About eight o’clock in the evening, the frenzied rioters having reached Printing House Square, commenced an attack on the Tribune office, hurling bricks and stones into its windows, and utterly destroying them. An entrance to the counting-room was next effected, and an attempt made to set the building on fire. At this instant a strong police force came upon the full run across the Park, scattering the rioters. A heavy rain soon set in, and the mob dispersed in every direction; though a great deal of petty mischief continued to be done during the night by those who did not seek their homes, or had none to seek. Whole blocks of buildings were burned during this one day’s riot; and the damage to government property alone was estimated at two hundred and fifty thousand dollars. THE SECOND DAY. At an early hour on Tuesday morning, after a night of sleepless anxiety to the inhabitants of the city, demonstrations of violence began, and the outrages of the previous day were renewed. At about half-past eight o’clock, it was reported at the Police Headquarters that a large body of rioters were gathering along the Second avenue, threatening every house along the thoroughfare. A police force of three hundred men was immediately detailed under Inspector Carpenter, for the purpose of breaking up the crowd; finding the railroad track obstructed, they left the street cars, and marched in solid column toward Second avenue, where the mob received them with ominous silence. When the whole force had reached the block between Thirty-fourth and Thirty fifth streets, they were closed in upon by the mob, and assailed by a thick shower of bricks and stones, which rained from the houses and windows in the neighborhood. For some moments the men wavered, and the peril was imminent, when the reassuring voices of the officers in command recalled them, and they returned the shower of stones with a volley of bullets from their revolvers. The order was then given to charge, and a most furious onset was made upon the rioters—the police driving them into the houses, chasing them all over the buildings and again into the street, where they were scattered by a most vigorous application of clubs. All the side streets were then cleared, and the police marched over the battle-ground victorious. The men behaved bravely, hunting every rioter, and clubbing him if he made any resistance. The police then marched through the Avenue, and were met by a detachment of the Eleventh regiment of the N. Y. S. V., headed by Colonel O’Brien and a couple of field-pieces, under command of Lieutenant Eagleson. The forces united, and countermarched down the avenue. The mob had in the mean time rallied, when the military formed a line of battle, and fired upon the crowd. Bullets whistled through the air in every direction, shattering shutters and doors.