JACKSON, MISS., November 2, 1862.

Major J. R. WADDY,

A. A. G., Dept. of Mississippi and East Louisiana, Jackson:

MAJOR: On the 30th ultimo I proceeded to Vicksburg and made an inspection of the main approaches from the Yazoo River to the Valley road, also of the batteries, and respectfully submit the following:

Lake's road, which runs rom the mouth of Chickasaw Bayou to Valley road, passing by Lake's house and through abatis 1 and 2, is a good road, sufficiently wide for troops and artillery. A good landing could ready be made at the river.

Abatis. No. 1 is not strong. No. 2 is better; still could be greatly improved. Where the road passes through it is open for at least 75 feet. The abatis are about 300 yards wide and 200 long. At low water the main road can be reached by passing over a good road along the bank of Chickasaw Bayou and crossing a bar in Fishing Lake. For artillery to pass the banks of the lake would have to be cut down. At the bar is the point to defend the road.

About one-half mile above Chickasaw Bayou is a good levee, running from the river nearly to the main road, at least 10 feet wide on top. With very little work this levee could be made a good road. It could, however, be easily obstructed and defended, particularly at the point where it runs close to the lake and has the swamp on the other side. A good landing can be made at the river. The levee can be used when the other roads are overflowed. The distance from the river to the Valley road is from 3 1/2 miles 4 miles.

The batteries at Vicksburg are generally in good condition. For amount of ammunition on hand I respectfully refer you to the ordnance officer's report.

Battery No. 1 (on Captain Lockett's plan of Vicksburg) is composed of three 32s (two rifled) and one 42-pounder. The magazine is not sufficiently protected.

Battery No. 2, one 32 rifled, in the fine commanding position. Magazine well protected.

No. 3, one 8-inch columbiad and one 18-pounder rifled. The magazine should have more earth upon it.

No. 4, one 8-inch columbiad. Carriage not in good condition.

No. 5, one 9-inch Dahlgren; has but 21 rounds of shell, 28 of grape, and 200 solid shot. I would not recommend using solid shot out of this gun. Magazine badly constructed.

No. 6, No gun yet mounted.

No. 7, two 42s, which work badly. Magazine not sufficiently protected.

No. 8, two 42s and two 32s rifled; one banded. Magazine requires more protection.

No. 9, two rifled 32s.

No. 10, two 10-inch columbiads, one 32 rifled, and one 10-inch mortar.

No. 11, one 32 rifled.

No. 12, one 8inch navy shell gun.

No. 13, one 7inch Blakely gun and one 8-inch Dahlgren.

No. 14, one 32-pounder siege gun. This gun and those is No. 13 are to be moved nearer the city.

I was informed by the ordnance officer that at Battery No. 12 there was 800 pounds of unserviceable powder, having become so by neglect of the officer who had charge of the battery. I would respectfully suggest that this powder be sent to the mill at Selma, Ala., to be reworked. A number of the carriages are too light for the guns mounted upon them,