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The phrases in their context!

Extract from A TREATISE OF HUMAN NATURE:

For in that case, both the passions, mingling with each other by means of the relation, become mutually destructive, and leave the mind in perfect tranquility.
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.
It is impossible by one steady view to survey the opposite chances, and the events dependent on them; but it is 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.
It is 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 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.