(and by experiment we can introduce into the pre-existing facts a change
perfectly definite), that we can, at least by direct experience, arrive
with certainty at causes. The method of agreement is chiefly useful as
preliminary to and suggestive of applications of the method of
difference, or as an inferior resource in its stead, when, as in the
case of many spontaneous operations of nature, we have no power of
producing the phenomenon.

When we have power to produce the phenomenon, but only by the agency,
not of a single antecedent, but of a combination, the method of
agreement can be improved (though it is even then inferior to the direct
method of difference) by a double process being used, each proof being
independent and corroborative of the other. This may be called the
Indirect Method of Difference, or the Joint Method of Agreement and
Difference, and its canon will be: _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 a
necessary part of the cause, of the phenomenon._

The fourth canon is that of the Method of Residues, viz.: _Subduct from
any phenomenon such part as is known by previous inductions to be the
effect of certain antecedents, and the residue of the phenomenon is the
effect of the remaining antecedents._ This method is a modification of
the method of difference, from which it differs in obtaining, of the
two required instances, only the positive instance, by observation or
experiment, but the negative, by deduction. Its certainty, therefore, in
any given case, is conditional on the previous inductions having been
obtained by the method of difference, and on there being in reality no
remaining antecedents _besides_ those given as such.

The fifth canon is that of the Method of Concomitant Variations, viz.:
_Whatever phenomenon varies in any manner whenever another phenomenon
varies in some particular manner, is either a cause or an effect of that
phenomenon, or_ (since they may be effects of a common cause) _is
connected with it through some fact of causation._ Through this method
alone can we find the laws of the permanent causes. For, though those of
the permanent causes whose influence is local may be escaped from by
changing the scene of