HEADQUARTERS FIRST BRIGADE, HOOKERS DIVISION, Camp at Pair Oaks, Va., June 19, 1862. SIR: I have the honor to report that, pursuant to instructions received on the 18th instant, I caused a reconnaissance to be made of that portion of the wooded country in front of onr right, lying between the Williamsburg road and the railroad, for the purpose of ascertaining the character and extent of what is kuown as the swamp, aiid of obtaining, if practicable, any information of the strength amid position of the enemy along that portion of his lines. The duty of making this reconnaissance was assigned to Colonel Wyman, commanding the Six- teenth Massachnsetts Volunteers, and I respectfully refer to his inclosed report for the details of that daring and well-executed service. Though it was the first time that this regiment had been under fire, the intre- pidity and good order displayed lL[)011 that occasiomi, under most adverse circumstances, cannot, I think, be surpassed. The co-oJ)eration of a section of Captain Bramhalls Sixth New Voik Independemit Battery, commanded by Lient. Joseph TWT. Martin, did most efficient and important service. The position occupied by this section was such as to enfilade the Williamsburg road. As the line of skirmishers advanced it met a very heavy fire from rifle pits in the immediate vicinity of the road, but concealed from view from the position of the battery. That fire was, however, quickly and effectually checked by the skilled handling of the pieces under Lieutenant Martin. The reconnaissance has established the following facts, viz: 1st. That the only obstacle worth notice at the present time between our lines and those of the enemy is the dense undergrowth in the standing timber. 2d. That the enemy has a strong line of works from one-half to three-quarters of a mile from our own, and that he holds it in strong force. Colonel Wyman reports 39 of the enemy as known to have been killed. Our killed numbered 16 (enlisted); our wounded 28; missing, 1 captain, 1 lieutenant, 13 enlisted. Total, 2 officers, 57 enlisted men. The large number of killed in proportion to the wonuded is believed to be due to the thickness of the underbrush, which prevented either party from seeing the other until at uncomnmonly short ranges. I am, sir, very respectfully, your obedient servant, C. GROVER, Brigadier- General, Commanding Brigade. To the ASSISTANT ADJUTANT-GENERAL, Hookers Division. No. 3. Report of Col. Powell T. Wyman, Sixteenth Massachusetts Infantry. IIDQRS. SIXTEENTH MASSACHUSETTS VOLUNTEERS, Camp at Fair Oaks, Va., June 18, 1862. CAPTAIN: In obedience to the order of the general my regiment this afternoon entered the woodM in front of Fair Oaks battle ground for the purpose of reconnaissance and feeling the enemy. As a general thing, the regiment penetrated the woods to the distance of about half a mile, One captain thinks he must have marched a mile forwmrd. Mammy of the companies saw the open country beyond, but in consequence of the