AUSTRALIA AND NEW ZEALAND.Advices from Melbourne to the dte of February 16th give the following intelligence:—The Governor of New South Wales (Lord Belmore)having granted a dissolution to 8 James Martin, the first of the new elections took place on Tuesday last, at East Sydney. The Premier and the Minister of Lands were both defeated, and four Opposition members were elected by large majorities. In the elections for West Sydney, although the Colonial Secretary and one Government supporter managed to save their seats, the Solicitor-General and another Government Bupporter were defeated, and two Opposition members headed the poll.The latest intelligence relative to the overland telegraph is of a more satisfactory character than has been the case for some time past. The several parties in the north are pushing on, and the Adela;de Government hopes, by means of horse express over that portion over which the wires are not yet stretched, to complete the communication with Europe within the next few weeks.The reports from the gold fields are of the most satisfactory description, and the prospects of the mines are better than they have bee n for a long time past