ariants can be precisely measured, the ratio of the
variation may be ascertained by the Method of Single Difference. We
may change an antecedent in degree, and watch the corresponding change
in the effect, taking care that no other agent influences the effect
in the meantime. Often when we cannot remove an agent altogether,
we may remove it in a measurable amount, and observe the result. We
cannot remove friction altogether, but the more it is diminished, the
further will a body travel under the impulse of the same force.

Until a concomitant variation has been fully explained, it is merely
an empirical law, and any inference that it extends at the same
rate beyond the limits of observation must be made with due caution.
"Parallel variation," says Professor Bain, "is sometimes interrupted
by critical points, as in the expansion of bodies by heat, which
suffers a reverse near the point of cooling. Again, the energy of a
solution does not always follow the strength; very dilute solutions
occasionally exercise a specific power not possessed in any degree
by stronger. So, in the animal body, food and stimulants operate
proportionally up to a certain point, at which their further operation
is checked by the peculiarities in the structure of the living
organs.... We cannot always reason from a few steps in a series to the
whole series, partly because of the occurrence of critical points,
and partly from the development at the extremes of new and unsuspected
powers. Sir John Herschel remarks that until very recently 'the
formulae empirically deduced for the elasticity of steam, those for
the resistance of fluids, and on other similar subjects, have almost
invariably failed to support the theoretical structures that have been
erected upon them'."[1]

II.--SINGLE RESIDUE.

_Subduct from any phenomenon such part as previous induction
has shown to be the effect of certain antecedents, and the
residue of the phenomenon is the effect of the remaining
antecedents._

"Complicated phenomena, in which several causes concurring, opposing,
or quite independent of each other, operate at once, so as to produce
a compound effect, may be simplified by subducting the effect of all
the known causes, as well as the nature of the case permits, either by
deductive reasoning or by appeal to experience, and thus leaving as it
were a _residual phenomenon_ to be explained. It is by this process,
in fact, that science, in its pre