the small parts of bodies within which the magnetic 
fluids can be separated. Supposing these elements to be sphe¬ 
rical, he would be enabled to determine the conditions of equi¬ 
librium of the free magnetic fluid at the surface of each element, 
by the same analysis as in the case of electricity; using, through¬ 
out his researches, those peculiar functions which we have termed 
Laplace’s coefficients, and which introduce such extraordinary 
facilities into researches of this kind. It further appears, from 
the nature of the equations (p. 283), that we need not know the 
form of these elements ; for the form of the elements, and the 
proportion of their sum to the whole mass of the body, enter into 
the result jointly, so that we do not trace the separate effect of 
these data. 
M. Poisson therefore (p. 290) takes the equation of equili¬ 
brium on the supposition that the magnetic elements are sphe¬ 
rical ; and he then finds (p. 306) that this equation coincides 
with the condition of equilibrium for electricity, on the supposi¬ 
tion that the sum of the magnetic elements is equal to the mass 
of the body (i. e. in his notation, k = 1). And in general (p. 
303), the magnetic action of a body of any form is equivalent to 
that of a thin stratum of magnetic fluid at the surface, although 
the fluids are separated in every part of the mass. In a subse¬ 
quent part of his memoir, M. Poisson applies his conclusions to 
determine the distribution of magnetic fluid in a solid or hollow 
sphere acted upon by the terrestrial magnetism. He refers to 
Mr. Barlow’s experiments, and to his inference that magnetism 
resides at the surface alone; he observes that the inference is 
not warranted, and that the only conclusion which we are jus¬ 
tified in drawing by the fact, as compared with the formulae, is 
that the sum of the magnetic elements is equal exactly, or very 
nearly, to the whole mass of the body. 
The force exerted by a body in which magnetism is induced, 
is a joint result of the distribution of the magnetism thus ex¬ 
cited, and of the position of the point acted on. The verification 
of M. Poisson’s theory would require experiments made with 
masses of iron of various forms, as well as measures of the ef¬ 
fect on a needle in various situations with reference to the mass ; 
and the theory, thus verified, would disclose to us the distribu¬ 
tion of the magnetism at the surface of iron under given circum¬ 
stances. 
The verification, with respect to the position of the point acted 
on, hag been executed to a satisfactory extent. M. Poisson ob¬ 
serves (p. 336) “that the laws of the deviation of compass needles 
are in accordance, whether we deduce them from theory, or from 
observation” as Mr. Barlow had done; “and thus that gentle- 
