The defeats at Gettysburgh and Vicksburgh had turned the tide of success in favor of the North, and although this was partially relieved by the minor victories of Plymouth and elsewhere, the hopes of ultimate success were becoming much darkened. Governor Graham had never doubted that the North had the physical ability to conquer, if her people could be kept up to a persevering effort, nor that our only chances depended on their becoming wearied of the contest. As our fortunes lowered, all men of prevision and sagacity turned their thoughts toward the possibility of overtures for peace as becoming daily of greater importance and more imminent necessity. But how could this be done? With a powerful enemy pressing us, with war established by law, with entire uncertainty as to the terms to be expected in case of submission, with the necessity imposed of making no public demonstration which should dampen the ardor of our troops, or depress still further the spirits of our people, and excite the hopes of the enemy; with such obstacles in the way, peace could not be approached by a public man without involving the risk of inaugurating greater evils than those he sought to avert. Besides all this, by the adoption of the Constitution of the Confederate States, (which, by the way, Governor Graham had vainly endeavored to prevent in convention, without a second,) all legal power to terminate the war had been surrendered to the President. Any other method would have been revolutionary, and have provoked civil strife among us, and, doubtless, sharp retribution. The only plan, therefore, which could afford reasonable hope of success was to operate upon and through the President. This was attempted at the first session of Congress of which Governor Graham was a member, by secret resolutions introduced by Mr. Orr, the present Governor of South-Carolina, which, however, failed to get a majority vote of the Senate. Governor Graham, who was deeply impressed with a sense of the absolute necessity of some movement toward peace, and who was not among the confidential friends of the President, attempted next to operate on him through those who were in some measure influential with him. By this means he had an agency in setting on foot the mission to Fortress Monroe, the result of which is well known. In the absence of Mr. Hunter on that mission, Governor Graham was president _pro tem._ of the Senate. Disappointed and mortified by that failure, he then approached President Davis directly, and the results were stated in his private correspondence with a confidential friend in North-Carolina. There can be no better exponent of Governor Graham's position and views at this momentous crisis in our history, than is found in these letters, and I esteem myself peculiarly fortunate in being able to present to my readers such extracts from them as will assist my purpose. They are the letters of a consummate statesman, and of a patriot, and need no heralding: