OFFICE CHIEF QUARTERMASTER ELEVENTH ARMY CORPS, May 25, 1863.

Brigadier General R. INGALLS,

Chief Quartermaster Army of the Potomac:

GENERAL: I desire to add, as supplemental to my report of yesterday, the following:

On the first two days' march, to wit, up to Kelly's Ford, scarcely an article of clothing was lost or abandoned by the Eleventh Corps. The camps of the Twelfth and Fifth Corps, near Mount Holly Church, which I passed directly after they had been abandoned by the troops, were covered with blankets and overcoats, and the road was lined with abandoned property, which was being collected by the inhabitants of the country, and I doubt not a search of their houses and out-buildings would repay the provost-marshal, and secure many wagon-loads of clothing and blankets.

The figures in the report of yesterday are indicative of the amounts drawn and distributed to the troops since their return, and are the nears approximation of losses I could make hastily in answer to your question. They should probably be varied somewhat-caps, shirts, blouses, boots, shoes, and stockings should probably be reduced two-fifths. Wool blankets, haversacks, knapsacks, canteens, dress coats, great-coast, and shelter-tents, are probably nearly correct, as the troops were all well supplied when they marched from camp.

A number of pack-mules in each division can be made, I am convinced, of great utility,and,as an adjunct to wagon transportation or as a sole means of transportation in winter and spring campaigns or sudden movements, are very desirable. The last march was by no means a test of the value of pack-mules, as the mules were not sufficiently accustomed to the packs and the drives were all green hands.

1. Pack-mules can go with the troops; and wherever troops can go pack-mules, properly loaded and conducted, can accompany them.

2. They cane employed successfully in transporting rations and forage to and from and through difficult place, when it might otherwise be impossible to carry supplies.

3. By the use of pack-mules the supply trains of wagons can be left at places more remote from danger and out of the way. In case of advance or retreat, the mules can march as fast as the troops and not materially obstruct the road.

The pack-mules used in the late movement were not only not trained, and the packers not expert, but the ordnance officers in charge were utterly regardless of their animals, and neglected to have their trains watered, fed, or unpacked. They seem to have been utterly ignorant of the equine necessity of daily oats, and to have used their trains without and judgment or many. The ordnance sergeant of the Second Division reports that he mules of his train were without forage four days, and on the fourth day the were so ak that it was almost impossible to get them to stand up and go along; also that the saddles were of only a few hours in seven days; that the backs of some were scalded and fairly rotten. The First and Third Division trains experienced similar neglect. The First Division had 59 mules packed with two boxes each small-arm ammunition, and 19 ridden by the divers. This train returned with a loss of 3 animals, and 13 were subsequently condemned and turned into depot at Aquia on account of sore backs. Two days and one night they were entirely without food and with their packs on. This train and some of the other divisions were unloaded and crossed the United States Ford, packed with a load of hard bread to the troops, and