he answers,

O throw away the worser part of it,
And live the purer with the other half.

The truth is that, though Hamlet hates his uncle and acknowledges the
duty of vengeance, his whole heart is never in this feeling or this
task; but his whole heart is in his horror at his mother's fall and in
his longing to raise her. The former of these feelings was the
inspiration of his first soliloquy; it combines with the second to form
the inspiration of his eloquence here. And Shakespeare never wrote more
eloquently than here.

I have already alluded to the significance of the reappearance of the
Ghost in this scene; but why does Shakespeare choose for the particular
moment of its reappearance the middle of a speech in which Hamlet is
raving against his uncle? There seems to be more than one reason. In the
first place, Hamlet has already attained his object of stirring shame
and contrition in his mother's breast, and is now yielding to the old
temptation of unpacking his heart with words, and exhausting in useless
emotion the force which should be stored up in his will. And, next, in
doing this he is agonising his mother to no purpose, and in despite of
her piteous and repeated appeals for mercy. But the Ghost, when it gave
him his charge, had expressly warned him to spare her; and here again
the dead husband shows the same tender regard for his weak unfaithful
wife. The object of his return is to repeat his charge:

Do not forget: this visitation
Is but to whet thy almost blunted purpose;