NEAR HAW'S SHOP, May 31, 1864-4 p.m. (Received 6 p.m., June 1.)

In the fight of yesterday evening Warren lost 500 killed and wounded. Crawford alone buried on the field 100 dead rebels. To-day our lines have been gradually pushed forward, the enemy giving way without much resistance, except at a point on the Cold Harbor road, which he holds with obstinacy. Our lines now extend from the left at Bethesda Church to near the railroad at a point south of Totopotomoy Creek. There is skirmish firing and an occasional discharge of artillery in the part of the front occupied by Burnside and Hancock, but no very earnest fighting anywhere. We are waiting for the return of Wilson from his railroad-destroying expedition and for the arrival of General Smith and his forces. Wilson can hardly get his work thoroughly done before to-morrow night, and Smith is delayed for his transportation and supplies. General Grant has directed him not to start till he has everything ready. A prisoner was taken this morning from Buckner's division, which he says is now a part of Longstreet's corps. The main line of rebel entrenchments in advance of Richmond, he says, is this side of the Chickahominy, having its strongest point at Mechanicsville. The wheaten is very hot and the roads exceedingly dusty.

C. A. DANA.

Honorable EDWIN M. STANTON,

Secretary of War.

NEAR BETHESDA CHURCH, June 1, 1864-10 a.m. (Received 4.10 a.m., 2nd.)

About 5 p.m. yesterday Sheridan, perceiving a force of rebel cavalry at Cold Harbor, which proved to be Fitz Lee's division, attacked and, after a hard fight, routed it, together with Clingman's brigade of infantry, which came to Lee's support. Sheridan remained in possession of the place. He reported at dark that he had a considerable number of prisoners, and that there were many rebel dead and wounded on the field. He was ordered to hold the position, and at 10 p.m. the Sixth Corps set out to occupy it. Smith's corps, of which two divisions camped last night near New Castle, was also ordered to march upon Cold Harbor and post itself between Wright and Warren. We have not yet heard from Wright or Sheridan this morning, and do not know whether the former has got his troops to their destination. Smith must be close upon Wright's column, though a mistake in the terms of his order, in which the words New Castle were inserted instead of Cold Harbor, delayed his starting this morning. The enemy are also moving a heavy column in the same direction. The order has just gone to Warren to fall upon their flank. Wilson had a fight last evening near Hanover Court-House with Young's brigade of cavalry. He routed Young, killing and capturing many, but there has been a good deal of artillery firing in that direction this morning. Warren reported last night that in his fight on Monday afternoon, near Bethesda Church, Colonel Terrill, Thirteenth Virginia, and Colonel Willis, commanding Pegram's [Doles'] brigade, were killed. Colonel Christian, Forty-ninth Pennsylvania [Virginia], was wounded and captured; so was the assistant