onsiderable body of
valuable truth; though it admits of being usefully applied in aid of the
method _a priori_, and even forms an indispensable supplement to it.

There is a property common to almost all the moral sciences, and by
which they are distinguished from many of the physical; this is, that it
is seldom in our power to make experiments in them. In chemistry and
natural philosophy, we can not only observe what happens under all the
combinations of circumstances which nature brings together, but we may
also try an indefinite number of new combinations. This we can seldom do
in ethical, and scarcely ever in political science. We cannot try forms
of government and systems of national policy on a diminutive scale in
our laboratories, shaping our experiments as we think they may most
conduce to the advancement of knowledge. We therefore study nature under
circumstances of great disadvantage in these sciences; being confined to
the limited number of experiments which take place (if we may so speak)
of their own accord, without any preparation or management of ours; in
circumstances, moreover, of great complexity, and never perfectly known
to us; and with the far greater part of the processes concealed from our
observation.

The consequence of this unavoidable defect in the materials of the
induction is, that we can rarely obtain what Bacon has quaintly, but not
unaptly, termed an _experimentum crucis_.

In any science which admits of an unlimited range of arbitrary
experiments, an _experimentum crucis_ may always be obtained. Being able
to vary all the circumstances, we can always take effectual means of
ascertaining which of them are, and which are not, material. Call the
effect B, and let the question be whether the cause A in any way
contributes to it. We try an experiment in which all the surrounding
circumstances are altered, except A alone: if the effect B is
nevertheless produced, A is the cause of it. Or, instead of leaving A,
and changing the other circumstances, we leave all the other
circumstances and change A: if the effect B in that case does _not_ take
place, then again A is a necessary condition of its existence. Either of
these experiments, if accurately performed, is an _experimentum crucis_;
it converts the presumption we had before of the existence of a
connection between A and B into proof, by negativing every other
hypothesis which would account for the appearances.

But this can seldom be don