every concomitant but one, he would have attained
complete proof on the principle of Single Difference. But this being
impracticable, he followed a course which approximated to the method
of eliminating every circumstance but one from instances of dew, and
every circumstance but one in the instances of no-dew. Mill sums up as
follows the results of his experiments: "It appears that the instances
in which much dew is deposited, which are very various, agree in
this, and, _so far as we are able to observe, in this only_, that they
either radiate heat rapidly or conduct it slowly: qualities between
which there is no other circumstance of agreement than that by virtue
of either, the body tends to lose heat from the surface more rapidly
than it can be restored from within. The instances, on the contrary,
in which no dew, or but a small quantity of it, is formed, and which
are also extremely various, agree (_as far as we can observe_) _in
nothing except_ in _not_ having this same property. We seem therefore
to have detected the characteristic difference between the substances
on which the dew is produced, and those on which it is not produced.
And thus have been realised the requisitions of what we have termed
the Indirect Method of Difference, or the Joint Method of Agreement
and Difference." The Canon of this Method is accordingly stated by
Mill as follows:--

If two or more instances in which the phenomenon occurs have
only one circumstance in common, while two or more instances
in which it does not occur have nothing in common save the
absence of that circumstance; the circumstance in which alone
the two sets of instances differ, is the effect, or the cause,
or an indispensable part of the cause, of the phenomenon.

In practice, however, this theoretical standard of proof is never
attained. What investigators really proceed upon is the presumption
afforded, to use Prof. Bain's terms, by Agreement in Presence combined
with Agreement in Absence. When it is found that all substances which
have a strong smell agree in being readily oxidisable, and that the
marsh gas or carbonetted hydrogen which has no smell is not oxidisable
at common temperatures, the presumption that oxidation is one of the
causal circumstances in smell is strengthened, even though we have not
succeeded in eliminating every circumstance but this one from either
the positive or the negative instances. So in the following examples
g