In response to resolutions of thanks from the Indiana Legislature, Gen. ROSECRANS has written the following letter:

GENTLEMEN: In the name of the officers and soldiers of the Army of the Cumberland, I thank you for the resolutions of congratulation, approval and condolence you have sent us on account of the battle of Stones River.

At the call of constitutional liberty, the brave and true men of the West laid aside peaceful pursuits, left their homes and sought to qualify themselves to fight for a Government that had cost the blood and treasures of two great wars and eighty years of time to establish.

For twenty weary months this army has stood guard to keep the Confederate wolf from your doors. They know what hunger, cold, weary marches and painful watchings it has cost to preserve our homes from invasion, and our friends and neighbors from conscription; it is, therefore, doubly a pleasure to hear these free and cheering words now from home.

The unscrupulous despots in our front call us "Lincoln hirelings," and we hear that this calumny has lately been repeated at home by some of the men whose property and persons have been kept safe, by our toil and blood, from the ruthless hands of KIRBY SMITH, BRAGG and MORGAN. Presuming on our absence, these men talk as if we were not citizens, and speak mockingly of our patriotism. They stab in the back the most generous, true-hearted men in the country, while standing guard in front of their doors, and they prolong the war by encouraging the rebels to hope for divided counsels at our homes.

I speak the conviction of the officers and men of this army, when I say we fight to secure equal rights to all, under the Constitution and the laws -- we fight in defence of our homes and hearths, sure to be invaded, if the rebel despots who began the war, can get the power. But we long for peace -- we pray for peace, and we fight for peace -- not for a dishonorable peace -- not for a hollow truce. We have once been deceived by the cry of "No coercion," and of "State rights." and have seen how the rebel leaders practice, in East Tennessee, Missouri, Western Virginia and Kentucky. We have met the masses of the South, and are witnesses of the falsehood, calumny and perfidy by which they have been led to wage war against us. We have seen flags of truce violated -- hospitals, ambulances and boats, bearing flags, fired upon, and our sick and wounded stripped of their blankets and robbed of their food and medicines -- we have been approached in battle by rebels wearing our uniforms and carrying our colors.

After witnessing the wholesale slander of us, their perfidy and treachery toward the masses of their own people, and the unfair and dishonorable means to which they resort to gain an advantage, we have been forced to the immovable out sad conviction, that the LEADERS of the rebellion are perfidious, treacherous, unscrupulous and cruel -- their leaders never will nor can be peaceable, or true friends and neighbors. And that, as Mr. DAVIS has said, they only want the power, not the will, to invade and subjugate us.

We should rejoice to see the power of these leaders fall by the hand of their own people, whom they oppress; that people for whose rights we fight, in common with our own; but unless it does thus fall, we must destroy it, or it will destroy our Nation, and our children will pass under the yoke of a military despotism raised on the sable foundation of negro Slavery, and the more degrading servitude of the "poor whites," such as now overshadows the South. I say "our children will pass under the yoke," for that could only happen after the brave and true men of the country -- her citizen-soldiers -- shall have perished, of, deserted by the wretches whose homes they have hitherto protected, heart-broken and despairing, shall quit the field and give to Slavery and to its domination all those who love money more than honor, and peace more than freedom.

The issue is a plain one. If we who battle for national existence are not to be sustained by our own friends at home, the sooner we know it the better. We do not wish to be deceived as to our position, nor fall victims to the treachery, cowardice or selfishness of those whom we have loved and trusted.

W.S. ROSECRANS, Major-Gen.

To the Honorable the Legislative Assembly of the State of Indiana.