For a week past, the people of the loyal States have been surfeited with extracts from the Richmond journals, boasting that the Rebels took 10,000 prisoners in the recent battles between Gen. Hooker's army on the Rappahannock and the Rebel forces led by Gen. Lee. At length, those prisoners are forwarded to City Point for exchange, and the actual count reduces them to 4,500. The Rebels in Virginia have Seven Thousand prisoners in all to exchange; but only 4 500 of them belong to the Army of the Potomac. — Here are facts in correction of bulletins whereby we may confidently measure past and future vaunts of Rebel triumphs.

Meantime, the fact remains unquestioned and unexplained that Gen. Lee had ample notice of Gen. Hooker's retreat across the Rappahannock, yet did not venture to assail or molest him. Crossing a deep and rapid river in the face of a resolute enemy is always a hazardous and costly undertaking; but retreating across such a river in presence of a hostile force is ten times more difficult and perilous than advancing. Had Lee's army been on fighting condition, it is not possible that he would have suffered this passage with out even an attempt to profit by it.

The simple truth manifestly is that Lee's army, which consisted of but 50 000 men at the outset, had suffered to terribly and been overworked so tearfully during the four or five days preceding, that it could not attempt to press on Hooker's rear during the passage of the Rappahonnock. Lee is a good General, thoroughly wide-awake, and his army is brave and resolute, but there are limits to human capacity and endurance. They had fought Hooker on Saturday and Sunday, and Sedgwick on Monday, and, though they crowded out men in either case, this fact compelled them to expose compact bodies of infantry to the murderous fire [unknown] powerful and well-served artillery, so that their losses in killed and wounded were doubtless greater than ours, [unknown] as they were handled. Then they must have nearly or quite exhausted their ammunition for their great guns; as they made little or no use of these in the later conflicts — Had Gen. Hooker known how incapable were his adversaries for further exertion, he would not have recrossed the Rappahannock; and though the prestige of success is with them, their losses, including that of Stonewall Jackson, trench more severely on their resources than ours do upon our own. Their "victory" is like that of Pyrrhus of Macedon over the Romans, of which he remarked that one more such would be his ruin. — [New York Tribune, May 18th.