EARL GREY. -- We are glad to learn, that letters were received in Stanhope-street on Tuesday, which state that Lord GREY had enjoyed sleep during several hours for some nights past.  The noble lord had also suffered less pain lately, and his pulse and appetite were quite good.  His medical attendants are of opinion that the malady with which his lordship is afflicted is running its course in the manner best calculated to encourage the strongest hopes of a favourable termination.  There is some, however, danger, and considerable cause for the anxiety for his friends.  The great age of his lordship (eighty years in March next), of course rendered him less able to combat successfully with the attack.  Were the noble Earl some years younger it would no be considered a case to cause much serious alarm.  Should the next accounts prove favourable it is confidently hoped that his lordship will speedily recover.  The noble Earl bears his sufferings with great fortitude.