FIFTH REPORT— 1835. 
like the first-born of their race, filled the civilized world with the 
noise of their fame. Moreover, it is allowed, or rather boasted, 
that it is only very recently that the mathematical train of rea¬ 
soning which belongs to several of these new sciences has been 
rendered complete. It may therefore be of service to examine 
the claims of these parts of knowledge so far as they profess to 
be mathematical and mechanical sciences. I hope the under¬ 
taking will lose all appearance of presumption, when it is recol¬ 
lected that, in executing it, my main task will be, to study certain 
mathematical theories and calculations, to look at the recorded 
facts which are alleged to confirm these theories, and to describe 
as distinctly as possible the result of the comparison. Such an 
employment will not lead the writer to trespass on the domain of 
any one whose business is with new classes of facts, nor tempt 
him to judge any theory which does not profess to depend en¬ 
tirely on mathematical calculation from measured observations. 
The Sciences to which I shall at present direct my attention 
are those of Electricity, Magnetism, and Heat. These sciences 
have sufficient connexion, both in the mathematical reasoning 
by which they have been established and the philosophical prin¬ 
ciples on which they depend, to make them a fit group to be 
treated of together. Though they have several features in com¬ 
mon, I shall give a brief account of each separately. 
Electricity.— -Electricity, after being brought under distinct 
conceptions by Franklin and his contemporaries, was formed into 
a mathematical science by yEpinus; the theory of iEpinus was 
reformed by Coulomb; the calculations which Coulomb could not 
execute, Poisson in our own time has performed: such are the 
main steps in the history of electricity as a mathematical science. 
The theory of electricity of /Epinus assumed one electric fluid 
only : it invested this fluid with these two properties, that its 
particles repelled each other with forces increasing with a dimi¬ 
nution of their mutual distance; and that its particles attracted 
the particles of all other bodies with a force following the same 
law. On these suppositions (assuming also the difference of 
conductors and electrics with respect to the easy transfer of the 
fluid) a great part of the facts of electricity by induction, and of 
electrical attraction and repulsion, could be explained in a man¬ 
ner strictly mechanical. 
But taking the whole of the experimental facts, a third sup¬ 
position was found to be necessary;—that the particles of all 
bodies repel each other with the same force with which they at¬ 
tract the electric fluid. For, without this addition to the theory, 
how could two negatively electrified bodies repel each other with 
the same force as two positively electrified, since by supposition 
