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 alcali 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.

The passions of fear and hope may arise when the chances are equal on both sides, and no superiority can be discovered in the one above the other.  Nay, in this situation the passions are rather the strongest, as the mind has then the least foundation to rest upon, and is tossed with the greatest uncertainty.  Throw in a superior degree of probability to the side of grief, you immediately see that passion diffuse itself over the composition, and tincture it into fear.  Encrease the probability, and by that means the grief, the fear prevails still more and more, till at last it runs insensibly, as the joy continually diminishes, into pure grief.  After you have brought it to this situation, diminish the grief, after the same manner that you encreased it; by diminishing the probability on that side, and you’ll see the passion clear every moment, until it changes insensibly into hope; which again runs, after the same manner, by slow degrees, into joy, as you encrease that part of the composition by the encrease of the probability.  Are not these as plain proofs, that the passions of fear and hope are mixtures of grief and joy, as in optics it is a proof, that a coloured ray of the sun passing through a prism, is a composition of two others, when, as you diminish or encrease the quantity of either, you find it prevail proportionably more or less in the composition?  I am sure neither natural nor moral philosophy admits of stronger proofs.

Probability is of two kinds, either when the object is really in itself uncertain, and to be determined by chance; or when, though the object be already certain, yet it is uncertain to our judgment, which finds a number of proofs on each side of the question.  Both these kinds of probabilities cause fear and hope; which can only proceed from that property, in which they agree, viz, the uncertainty and fluctuation they bestow on the imagination by that contrariety of views, which is common to both.