The metaphor and its purpose from the excerpt from "On Beholding the Mountain" is "The heart's flame illustrates the intensity of the writer's emotion".
A metaphor is a figure of speech which is used to compare two things without using "like" or "as", by making the object of the metaphor take on the characteristic of the other thing.
It is also the use of a word or phrase to refer to something that it is not, invoking a direct similarity between the word or phrase used and the thing described but without the words like or as, which would imply a simile.
Therefore, the correct answer is option D; The heart's flame illustrates the intensity of the writer's emotion.
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