(212.) With regard to the first process of the three above enumerated,
it is in fact an induction of the kind described in § 185.; and all
the remarks we there made on that kind of induction apply to it in
this stage. The direct assumption of a particular hypothesis has been
occasionally practised very successfully. As examples, we may mention
Coulomb’s and Poisson’s theories of electricity and magnetism, in
both which, phenomena of a very complicated and interesting nature
are referred to the actions of attractive and repulsive forces,
following a law similar in its expression to the law of gravitation.
But the difficulty and labour, which, in the greater theories, always
attends the pursuit of a fundamental law into its remote consequences,
effectually precludes this method from being commonly resorted to as
a means of discovery, unless we have some good reason, from analogy
or otherwise, for believing that the attempt will prove successful,
or have been first led by partial inductions to particular laws which
naturally point it out for trial.
(213.) In this case the law assumes all the characters of a general
phenomenon resulting from an induction of particulars, but not yet
verified by comparison with _all_ the particulars, nor extended to all
that it is capable of including. (See § 171.) It is the verification
of such inductions which constitutes theory in its largest sense, and
which embraces an estimation of the influence of all such circumstances
as may modify the effect of the cause whose laws of action we have
arrived at and would verify. To return to our example: particular
inductions drawn from the motions of the several planets about the
sun, and of the satellites round their primaries, &c. having led us
to the general conception of an attractive force exerted by every
particle of matter in the universe on every other according to the law
to which we attach the name of gravitation; when we would verify this
induction, we must set out with assuming this law, considering the
whole system as subjected to its influence and implicitly obeying it,
and nothing interfering with its action; we then, for the first time,
perceive a train of modifying circumstances which had not occurred to
us when reasoning upwards from particulars to obtain the fundamental
law; we perceive that _all the planets_ must attract _each other_,
must therefore draw each other out of the orbits which they would
have if acted on only by the sun; and as this was never contemplated
in the inductive process, its validity becomes a question, which can
only be determined by ascertaining precisely how great a deviation
this new class of mutual actions will produce. To do this is no easy
task, or rather, it is the most difficult task which the genius of
man has ever yet accomplished: still, it _has_ been accomplished by
the mere application of the general laws of dynamics; and the result
(undoubtedly a most beautiful and satisfactory one) is, that all
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