NEW ORLEANS, LA., October 4, 1864.

(Received 7 p. m., 16th.)

Major-General HALLECK,

Chief of Staff:

The public estimate of Price's and Shelby's forces are, I think, greatly exaggerated. My scouts have been through their forces, and a comparison of their statements gives Price about 8,000 men, 400 wagons, a pontoon bridge, and ten pieces of artillery. The highest estimate of Price's force is 10,000 men and eighteen pieces of artillery; Shelby, I think, has not more than 5,000. Both forces will probably be increased by conscripts. I know that they count upon this and are prepared to arm and equip them. The infantry force arriving in Arkansas has been concentrated at Monticello, and number about 13,000. About 10,000 men are in the neighborhood of Monroe and Saint Joseph, under orders to cross the Mississippi and join Dick Taylor in East Louisiana. Steele has been re-enforced sufficiently by about 15,000 men to prevent the invasion of Missouri by an infantry force; if necessary will be strengthened from Vicksburg, and if the force now in the Washita country should move into Arkansas I will send the force that is watching them into Arkansas.

ED. R. S. CANBY,

Major-General.

(Copy to Major-General Rosecrans.)

U. S. MISSISSIPPI SQUADRON, FLAG-SHIP BLACK HAWK,

Mound City, Ill., October 4, 1864.

Major General E. R. S. CANBY,

Commanding Mil. Div. of West Mississippi, New Orleans, La.:

GENERAL: I have the honor to acknowledge the receipt of your communication of the 20th ultimo to Admiral Porter, and to inform you that, previous to his departure for the East, he ordered the double-turreted monitors Milwaukee and Kickapoo to be sent as soon as possible to Admiral Farragut at Mobile. We shall then be left with only two small monitors, both undergoing repairs. I trust the admiral will send us, in exchange, the monitor Manhattan and the ram Tennessee, as we require their services in the lower Mississippi. It will give me great pleasure, general, to co-operate with you, and afford you all the assistance in my power should you require it. The Milwaukee may be retained a few days between Cairo and Memphis on account of low water.

Very respectfully, your obedient servant,

A. M. PENNOCK,

Captain, Commanding Mississippi Squadron.

OFFICE OF CHIEF ENGINEER, MIL. DIV. OF WEST MISS.,

New Orleans, October 4, 1864.

APALACHICOLA, CHATTAHOOCHEE, AND FLINT RIVERS.

Memorandum of information obtained from Mr. Pitfield, who, as supervising inspector of steam-boats under the Federal Government before the war, has visited the whole navigable portions of the rivers.