A new mission for exploring the interior of Africa has been proceeded on, under the direction of Mr. Ritchie, late private Secretary to our Ambassador at Paris. His companion and second in the mission is Lieut. Lyon, late of his Majesty's ship Albion, now at Malta, who volunteered, and was appointed at the recommendation of Admiral Sir Charles Penrose, as being peculiarly qualified for this service. They are accompanied by Monsieur Duponte, a French naturalist; also by a surgeon and a carpenter. The Bashaw and a military escort attend them from Tripoli (where they now are) to Mouzuk, and they are to have a like escort throughout their progress. Mr. Ritchie is a young man of great research, abilities, and prudence.