AUGUST 2, 1861.-Skirmish at Dug Springs, Mo.

REPORTS.

Numbers 1.-Brigadier General Nathaniel Lyon, U. S. Army.

Numbers 2.-Captain Frederick Steele, Second U. S. Infantry.

Numbers 3.-Brigadier General James S. Rains, Missouri State Guard (Confederate.)

Numbers 4.-Captain James McIntosh, C. S. Army.

Numbers 1. Report of Brigadier General Nathaniel Lyon, U. S. Army.

HDQRS. U. S. TROOPS, McCULLA'S FARM,
24 miles from Springfield, Fayetteville Road, August 4, 1861.

SIR: On the 1st instant I found the enemy advancing upon Springfield, and, so far as my information went, it was his intention to center upon it three columns, and this road being the one on which was the largest force and most advanced, I started out to meet it, in hopes to drive it back in time to turn upon other points to the west, where the other points to the west and northwest, where the other columns are expected. I reached Wilson's Creek, about 10 miles out, on the first day, and on the second moved about 6 miles, and found an advanced party about 1 mile on from Hayden's farm. Having little else than meat for my troops, and for nearly three weeks past having less than half rations of everything but beef, which has caused considerable diarrhea, my command of volunteers, badly disciplined and clothed, were unfit ot march forward and drive in the enemy's advance, and proceed to the only camp in advance where water could be obtained, some 4 or 5 miles farther on, and where the rebel forces under Rains were some 3,000 strong, and who must be dislodged before we could camp for the night. I therefore stopped at Hayden's.

The rebels' advance perceived my halt, and being mostly mounted, became bold, and threatened me from various points, though in small force-though about 1,000 infantry advanced pretty well forward at one time under an advance of cavalry force. My advance guards of infantry opened fire upon them, and without orders from me, by a spontaneous emotion, the advance of cavalry force. My advance guards of infantry opened fire upon them, and without orders from me, by a spontaneous emotion, the advance guard of my cavalry charged and drove back the rebels, but lost 4 killed and 5 wounded. Cavalry again advanced, but were driven back by my artillery, under Captain Totten.

Yesterday (3rd) I advanced to this point, where General Rains, of Jackson's forces, had his headquarters, and from which he retired without resistance. I cannot say with definiteness how far n advance the main body is, but without supplies, and the danger of being turned by a force to duct off our communication with Springfield, I deem it impracticable to advance; and now, as I determine to fall back upon Springfield, I perceive evidence of an attempt on the part of the enemy to reach Springfield, by a road to the north of us, in advance of our return. I hope the forces in Springfield will be able to hold out till our return. But, painful as it is to announce, I fear much my inability to retain position in Springfield, for the enemy, mostly mounted and very numerous, will cut off our means of obtaining flour, and we shall be forced to retire. I should still hope to retain Springfield and hold out against the enemy in this region but for the expiration of the term of the three-months' volunteers, of whom Colonel Bates' First Iowa Regiment claiming discharge on the 14th instant, Colonel Solomon's Fifth Missouri Regiment at different periods by companies from the 9th to the 18th instant, and a considerable portion of Colonel Sigel's regiment in a similar manner,