PETERSFIELD.]—THE MAILS.—A petition to the Post Office authorities has been got up to re-establish the morning mail, usually dispatched from the Petersfield Post Office, at 10 p.m., which has been withdrawn since the 6th ultimo. It is also in contemplation to advise the officials to forward the morning mail bags in future by the 12.27 up train from the Petersfield station, and the down London bags by the train which leaves the Waterloo station at 11.30, and which would give us a second delivery at a quarter to 2, conferring on us a great boon.