On the other hand, Mulgrave expressly denied Dryden's being the author, in the lines in his Essay on Poetry,—
"Tho' praised and punished for another's rhymes."
and by inference claimed the poem, or at least the lines on Rochester, as his own. Dryden, in the Preface to his Virgil, praises the Essay on Poetry in the highest terms; but says not a word to dispute Mulgrave's statement, though he might then have safely claimed the Essay on Satire, if his own; and though he must have been aware that, by his silence, he was virtually resigning his sole claim to its authorship. It was subsequently included in Mulgrave's works, and has ever since gone under the joint names of himself and Dryden.
On the question of internal evidence critics differ. Your correspondent can see in it no hand but Dryden's; while Malone will scarcely allow that Dryden made even a few verbal alterations in it (Life, p. 130.); and Sir Walter Scott is not inclined to admit any further participation on the part of the great poet than "a few hints for revision," and denies its merit altogether—a position in which I think very few, who carefully peruse it, will agree with him.
I am disposed to take a middle course between your correspondent and Dryden's two biographers, and submit that there is quite sufficient internal evidence of joint ownership. I cannot think such lines as—
"I, who so wise and humble seem to be,
Now my own vanity and pride can't see;"
or,—
"I, who have all this while been finding fault,
E'en with my master who first satire taught,