Having crossed White River, the important point to be gained is Little Rock. That or some point near it will, I presume, be defended obstinately. I am not informed to what extent it is fortified, if at all; but presume it will be found necessary to reduce some place of considerable strength on the Arkansas River, not far from Little Rock. this, I hope, will end the main part of the work to be done by our troops as a body in that part of the country. I presume the rebel army, being driven from the vicinity of Little Rock, will retreat to Arkadelphia, perhaps beyond. How far they may be pursued will depend upon contingencies which it is impossible to foresee, and must be left for the future to determine.

It is my desire to get possession of the whole length of the Arkansas River to Fort Smith, and open communication by that line with the troops now under General Blunt in the Indian Territory. This probably cannot be done for the present on account of the low stage of water above as well as below Little Rock; but in a comparatively short time the fall rains will make the river navigable to Fort Smith. We ought to be in condition to take advantage of high water as soon as it comes, to send supplies to Fort Smith, and make preparations for a winter campaign south and west of that point, as well as Little Rock.

On account of the unnavigable condition of the Arkansas during a large portion of the year, it is important to have easy communication from Little Rock to some point on White River. The rolling stock on the Little Rock and Memphis Railroad should be secured, if possible. Failing in this, the wagon road from Des Arc or Clarendon should be made practicable at all seasons.

I desire to obtain telegraphic communication with Little Rock as soon as possible after it shall be occupied by our troops. Presuming the line From Cairo to Memphis will soon be repaired and kept in order, the best line for my purposes will be directly from Little Rock to Memphis. This line can, I presume, be protected with very little difficulty. I will send a telegraph corps in time to construct it, as soon as they can be protected.

It was my intention, when General Davidson was ordered forward from Bloomfield, that he should preserve his connection with that place, and operate against the enemy's cavalry until the movements of the force from Helena should compel them to retreat, or cut them off, and enable him to destroy them. Meanwhile he would have protected my present line. His movement to Wittsburg, leaving Marmaduke so far in his rear, exposed my advanced posts to attack and capture, and compelled me to withdraw some of them, which was done in time to prevent any loss beyond the capture of a considerable train and its escort.

During the past few days the rebel cavalry has shown no disposition to advance farther in this direction, and perhaps their timidity may save us from the damage which they could easily inflict without any great danger to themselves. If General Steele's column moves soon, or General Davidson threatens Marmaduke while Steele is completing his preparations, nothing further will be probably necessary to prevent any movement of the enemy in this direction in greater force than I can take care of. General Davidson's movement to Wittsburg was doubtless caused by the belief that the column from Helena was to start immediately, and, hence, that his best plan was to join it as soon as possible. General Davidson is a most excellent and energetic officer, and has a splendid division of cavalry. I presume General Davidson has already reported to General Steele, and is now acting under his orders. If not, General Steele is authorized to assume command of General