New South Wales.--As a proof of the increasing trade betwixt Leith and New South Wales, it may be mentioned that the Australian Company have chartered a fine new brig the Mary of Alloa, about 300 tons register, in addition to their regular traders, which vessel sailed from the Road on Saturday afternoon, at three o'clock for that colony, with a full general cargo, and a number of passengers. Another vessel, the Margaret, a brig, also about 300 tons, is now loading for the same place, chartered by a merchant in Leith.

