To insist upon the cogency of ‘negative instances’ was Bacon’s great contribution to Inductive Logic.  If we neglect them, and merely collect examples of the sequence A-p, this is ‘simple enumeration’; and although simple enumeration, when the instances of agreement are numerous enough, may give rise to a strong belief in the connection of phenomena, yet it can never be a methodical or logical proof of causation, since it does not indicate the unconditionalness of the sequence.  For simple enumeration of the sequence A-p leaves open the possibility that, besides A, there is always some other antecedent of p, say X; and then X may be the cause of p.  To disprove it, we must find, or make, a negative instance of X—­where p occurs, but X is absent.

So far as we recognise the possibility of a plurality of causes, this method of Agreement cannot be quite satisfactory.  For then, in such instances as the above, although D is absent in the first, and B in the second, it does not follow that they are not the causes of p; for they may be alternative causes:  B may have produced p in the first instance, and D in the second; A being in both cases an accidental circumstance in relation to p.  To remedy this shortcoming by the method of Agreement itself, the only course is to find more instances of p.  We may never find a negative instance of A; and, if not, the probability that A is the cause of p increases with the number of instances.  But if there be no antecedent that we cannot sometimes exclude, yet the collection of instances will probably give at last all the causes of p; and by finding the proportion of instances in which A, B, or X precedes p, we may estimate the probability of any one of them being the cause of p in any given case of its occurrence.

But this is not enough.  Since there cannot really be vicarious causes, we must define the effect (p) more strictly, and examine the cases to find whether there may not be varieties of p, with each of which one of the apparent causes is correlated:  A with p^{1} B with p^{11}, X with p^{111}.  Or, again, it may be that none of the recognised antecedents is effective:  as we here depend solely on observation, the true conditions may be so recondite and disguised by other phenomena as to have escaped our scrutiny.  This may happen even when we suppose that the chief condition has been isolated:  the drinking of foul water was long believed to cause dysentery, because it was a frequent antecedent; whilst observation had overlooked the bacillus, which was the indispensable condition.

Again, though we have assumed that, in the instances supposed above, immediate sequence is observable, yet in many cases it may not be so, if we rely only on the canon of Agreement; if instances cannot be obtained by experiment, and we have to depend on observation.  The phenomena may then be so mixed together that A and p seem to be merely concomitant; so that, though connection of some sort may be rendered highly probable, we may not be able to say which is cause and which is effect.  We must then try (as Bain says) to trace the expenditure of energy:  if p gains when A loses, the course of events if from A to p.