Major-General GRANT, Louisville.

GENERAL: In compliance with my promise, I now proceed to give you a brief statement of the objects aimed at by General Rosecrans and General Burnside's movement into East Tennessee, and of the measures directed to be taken to attain these objects.

It has been the constant desire of the government, from the beginning of the war, to rescue the loyal inhabitants of East Tennessee from the hands of the rebels, who fully appreciated the importance of continuing their hold upon that country. In addition to the large amount of agricultural products drawn from the upper valley of the Tennessee, they also obtained iron and other materials from the vicinity of Chattanooga. The possession of East Tennessee would cut off one of their most important railroad communications, and threaten their manufactories at Rome, Atlanta, etc.

When General Buell was ordered into East Tennessee in the summer of 1882, Chattanooga was comparatively unprotected; but Bragg reached there before Buell, and, by threatening his communications, forced him to retreat on Nashville and Louisville. Again, after the battle of Perryville, General Buell was urged to pursue Bragg's defeated army, and drive it from East Tennessee. The same was urged upon his successor, but the lateness of the season or other causes prevented further operations after the battle of Stone River.

Last spring, when your movements on the Mississippi River had drawn out of Tennessee a large force of the enemy, I again urged General Rosecrans to take advantage of that opportunity to carry out his projected plan of campaign, General Burnside being ready to cooperate, with a diminished but still efficient force. But he could not be persuaded to act in time, preferring to lie still till your campaign should be terminated. I represented to him, but without avail, that by this delay Johnston might be able to reenforce Bragg with the troops then operating against you.

When General Rosecrans finally determined to advance, he was allowed to select his own lines and plans for carrying out the objects of the expedition. He was directed, however, to report his movements daily, till he crossed the Tennessee, and to connect his left, so far as possible, with General Burnside's right. General Burnside was directed to move simultaneously, connecting his right, as far as possible, with General Rosecrans's left so that, if the enemy concentrated upon either army, the other could move to its assistance. When General Burnside reached Kingston and Knoxville, and found no considerable number of the enemy in East Tennessee, he was instructed to move down the river and cooperate with General Rosecrans.

These instructions were repeated some fifteen times, but were not carried out, General Burnside alleging as an excuse that he believed that Bragg was in retreat, and that General Rosecrans needed no reenforcements. When the latter had gained possession of Chattanooga he was directed not to move on Rome as he proposed, but simply to hold the mountain-passes, so as to prevent the ingress of the rebels into East Tennessee. That object accomplished, I considered the campaign as ended, at least for the present. Future operations would depend upon the ascertained strength and; movements of the enemy. In other words, the main objects of the campaign were the restoration of East Tennessee to the Union, and by holding the two extremities of the valley to secure it from rebel invasion.

The moment I received reliable information of the departure of Longstreet's corps from the Army of the Potomac, I ordered forward to General Rosecrans every available man in the Department of the Ohio, and again urged General Burnside to move to his assistance. I also telegraphed to Generals Hurlbut, Sherman, and yourself, to send forward all available troops in your department. If these forces had been sent to General Rosecrans by Nashville, they could not have been supplied; I therefore directed them to move by Corinth and the Tennessee River. The necessity of this has been proved by the fact that the reinforcements sent to him from the Army of the Potomac have not been able, for the want of railroad transportation, to reach General Rosecrans's army in the field.

In regard to the relative strength of the opposing armies, it is believed that General Rosecrans when he first moved against Bragg had double, if not treble, his force. General Burnside, also, had more than double the force of Buckner; and, even when Bragg and Buckner united, Rosecrans's army was very greatly superior in number. Even the eighteen thousand men sent from Virginia, under Longstreet, would not have given the enemy the superiority. It is now ascertained that the greater part of the prisoners parolled by you at Vicksburg, and General Banks at Port Hudson, were illegally and improperly declared exchanged, and forced into the ranks to swell the rebel numbers at Chickamauga. This outrageous act, in violation of the laws of war, of the cartel entered into by the rebel authorities, and of all sense of honor, gives us a useful lesson in regard to the character of the enemy with whom we are contending. He neither regards the rules of civilized warfare, nor even his most solemn engagements. You may, therefore, expect to meet in arms thousands of unexchanged prisoners released by you and others on parole, not to serve again till duly exchanged.

Although the enemy by this disgraceful means has been able to concentrate in Georgia and Alabama a much larger force than we anticipated, your armies will be abundantly able to defeat him. Your difficulty will not be in the want of men, but in the means of supplying them at this season of the year. A single-track railroad can supply an army of sixty or seventy thousand men, with the usual number of cavalry and artillery; but beyond that number, or with a large mounted force, the difficulty of supply is very great.