I have spent the time thus far with the commander and the chief officers of this army. It is difficult for the leaders to abstain from claiming a complete victory. They believe they could have remained upon the battle-field, and that in that case the enemy would have retired. The crushing of the right and center, or of a portion there of, led to the movement by which the army fell back upon and occupied Chattanooga. Chattanooga is fast becoming a fortress and depot which will serve as a base of future operations. As I now see this field it appears to me that the great effort of the rebels by which, concentrating in Georgia, they hoped to crush this army and recover possession of Tennessee and Kentucky, has failed. If so, the fruits of victory are with General Rosecrans, though the trophies, the battle-field, and part of the wounded have fallen into the hands of the enemy. Still, the rebels have not yet abandoned their purpose. Their camp-fires covered the hills last night. Their pickets are within rifle shot, and are visible from the intrenchments. The men await them with confidence. I doubt their attempting an assault. If they are wise I think they will not.

The railroad from Nashville to Reynoldsburg, on the Tennessee River, should be completed, securing water transportation to that point on the Tennessee River, should be completed, securing water transportation to that point on the Tennessee, and supplying Nashville depot while the Cumberland is low and the Louisville and Nashville Railroad broken or overtasked. The iron is reported on the ground; all but 4 miles graded. I have ordered ship-carpenters to be sent from Louisville to build boats at Bridgeport. Things look much better here than I expected to find them when I left Nashville; still success will demand efforts from the army and from the country. Of the rugged nature of this region, I had no conception when I left Washington. I never traveled on such roads before.

M. C. MEIGS,

Quartermaster-General.

PHILADELPHIA, September 27, 1863.

Honorable E. M. STANTON,

Secretary of War:

SIR: I inclose estimate of stock required for Louisville and Nashville Railroad and for Nashville and Chattanooga Railroad, to enable these lines to do the amount of work named in your note of yesterday. There were on the Nashville and Chattanooga Railroad, when I left there, 23 engines in working order and 2 undergoing repairs. These, if in like good order, will, with the 12 stated in the inclosed estimates, bring that road up to its full capacity.

I am, very respectfully, your obedient servant,

J. B. ANDERSON.

N. B.- I have been confined to my bed by indisposition all day. If at all able I will come to Washington to-morrow.

J. B. A.

[Inclosure.]

To enable the Louisville and Nashville and the Nashville and Chattanooga Railroads to do the work required of them, there should be put on those lines, in addition to their present stock as follows: Lou-