But suppose, in the third place, that the object is not a compound of good or evil, but is considered as probable or improbable in any degree; in that case I assert, that the contrary passions will both of them be present at once in the soul, and, instead of destroying and tempering each other, will subsist together, and produce a third impression or affection by their union. Contrary passions are not capable of destroying each other, except when their contrary movements exactly rencounter, and are opposite in their direction, as well as in the sensation they produce. This exact rencounter depends upon the relations of those ideas from which they are derived, and is more or less perfect, according to the degrees of the relation. In the case of probability, the contrary chances are so far related that they determine concerning the existence or non-existence of the same object. But this relation is far from being perfect, since some of the chances lie on the side of existence, and others on that of non-existence, which are objects altogether incompatible. 'Tis impossible, by one steady view, to survey the opposite chances, and the events dependent on them; but 'tis necessary that the imagination should run alternately from the one to the other. Each view of the imagination produces its peculiar passion, which decays away by degrees, and is followed by a sensible vibration after the stroke. The incompatibility of the views keeps the passions from shocking in a direct line, if that expression may be allowed; and yet their relation is sufficient to mingle their fainter emotions. 'Tis after this manner that hope and fear arise from the different mixture of these opposite passions of grief and joy, and from their imperfect union and conjunction. Upon the whole, contrary passions succeed each other alternately, when they arise from different objects; they mutually destroy each other, when they proceed from different parts of the same; and they subsist, both of them, and mingle together, when they are derived from the contrary and incompatible chances or possibilities on which any one object depends. The influence of the relations of ideas is plainly seen in this whole affair. If the objects of the contrary passions be totally different, the passions are like two opposite liquors in different bottles, which have no influence on each other. If the objects be intimately connected, the passions are like an _alkali_ and an _acid_, which, being mingled, destroy each other. If the relation be more imperfect, and consists in the contradictory views of the same object, the passions are like oil and vinegar, which, however mingled, never perfectly unite and incorporate. As the hypothesis concerning hope and fear carries its own evidence along with it, we shall be the more concise in our proofs. A few strong arguments are better than many weak ones.