HEADQUARTERS DIVISION, Arlington, Virginia, January 26, 1862.

Brigadier General S. WILLIAMS,
Asst. Adjt. General, Hdqrs. Army of the Potomac, Washington, D. C.:

GENERAL: I have the honor to report as follows in answer to your telegram of the 23rd instant, enquiring whether, in the event of a forward movement, there are any regiments in my command unfit either in point of equipments or discipline for the emergencies of the field:

WADSWORTH'S BRIGADE.

Twentieth New York, armed with Austrian rifled muskets.

Twenty-first New York, armed with Springfield rifled muskets.

Twenty-third New York, armed with Enfield rifled muskets.

Twenty-fifth New York, armed with Austrian rifled muskets.

Equipped and well disciplined for volunteers.

KING'S BRIGADE.

Second Wisconsin, Austrian rifled muskets.

Sixth Wisconsin, Belgian rifled muskets.

Seventh Wisconsin, Springfield altered smooth bore.

Nineteenth Indiana, Springfield rifled muskets.

The muskets of the Seventh Wisconsin are reported as bad, and that the men lack confidence in them.

The brigade is equipped, with some slight exceptions, and well disciplined for volunteers. The Nineteenth Indiana the least so. A special report will be made as to this regiment after a special inspection next Monday.

AUGUR'S BRIGADE.

Fourteenth New York (Brooklyn), Springfield rifled.

Twenty-second New York, smooth-bore Springfield.

Twenty-fourth New York, rifled muskets, caliber 58.

Thirtieth New York, Springfield rifled.

Equipped and well disciplined for volunteers. The Twenty-second need other guns.

CAVALRY.

Second New York (Ira Harris). Equipped, save that 100 horses are required. Drill and discipline good for volunteers; above average. One company-a new one-defective in drill, but are armed with carbines, and are said to be good marksmen.

ARTILLERY.

Company B, Fourth Artillery. Manned mostly by volunteers; good..

Rhode Island Battery. Good for volunteers.

New Hampshire Battery. Good for volunteers. Not as good as Rhole Island.

Pennsylvania Battery. Reported by Captain Gibbon as not in a fit condition to take the field. The materials, the officers and men and horses are all good, but the battery is not instructed.

The batteries lack ammunition, and the regular battery, Napoleon guns, need extra caisson to carry sufficient ammunition.

The change of small-arms leaves the division for the moment short of ammunition; a deficiency soon supplied.

The men would suffer much less were they supplied with-

1st. India-rubber ponchos, to answer for shelter tents.

2nd . Cowhide boots; two-thirds have them.