All the instances examined must agree in one circumstance--hence the title Method of Agreement. But it is not in the agreement merely that the proof consists, but the agreement in one circumstance combined with difference in all the other circumstances, when we are certain that every circumstance has come within our observation. It is the singleness of the agreement that constitutes the proof just as it is the singleness of the difference in the Method of Difference.[3] It has been said that Mill's Method of Agreement amounts after all only to an uncontradicted _Inductio per enumerationem simplicem_, which he himself stigmatised as Induction improperly so called. But this is not strictly correct. It is a misunderstanding probably caused by calling the method that of agreement simply, instead of calling it the Method of Single Agreement, so as to lay stress upon the process of elimination by which the singleness is established. It is true that in the course of our observations we do perform an induction by simple enumeration. In eliminating, we at the same time generalise. That is to say, in multiplying instances for the elimination of non-causes, we necessarily at the same time multiply instances where the true causal antecedent, if there is only one possible, is present. An antecedent containing the true cause must always be there when the phenomenon appears, and thus we may establish by our eliminating observations a uniformity of connexion between two facts. Take, for example, Roger Bacon's inquiry into the cause of the colours of the rainbow. His first notion seems to have been to connect the phenomenon with the substance crystal, probably from his thinking of the crystal firmament then supposed to encircle the universe. He found the rainbow colours produced by the passage of light through hexagonal crystals. But on extending his observations, he found that the passage of light through other transparent mediums was also attended by the phenomenon. He found it 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.