n common, while_ (2)
_two or more instances in which it does not occur (though in important
points they resemble the former set of instances) have nothing else in
common save the absence of that circumstance--the circumstance in which
alone the two sets of instances differ throughout (being present in the
first set and absent in the second) is probably the effect, or the
cause, or an indispensable condition of the phenomenon._

The first clause of this Canon is the same as that of the method of
Agreement, and its significance depends upon the same propositions
concerning causation. The second clause, relating to instances in which
the phenomenon is absent, depends for its probative force upon Prop. II.
(a), and I. (b): its function is to exclude certain circumstances (whose
nature or manner of occurrence gives them some claim to consideration)
from the list of possible causes (or effects) of the phenomenon
investigated. It might have been better to state this second clause
separately as the Canon of the Method of Exclusions.

To prove that A is causally related to _p_, let the two sets of
instances be represented as follows:

Instances of Presence. Instances of Absence.
A B C C H F
_p q r_ _r x v_
A D E B D K
_p s t_ _q y s_
A F G E G M
_p u v_ _t f u_

Then A is probably the cause or a condition of _p_, or _p_ is dependent
upon A: first, by the Canon of Agreement in Presence, as represented by
the first set of instances; and, secondly, by Agreement in Absence in
the second set of instances. For there we see that C, H, F, B, D, K, E,
G, M occur without the phenomenon _p_, and therefore (by Prop. II. (a))
are not its cause, or not the whole cause, unless they have been
counteracted (which is a point for further investigation). We also see
that _r, v, q, s, t, u_ occur without A, and therefore are not the
effects of A. And, further, if the negative instances represent all
possible cases, we see that (according to Prop. I. (b)) A is the cause
of _p_, because it cannot be omitted without the cessation of _p_. The
inference that A and _p_ are cause and effect, suggested by their being
present throughout the first set of instances, is therefore strengthened
by their being both absent throughout the second set.

So far as this Double Method, like t