SAINT LOUIS, January 5, 1863.

Major-General GRANT:

Dispatch received. Shipping to-day a large quantity of small arm ammunition to Memphis for General Sherman, and ammunition for field-guns, including a large supply for 10 and 20-pounder Parrotts, to replace that captured on the steamer Blue Wing.

F. D. CALLENDER.

HEADQUARTERS ARMY OF THE MISSISSIPPI,
Steamer Tigress, January 5, 1863.

Major General WILLIAM T. SHERMAN, Commanding, &c.:

GENERAL: The following instructions are transmitted for your information. They only give an outline of the movement contemplated against Post Arkansas, Ark., and are based in part upon information respecting the nature and condition of the ground in the vicinity of the Post. This information has bee hastily obtained, and in some instances from sources not authentic. Commanders of army corps will therefore be indulged in the exercise of a discretion as to the best modifications of the method proposed for the accomplishment of the object in contemplation. This method is set forth in the following instructions:

1st. Having arrived at the mouth of the White River the commanders of the army corps of the Army of the Mississippi will lose no time in moving their commands upon their transports up that river to the cut-off, and through it into and up the Arkansas River to a suitable point on the left or east bank of the same near and below Post Arkansas for disembarkation.

2d. The army corps will move from the mouth of the White River in the following order: The Second Army Corps, Major-General Sherman commanding, forming the right wing, right in front, first; the First Army Corps, Brigadier-General Morgan commanding, following the left wing in the same order, next.

3d. Arrived at the proposed point for debarkation the two corps will immediately debark, being careful to preserve their distinctness, protect their landing by skirmishers and advanced detachments, leaving all the means of land transportation and other encumbrances on board the steamers until otherwise ordered by the general commanding the army, and rapidly march as follows:

The Second Corps by the rear of the Post until its right has reached the river above it. In executing this movement the commander may find it expedient to make the Brownsville road a point d'appui on or from which to deploy his column for the purpose of investing the enemy's works and preparatory to attacking him. The First Corps, following the Second to or near the Lawrenceville road, may also find it expedient to make the latter road a point d'appui for the deployment of its column for the purpose aforesaid.

4th. Each army corps should extend its lines so as to complete the investment of the enemy's works, and if in order to do so the left wing has to move so far to the right as to leave too great a space between its left and the river, the same will be secured by a detachment of infantry and artillery from the First Corps, posted in a commanding position for that purpose.

5th. Notwithstanding what precedes, the commander of the First Army Corps will debark two regiments of infantry, one company of cavalry,