a raid into Kentucky through Pound Gap, Pendleton's Gap, or Crank Gap (Cumberland Gap being held by us), a column formed of the disposable force at Knoxville, marching rapidly on his heels, can easily close the gaps in his rear, and perhaps capture his trains; while a force may be thrown around by rail from Chattanooga sufficient, with that in Kentucky, to destroy him. No large force will be thrown into East Tennessee by the rebels, unless we force them to do so by increasing our force and taking the offensive. It is in their power to increase Longstreet's force between this and the 1st of April by detaching from General Lee's army, but after that time they will not dare no diminish General Lee's force. If by great sacrifices General Longstreet be now driven from East Tennessee, he will re-enforce other rebel armies where his presence may be productive of more harm than in East Tennessee. While he is in his present position he can neither do damage in Virginia, North Carolina, nor assist General Johnston to resist our armies in Alabama and Georgia. The best policy seems to be to let him remain until the objects of the movements farther south are attained, and until the offensive can be taken with advantage; even then it is questionable whether the engagements with him should not have for object to retain him where he is until Atlanta, Mobile, Montgomery, and perhaps Augusta and Savannah, fall. Knoxville is only the left wing of the united armies under General Grant. It is 110 miles from the center at Chattanooga, a secondary base, which is still distant from the right wing and the primary base in Tennessee. It is very questionable whether the left wing should be pushed beyond Knoxville. By keeping the army there on the defensive, a considerable force may be spared from it to re-enforce the large army of the center to penetrate into Georgia, where every mile gained in advance tends to dissever the Confederacy. General Longstreet's force has been increased by a force from North Carolina, said to be Pickett's division, numbering 2,800 men. General Pickett did not come with it, but remained in North Carolina. Added to the above about 1,000 convalescents arrived from Richmond.

On the other side, he had suffered from desertions at the rate of 20 a day, and had allowed 5 per cent. of his force to go home on furloughs ranging from twenty-five to thirty-five days each. His present strength is 21,000 infantry and artillery and 6,000 cavalry. The Army of the Ohio, numbered (Twenty-third Corps, 7,000; Ninth Corps, 4,000; Fourth corps, 8,000) 19,000 infantry and artillery, and 6,000 cavalry, of which, however, only about 3,500 were mounted. The question of supplies is satisfactorily settled. The railroad from Chattanooga to Loudon was opened. The work on the bridge at Loudon was being rapidly carried on; it should be finished is seventy days. A wagon bridge having been completed across the Holston at Knoxville, I ordered the pontoon bridge removed to Loudon, to enable the supplies brought up by rail to be wagoner across the river and thence conveyed by rail to Knoxville. The number of light-draught steamers on the river is to be increased. In general the condition of affairs in East Tennessee was so much improved as to produce a decided feeling of confidence.

I have the honor to be, very respectfully, your obedient servant,

J. G. FOSTER,

Major-General of Volunteers.

Major General H. W. HALLECK,

General-in-Chief, U. S. Army, Washington, D. C.