in dewdrops, in the spray of waterfalls, in
drops shaken from the oar in rowing. He thus eliminated the substance
crystal, and at the same time established the empirical law that
the passage of light through transparent mediums of a globular or
prismatic shape was a causal antecedent of the rainbow colours.[4]

Ascertainment of invariable antecedents may thus proceed side by side
with that of variable antecedents, the use of the elimination being
simply to narrow the scope of the inquiry. But the proof set forth in
Mill's Canon does not depend merely on one antecedent or concomitant
being invariably present, but also on the assumption that all the
influential circumstances have been within our observation. Then only
can we be sure that the instances have _only one_ circumstance in
common.

The truth is that owing to the difficulty of fulfilling this
condition, proof of causation in accordance with Mill's Canon is
practically all but impossible. It is not attained in any of the
examples commonly given. The want of conclusiveness is disguised
by the fact that both elimination and positive observation of mere
agreement or uniform concomitance are useful and suggestive in the
search for causes, though they do not amount to complete proof such as
the Canon describes. Thus in the inquiry into the cause of goitre, the
elimination serves some purpose though the result is purely negative.
When the inquirer is satisfied that goitre is not originated by any
directly observable local conditions, altitude, temperature, climate,
soil, water, social circumstances, habits of exertion, his search
is profitably limited. And mere frequency, much more constancy of
concomitance, raises a presumption of causal connexion, and looking
out for it is valuable as a mode of reconnoitring. The first thing
that an inquirer naturally asks when confronted by numerous instances
of a phenomenon is, What have they in common? And if he finds that
they have some one circumstance invariably or even frequently present,
although he cannot prove that they have no other circumstance in
common as the Cannon of Single Agreement requires, the presumption of
causal connexion is strong enough to furnish good ground for further
inquiry. If an inquirer finds an illness with marked symptoms in a
number of different households, and finds also that all the households
get their milk supply from the same source, this is not conclusive
proof of causation, but it is a suff