" Between 4 and C o'clock this iThmsday) morning the pontoon train in charge of the 17th and 50th Now York Engineers, under command of General Wood bury, proceeded to the river bank, where, with infantry supports, an attempt was made to throw thr^e bridges across the river— one at the point where the railroad bridge formeily crossed, and two more opposite the city, but nearer Falinouth. A dull haze obscured the movements for a time, and the pontooneera succeeded in partially constructing the bridges, when the rebels suddenly opened a very brisk and deadly (he of mus ketry from along the banks of the river and windows of the houses, compelling a cessation of the woik. Some of our men were shot midway in the stream, and falling overboard floated down the river. Returning to the cover of the surrounding hills, the men were again formed, and about 6 o'clock the attempt to bridge the river was again renewed, but the rebels with reinforcements of sharpshooters swarmed on the opposite banks and in the houses. Nothing daunted by the hot fire poured in at the reappeaiance of our tioopi, the pontooneers went gallantly to work, but in vain. The storm of bullets enveloped them ; planks nnd boats were riddled by every volley, and they wero compelled once more to fall back to the cover of the hills. As it was evident that the rebels were deter mined to use the houses for defence, contrary to the implied agreement in the correspondence which recently passed by a flag of truce, outers weie given to our aitillerymen to open fire upon the city. The fog was so denie that it was impossible to see but a short distance beyond the edge of the river, but the houses, however, in which the rebel sharpshooters exposed themselves were plainly visible, and to them our firo was for the time particularly directed. By 7 o'clock the borabaidmont had become general, and from that time until 1 o'clock the roar of artillery was incessant, while bhot and shell fell fast and thick into the doomed city. About 10 o'clock the engineers weio f oi mod for the third attempt to construct a bridge. The Bth Connecticut Regiment, under Major Ward, was lying near the river bank in support of one of our batteries. 