THE existence of Royalty at Brighton has been rather monotonous this week. The weather has been generally unpleasant ; but every fine morning the Queen rides out with Lord Melbourne, Baroness Letzen, Lady Mary Stopford, and Sir George Quentin ; and every evening Lord Melbourne and a small party dine with her Majesty. Lord Palmerston went to Brighton on Saturday. and returned on Thursday to town. Lord John Russell and his Lady are at the Bed- ford Hotel. Lord John has been unwell, but except on Sunday last, has dined every evening at the Palace. On Wednesday, the Queen sat to Mr. Ilayter for her portrait; and the artist, when dismissed by her Majesty, repaired to Lord Melbourne's apartments, and commenced his full-lergth portrait. Signor Pistrueci has accomplished the model for the coamation-medul of the Queen. It is expected that the Court will leave Brighton on Saturday next.