The enemy were busily engaged firing from the opposite heights yesterday and last night at the dredge-boat nearest the lower end of the canal. Their shots did no damage, though many of the large ones reached half way across the point.

Ordinary Ohio River boats can now pass from Lake Providence into Bayou Macon, and thence, by easy navigation, to the mouth of Red River.

I make no calculations upon using this route for the present, but it may be turned to practical use after effecting present plans. The same may be said of the canal across the point.

I learn from Jackson (Miss.) papers, of the 14th, that one of our gunboats had run down to Greenwood and exchanged a few shots with the fort at that point. Further information from the enemy shows that several thousand troops have gone from Vicksburg up the Yazoo River. Besides four gunboats (one of them iron-clad) I have a DIVISION of troops there now, and Quinby's DIVISION in the pass on their way down. One DIVISION from Memphis should also be on their way down. The great difficulty of getting small-class steamers adapted to this service has retarded movements by the way of Yazoo Pass materially.

To hem in the enemy on the Yazoo, Admiral Porter has gone into Deer Creek by the way of Steele's Bayou and Little Black Bayou. From there he can get into the Yazoo either by running up Deer Creek to Rolling Fork, thence through the fork and down the Big Sunflower, all of which are navigable, or down Deer Creek to the Yazoo.

Admiral Porter and myself went up Steele's Bayou to Little Black Bayou on the 15th. With the exception of overhanging trees in some places, the navigation was good for the gunboat General Price. I am having those obstructions removed. We were preceded by four of the old iron-clads, that found no difficulty in the navigation. I returned in the evening for the purpose of hurrying up men and means for clearing the channel. I also sent Sherman to make a reconnaissance in company with the gunboats, with a view of effecting a landing with troops on high ground on the east bank of the Yazoo, from which to act against Haynes' Bluff.

Last night I received a dispatch from Admiral Porter saying that the iron-clads had pushed into Black Bayou, and had reached to within a quarter of a mile of Deer Creek, where they had become entangled in the timber, and could not move until it was cut out, and asking me for a force of 3,000 men to act with him. Fortunately I had already sent all that the boats at hand suitable for that navigation and immediately available could carry. I am now sending the remainder of Sherman's old DIVISION, and will push troops through, if Sherman reports favorably, as fast as our means will admit. These troops go up the Mississippi River in large transport about 30 miles, and to where Steele's Bayou comes within 1 mile of the Mississippi. The small-class boats can ferry them from that point, and thus save the distance from the mouth of the Yazoo to, and also the most difficult part of the navigation in, Steele's Bayou.

There is evident indication of considerable excitement in Vicksburg. I think they are removing many of their troops, but cannot satisfy myself to what point. Some we know have gone up the Yazoo, and it may be that others are going to Port Hudson. I have no means of learning anything from below, except what is occasionally learned through Southern papers.

U. S. GRANT,

Major-General.