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 the Single Method of Agreement, relies on observation, sequence may not be perceptible in the instances observed, and then, direct causation cannot be proved by it, but only the probability of causal connection; and, again, the real cause, though present, may be so obscure as to evade observation.  It has, however, one peculiar advantage, namely, that if the second list of instances (in which the phenomenon and its supposed antecedent are both absent) can be made exhaustive, it precludes any hypothesis of a plurality of causes; since all possible antecedents will have been included in this list without producing the phenomenon.  Thus, in the above symbolic example, taking the first set of instances, the supposition is left open that B, C, D, E, F, G may, at one time or another, have been a condition of p; but, in the second list, these antecedents all occur, here or there, without producing p, and therefore (unless counteracted somehow) cannot be a condition of p.  A, then, stands out as the one thing that is present whenever p is present, and absent whenever p is absent.

Stated in this abstract way, the Double Method may seem very elaborate and difficult; yet, in fact, its use may be very simple.  Tyndall, to prove that dispersed light in the air is due to motes, showed by a number of cases (1) that any gas containing motes is luminous; (2) that air in which the motes had been destroyed by heat, and any gas so prepared as to exclude motes, are not luminous.  All the instances are of gases, and the result is:  motes—­luminosity; no motes—­no luminosity.  Darwin, to show that cross-fertilisation is favourable to flowers, placed a net about 100 flower-heads, and left 100 others of the same varieties exposed to the bees:  the former bore no seed, the latter nearly 3,000.  We must assume that, in Darwin’s judgment, the net did not screen the flowers from light and heat sufficiently to affect the result.