BROOKLYN BRIDGE.Formal Opening: to the Public of the Great Structure Connecting the CItiea of New York and llrooklyn-The Two Cities in Gala Attire—A Grand PyrotechnicDisplay. jfBW York, May 25,Although the day opened cloudy and threatening, the streets approaching the great suspension bridge across Last River, both in New York and Brooklyn, were thronged with people, and the grand ceremonies of the formal opening of the structure to the public began according to the published programme. President Arthur and his Cabinet officers, Governor Cleveland and other distinguished guests, had special escorts of jtoliee and military- Brooklyn was one mass of decoration and animation. Throughout the city there appeared to be a general surrender of business to sight-seeing and celebrating. The main business avenues, the heights, and many streets clear out into the suburbs, were decked most gayly with ilags and bunting and flowers for the bridal with the city over the river. Public buildings, private bouses, and the street cars and trucks flv the colors of all nations in honor of the opening of the “ big bridge.”The following cut, which is a correct view' of the massive structure, we are enabled to present to our readers through the courtesy of the Chicago Tribune: