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June 3. During the early part of this day, or even the whole morning, all was quiet at Port Hudson and on the Mississippi. During early part of the afternoon the steamer General Sterling Price arrived from Vicksburg; fighting still going on in that quarter; at five thirty the steamer Price and Gen. Banks went up the river. Heard heavy cannonading going on at Port Hudson, between the two contending armies, and I am not aware as yet who’s who, or who is getting the best of it; at six thirty P. M. ram Switzerland came down the river, and anchored, communicating with us. She returned up the river, again. Mortar vessels below, commenced about nine o’clock, and continued firing during the watch, three of the enemy’s guns at the same time firing inland upon our army in rear of Port Hudson, and continuing their firing until a late hour; at eleven P. M.; quick discharges of musketry heard in rear of Port Hudson, and two rockets seen sent up from that vicinity. It is reported as being true, that Banks has lost, up to the present time, from his late engagements with the enemy, some two thousand men in killed and wounded. Of one negro regiment, numbering a thousand men, when they charged the rebel works on the morning of the 27th of May last, six hundred remain to tell the fate of their comrades. This speaks well for their bravery.