TULLAHOMA, July 3, 1863.

Major-General ROSECRANS, Estell Springs:

The following received from Washington, being an extract from a dispatch from Grant to Halleck, forwarded by order of the Secretary of War, dated June 27:

Joe Johnston has postponed his attack until he can receive 10,000 re-enforcements, now on their way from Bragg's army. They are expected early next week.

T. T. ECKERT.

I sent copy of this, by courier, before line was opened. General Granger telegraphs, proposing to send General Ward back to command at La Vergne, and to put Colonel Dan. McCook in command at Murfreesborough, and asks immediate answer. I have also a dispatch from General Morton about pontoons. I have telegraphed him to see you.

C. GODDARD,

Assistant Adjutant-General.

HEADQUARTERS DEPARTMENT OF THE CUMBERLAND,
Tullahoma, July 3, 1863 - 1.30 a. m.

Major General THOMAS L. CRITTENDEN:

Have heard from General Stanley, at Morris' Ford. General Palmer is at Hart's tan-yard. The rear of the forces are at Elk River, from Johnson's Ford and above to the mouth of Rock Creek, below the railroad bridge over Elk River. They think the river will be fordable to-morrow morning. Whether this will meet opposition or not, remains yet to be seen. General Thomas thinks this is evidence that a portion of Bragg's army will endeavor to escape, by way of Pelham, across the mountains. The general commanding directs you to proceed to Pelham, with Wood's division, and intercept any such force, if possible. It can only be a fragment that will attempt to escape by that route. The enemy's force are greatly demoralized, and are deserting hourly. Good news from both East and West. Strong reasons for believing that Vicksburg has fallen. The general commanding goes to the front early to-morrow morning.

Very respectfully, your obedient servant,

J. A. GARFIELD,

Brigadier-General and Chief of Staff.

HEADQUARTERS FOURTEENTH ARMY CORPS,
Jones' Ford, July 3, 1863 - 6.30 a. m.

Brigadier General JAMES A. GARFIELD,

Chief of Staff:

In my dispatch of last evening, reporting operations for the day, I endeavored to locate my position on Elk River (not Duck) so that the general commanding should know where I was, and have to express my regret that I have failed to locate my position perfectly. I have had no means of opening communication with General Crittenden or General Stanley, as up to yesterday afternoon I did not know what route they had taken. General Negley was endeavoring all day yesterday to open communication with General McCook's corps, and although his couriers were at several points on the railroad, he did not succeed until last evening in finding where General Sheridan had commenced cross