PURSUANT to a decree of the Hon. HUGH RUTLEDGE, Esq, Judge of the Court of Admiralty in this State, will be sold by publick vendue on Tuesday the 16th of June instant, on Galliard's wharf, the SLOOP LYDIA, with all her tackle, furniture, apparel, and cargo on board, consisting of melasses at the same wharf will be sold the BRIGANTINE NEPTUNE, with all her tackle, furniture, apparel and cargo, consisting of lumber, staves and shingles.— Likewise will be sold, the BRIGANTINE BETSY, with all her tackle, furniture, apparel and cargo, consisting of staves, shingles and tar. The vessels sail remarkably fast, and an inventory may be seen on board each of them; lately made prizes of by the Notre Dame, Brigantine of War, Capt. William Hall, belonging to the State of South-Carolina.¹ The condition of the sale is ready money.