SIR: The following is a report of the part taken by the First Squadron of the Tenth Cavalry, consisting of Troops A, B, E, and I, in action with the Spaniards on the 1st, 2d, and 3d instants:

On the evening of June 30 the regiment, as part of the Second Brigade, Cavalry Division, took position on the extreme left of the line, about 5 miles from Santiago.

On the morning of the lst, after an artillery duel of short duration between Grimes's battery and the artillery of the enemy, the regiment moved forward toward the town to the crossing of the San Juan River, when it immediately became engaged. The regiment took position in a wood, and here suffered considerable loss, due to the fact that the whole of the enemy's fire appeared to be directed to this point. In a short time we moved out of the wood by the right flank and then deployed to the left, being then directly in front of the enemy and about 1 mile distant from his works, marked by three houses about half a mile from one another. The enemy were strongly intrenched in front of these houses. The line, consisting of the Cavalry Division, under direction of Brigadier-General Sumner, moved forward in double time, under a terrific fire of the enemy. We had a very heavy jungle to march through, besides the river (San Juan) to cross, and during our progress many men were killed and wounded. The troops became separated from one another, though the general line was pretty well preserved. The works of the enemy were carried in succession by the troops and the Spaniards were steadily driven back toward the town to their last ditches. We now found ourselves about half a mile from the city, but the troops being by this time nearly exhausted, here intrenched themselves for the night under a heavy fire. By dark this line was occupied by all the troops engaged during the day.

July 2 we changed our position to about 600 yards to the right, and were under a heavy fire during the whole day until dark, when we were again changed to about half a mile to the right and a little nearer to the works of the enemy.

July 3 and until noon we were engaged with the enemy. At noon firing was suspended on both sides by reason of a flag of truce being sent forward, presumably to give notice of the bombardment of the city.

The conduct of the officers and enlisted men of my squadron was simply superb.

The following is a list of the killed and wounded: Killed-Troop A, Private John H. Smart; Troop B, Corpl. William F. Johnson. Wounded- Troop A, First Lieut. R. L. Livermore, Second Lieut. F. R. McCoy, Sergt. Smith Johnson, Corpl. Joseph G. Mitchell, Trumpeter Nathan Wyatt, Privates William A. Cooper, Benjamin Franklin, Wiley Hipsher, Richard James, Daniel Blue. All July 1. July 2. Private Luther D. Gould. July 3, William H. Brown. Troop B, July 1. Privates John Prim and William Gregory; July 2, Second Lieut. Harry O. Williard. Missing- Saddler John H. Ubanks, George Berry, and William Jackson. Troop E, July 1, Sergt. William Payne, Blacksmith Lewis L. Anderson; Privates Henry McCormick, Gilmore Givens, Hilly Brown. Troop I, July 1, First Sergt. Robert Millbrown, Sergt. W. G. Gunter, Privates Frank D. Bennett, Thornton Berkley, Thomas H. Hardy, Wesley Jones, Houston Riddle. Missing- Private John F. Chinn.

Respectfully submitted.

Major, Tenth Cavalry, Commanding First Squadron.