Of artillery, Price has in all four batteries, of four guns each. In Louisiana are three brigades of Texans, two of which are commanded by Randal and McCulloch, and one brigade of Arkansians, under Tabbat [Tappan?]. These four brigades count together 5,000 men. There is also a cavalry brigade, under Parsons, of 1,600 men; artillery, four batteries, of four guns each, and Richard Taylor's DIVISION, headquarters Alexandria, 4,000 men.

Thus, according to Mr. Ross, Kirby Smith's whole force is little more than 20,000 effective men. Powder he says, is manufactured at Arkadelphia; other ammunition at Camden, on the Washita. Both places are very lightly garrisoned. The number of negroes carried off from the leased plantations in Louisiana is 400.

C. A. DANA.

Honorable E. M. STANTON.

Numbers 4. Reports of Captain Frederick E. Prime, U. S. Corps of Engineers, Chief Engineer, of operations January 30-May 4.

STEAMER MAGNOLIA,

Camp opposite Vicksburg, MISS., January 30, 1863.

GENERAL: I have the honor to forward herewith tracing of point opposite Vicksburg. The dotted line at the entrance of the canal shows the new direction so as to correspond with the course of the current. Ground was broken to-day. Tomorrow I shall try and dam the canal at the point marked, not having any levels but such as used by masons. I shall then be enabled to obtain the approximate difference of level between the water level at the entrance and exit of the canal. At present it is variously estimated from 28 inches to 3 feet. The velocity, as roughly measured to-day by using a floating body, was 422 feet in two minutes. I shall commence making a few fascines and gabions tomorrow. There is difficulty in procuring proper materials for withes and for gabions in the immediate neighborhood.

Should circumstances require the expedition to remain here for some length of time, and the river continues to rise, there will be much trouble from the backwater in the swamps coming form the crevasses in the levee. There is a crevasse above here, as shown on the map, which in a few days will probably be repaired. About 2 1/2 miles above the mouth of the Yazoo River there is another and more troublesome crevasse, which I have not been able to examine, nor have I any person to send. There is also another crevasse some 10 or 12 miles below here. The earth from the new entrance to the canal will by used on the east side to from a species of levee connecting with the old leave, in order to prevent the current (in case it should show a tendency to cut) from expending it self on the low land outside of the levee when the old levee is passed. The levee, as stated in my previous letter, is being constructed on the WEST side, in order to prevent the camping ground from being inundated.

I shall continue to give the Department all information that I can obtain in connection with the engineer part of the expedition. As I have no means or time to keep copies of my letters, any repetitions must be laid to that cause.

I am, general, very respectfully, your obedient servant,

FREDERICK E. PRIME,

Captain of Engineers.

Brigadier General JOSEPH G. TOTTEN,

Chief Engineer of the Army, Washington, D. C.