FUNERAL OF PETER PURCELL.--The remains of this distinguished and estimable Irishman were conveyed to their last resting place, in Marlborough street Chapel, this morning under circumstances as well calculated to soothe the feelings of his family as could be desired by their warmest friends. The hearse was followed by a train of gentlemen on foot ; extending from the late residence of Mr. Purcell in Rutland-square to the entrance of the chapel, and the procession was closed by a long line of carriages. Among those who paid this last tribute of respect to the deceased were men of the highest position in our city ; and the funeral service, which was performed by Archbishop Murray, was attended to its close by many who perhaps never, upon any former occasion, found themselves within the walls of a place of Roman Catholic worship. We understand that no leading member of the Repeal Association attended the funeral.--Evening Mail of Monday. --The Cork Examiner, 3 June 1846