The road from Taylor's Ferry is very narrow, and difficult for artillery and heavy wagons. It passes over high hills, and is very unfavorable to the movements of troops. Colonel Spear, agreeably to my orders, had destroyed all the bridges and ferry-boats below Littlepage's Bridge. The column was crossed on the evening of the 4th, and the advance was immediately made to the bridge of the Richmond and Fredericksburg Railroad across the South Anna. It was found to be held by a very large force, covered by earthworks. From the best information, this force was believed to be about 8, 000 men, with fourteen pieces of artillery. Three regiments had been brought down from Fredericksburg. From the evening of the 1st to the evening of the 4th, cars were coming from Richmond with troops inside and outside. Three trains passed up on the morning of the 4th with troops and with eight pieces of artillery. Believing that his own force would not justify an attack on the bridge, that he would sustain very heavy loss, and that success would be doubtful, he decided to destroy as much of the track as possible, and render the railroad unserviceable. General Foster was, therefore, directed to remove the rails, bend them, and burn the ties. This was accomplished from a point near the bridge to a road some 3 miles below. Major Stratton was sent with a detachment of cavalry to Ashland Station, on the same railroad, about 11 miles from Richmond, where he destroyed the railroad depot, brought off the telegraph instrument, and tore up the track above and below the place, burning the ties and bending the rails. He also destroyed a trestle bridge a mile below Ashland, and a number of cars loaded with materials for the reconstruction of the railroad bridge over the South Anna destroyed by Colonel Spear. He also tore up the track and disabled the rails. It is the opinion of Major Stratton, who is a very judicious man, and who was a railroad engineer before the rebellion, that the injury he did could not be repaired in less than a week, and it is the opinion of General Getty that, considering all the injuries done to the road, a fortnight will be necessary to put it in running order. The position of General Getty on the right bank of the Pamunkey, with Richmond in his front, a large force on his right, and a narrow bridge to recross the river, was a critical one, and if he had been attacked by a superior force he would have been in great danger. Having substantially accomplished the object of breaking up the direct railroad connection between Richmond and General Lee's army in Pennsylvania, he recrossed the Pamunkey, destroyed Littlepage's Bridge, and returned to the White House, bringing with him 21 prisoners, one a commissioned officer, and having lost 2 killed and 7 wounded. The information in regard to the strength of the enemy at the bridge is fully confirmed by the prisoners.

GENERAL KEYE'S DEMONSTRATION.

General Keyes, agreeably to his orders to attack Bottom's Bridge, advanced on the 1st of July to Baltimore, or Crump's, Cross-Roads, where he halted for the night, sending his advance, under Colonel West, 3 or 4 miler farther on. Bottom's Bridge is but 13 miles from the White House, and it was expected that General Keyes would take, on the evening of the 1st, a position which should command it, and prevent the enemy from crossing. The correspondence forwarded to you on the 12th instant whose that he proposed to me the same night to fall back to the White House; that I directed him to