The immediate object of this expedition is to keep open the river between New Madrid and Memphis, and secure safe navigation for our transports, until the fall of Vicksburg shall place us in condition to carry the war into the interior of Arkansas. To accomplish this I propose the following plan, in substance the same as that discussed by us, viz: Your division of cavalry to move down Crowley's Ridge, make a demonstration against Price's infantry, supposed to be at or near Jacksonport, and attack Marmaduke's cavalry along the ridge, and between that and the river. This, I presume, will compel him to withdraw from the river and mass his troops in your front; perhaps also to make or attempt, a junction with Price's infantry. If so, the immediate object will be accomplished.

If the enemy concentrate his force and offer you battle, you will be compelled to act with much caution. Your force being only cavalry and artillery, you may be unable to cope with the enemy's combined force; but I presume you can easily beat his entire cavalry. You may be able to bring on an engagement with the enemy's cavalry alone. If so, I shall look for the most fortunate and beneficial results. You may also be able, by operating upon the flank and rear of Price's position, to compel him to retire and leave Northeastern Arkansas entirely in your possession. In any event, endeavor to compel the enemy to keep his force so concentrated as to be unable to interfere with the navigation of the river, and, at the same time, hold yourself in such position as to prevent his making a raid into Missouri.

It is important for your to accomplish a decided result as soon as practicable, with a view to a charge of your base of operations to some point on the river. To enable you to accomplish this change of base with certainty as soon as your success will justify it, I will keep a force of infantry and artillery ready to move with supplies for your division to some point down the river. So far as I have been able to learn, Osceola is probably the best point for you to communicate with from Crowley's Ridge, but it will probably be best to leave this for you to determine, after you have advanced into the country and obtained more accurate information.

Please communicate with me frequently, and give me full information, so that I amy be able to act promptly and understandingly in supporting your movements.

I desire to keep the infantry here until your success shall remove all danger of any aggressive movement of the enemy in this direction.

Very respectfully, your obedient servant,

J. M. SCHOFIELD,

Major-General.

[Inclosure Numbers 2.] HEADQUARTERS DEPARTMENT OF THE MISSOURI, Saint Louis, July 8, 1863.

Major General U. S. GRANT,

Commanding Army of Tennessee, Vicksburg, Miss:

GENERAL: I congratulate you most heartily upon your glorious triumph at Vicksburg.

I desire, general, as soon as possible to commence active operations in Arkansas, now that you have removed the obstacle which has so long stood in our way, and forced us to remain comparatively idle. You are aware that since active operations in this department ceased last winter, nearly all the troops in my department, except those necessary for police