We have been favoured by the transmission of the following singular correspondence by the new Mayor of Dublin's private secretary. We hasten to lay the interesting documents before our readers, though we must decline incurring the extreme responsibility of advising which offer it would be most advantageous for Mr. O'Connell to accept. LETTER I. SIR,--I am requested by the management of the Royal Surrey Theatre to negotiate with you for a few nights' performance in a local drama, which shall be written for the occasion, and in which you are requested to represent the Civic dignitary in the identical robes which have become immortalised by your wearing. Mr. Dibdin Pitt is of opinion that something might be done with "Whittington and his Cat," merely transferring the scene from London to Dublin; and, as he hears your county is highly celebrated for the peculiar breed, sending to Ireland for one of the esteemed "Kilkenny species," which would give a greater reality to the _dramatis personae_ and feline adjunct. This is a mere suggestion, as any other subject you may prefer--such as the Rebellion of '98, Donnybrook Fair, the Interior of the Irish Mansion House, or the House of Commons, can be rendered equally effective. I beg to call your attention to the fact that you shall have a clear stage and every advantage, as Mr. N.T. Hicks will be left out of the cast altogether, or else play a very small dumb villain; so that you need not fear losing your oratorical reputation by being out-shouted. Should you feel disposed to accept the terms, one clear half the nightly receipt, pray forward an answer by return, that we may get out a woodcut of the small-clothes, and underline the identical stockings. I have the honour to be, Your obedient servant, BEN. FAIRBROTHER. _D. O'Connell, Esq._ _T.R.D.L._ SIR,--The intense interest created in the bosoms of mankind in general by the graphic account of your splendid appearance and astounding performance of the arduous character of the Lord Mayor of Dublin, induces Mr. W.C. Macready to make you an offer of engagement for the performance of Shakspere's heroic functionary in the forthcoming revival of Richard the Third, which is about to be produced under his classic management at the Theatre Royal Drury-lane, Mr. W.C. Macready offers to replace the breeches if cracked in stooping; also, to guarantee a liberal allowance of hair-powder to fall from the wig, and make the usual effective and dignified huge point while the Mayor is bowing to the king. An early answer will oblige your obedient servant, T.J. SERLE. P.S. Can you bring your own Aldermen, as we are anxious to do it with the [Illustration: MAYOR (MARE) AND CORPORATION.] P.P.S.--Think of the fame and the twelve-sheet posters, and be moderate. _Theatre Royal, Adelphi._