REPORT ON ELECTRICITY, MAGNETISM, AND HEAT. 15 
man’s numerous observations are a remarkable confirmation of 
the theory of magnetism here presented.” I do not think it 
necessary to dwell upon the necessity of a correction for the 
length of the needle, and its magnetic effect upon the iron sphere, 
which M. Poisson conceives to be requisite in calculating Mr. 
Barlow’s experiments. But it may be observed, that M. Pois¬ 
son’s assumption that his quantity k (which expresses the ratio 
of the sum of the magnetic elements of the body, to the sum of 
all its parts,) cannot exceed unity, does not appear to he incon¬ 
testable, since it involves the supposition that the whole mag¬ 
netic attraction or repulsion of each such element is the same 
as if its form were spherical, which supposition is introduced 
p. 290 of the memoir. 
The same volume of the Memoirs of the Institute contains a 
second memoir of M. Poisson on the same subject, read De¬ 
cember 27, 1824. In this the author observes, that though 
Mr. Barlow’s observations afford an important confirmation of 
the theory, it was desirable that it should be subjected to trials 
of a more varied kind. On returning to his formulae, he found 
that they could be very simply solved for the case of any ellip¬ 
soid whatever. Now a very flat ellipsoid may approach inde¬ 
finitely near to an elliptical or circular plate ; a very slender 
ellipsoid may approach indefinitely to a linear bar. Thus the 
mathematical theory of certain very obvious and extensive cases 
was attainable. We do not, however, possess any comparison of 
experiments with the formulae thus obtained ; and thus the ve¬ 
rification of M. Poisson’s theory, so far as the distribution of 
magnetism depends on the form of the mass of iron, is hitherto 
incomplete. M. Hansteen of Copenhagen, whose valuable work 
on terrestrial magnetism was published in German in 1819, had 
inferred from his own experiments, that in a linear magnet the 
magnetic intensity follows the law of the square of the distance 
from the middle point more nearly than any other power of that 
distance, a conclusion different from Coulomb’s, as we have 
seen (p. 11)*. 
It appears, however, to have been taken for granted, after the 
verification of the theory by Mr. Barlow’s experiments, that it 
might be considered as established, and that mathematical me¬ 
thods of deduction might for the future be used, not to confirm 
the truth of its principles, but to apply them to any requisite 
purposes. 
The most remarkable and important example of a ee Deductio 
ad Praxin ” of this kind, was that which Mr. Barlow made in the 
* Hansteen, Magnctisimis, chap. v. p. 165. 
