In the rear of the City Hall, and fronting on Chambers street, the authorities have been for eight years engaged in the erection of the NEW YORK COURT-HOUSE. The building is 250 feet long, 150 wide, and the crown of the dome when completed will be 210 feet above the pavement. The walls are of Massachusetts white marble, the beams, staircases, and outside doors are of iron, while black walnut and the choicest Georgia-pine are employed in finishing the interior. Some of the iron beams and girders weigh over twenty-five tons each. The halls are all covered with marble tiling. The main entrance on Chambers street is reached by a flight of broad steps ornamented with marble pillars. The architect has suggested the idea of making the tower crowning the apex of the dome a light-house, which from its great height could be seen from vessels far out at sea. The edifice is Corinthian in style, much larger and richer in finish than any public building hitherto erected on Manhattan, and is costing-the public vast sums. Many private purses are believed to have been unduly filled in connection with its construction.