umerous other cases, the mutual
influence of the sciences has been quite independent of any supposed
hierarchical order. Often, too, their inter-actions are more complex
than as thus instanced--involve more sciences than two. One illustration
of this must suffice. We quote it in full from the _History of the
Inductive Sciences_. In book xi., chap, ii., on "The Progress of the
Electrical Theory," Dr. Whewell writes:--

"Thus at that period, mathematics was behind experiment, and a
problem was proposed, in which theoretical results were wanted for
comparison with observation, but could not be accurately obtained;
as was the case in astronomy also, till the time of the approximate
solution of the problem of three bodies, and the consequent
formation of the tables of the moon and planets, on the theory of
universal gravitation. After some time, electrical theory was
relieved from this reproach, mainly in consequence of the progress
which astronomy had occasioned in pure mathematics. About 1801
there appeared in the _Bulletin des Sciences_, an exact solution of
the problem of the distribution of electric fluid on a spheroid,
obtained by Biot, by the application of the peculiar methods which
Laplace had invented for the problem of the figure of the planets.
And, in 1811, M. Poisson applied Laplace's artifices to the case of
two spheres acting upon one another in contact, a case to which
many of Coulomb's experiments were referrible; and the agreement of
the results of theory and observation, thus extricated from
Coulomb's numbers obtained above forty years previously, was very
striking and convincing."

Not only do the sciences affect each other after this direct manner, but
they affect each other indirectly. Where there is no dependence, there
is yet analogy--_equality of relations_; and the discovery of the
relations subsisting among one set of phenomena, constantly suggests a
search for the same relations among another set. Thus the established
fact that the force of gravitation varies inversely as the square of the
distance, being recognised as a necessary characteristic of all
influences proceeding from a centre, raised the suspicion that heat and
light follow the same law; which proved to be the case--a suspicion and
a confirmation which were repeated in respect to the electric and
magnetic forces. Thus again the discovery of