Sherman having been left in command in the south-west, with instructions to capture Atlanta, the vital point in Georgia, commenced that grand series of flanking movements, which, for a time, seemed to occasion intense satisfaction to the rebels, whose commander, Johnston, upon all occasions had Sherman exactly where he wished him; while Grant--taciturn, cool, and collected, with no set speeches, no flourish of reviews--proceeded with the difficult task which he had taken in hand--the annihilation or capture of Lee’s army, the mainstay of the rebels’ military resources, and the occupation of Richmond. On the 30th of April, the President addressed the following letter to the new Commander: “LIEUTENANT-GENERAL GRANT:--Not expecting to see you before the spring campaign opens, I wish to express in this way my entire satisfaction with what you have done up to this time, so far as I understand it. The particulars of your plan I neither know, nor seek to know. You are vigilant and self-reliant; and pleased with this, I wish not to obtrude any restraints or constraints upon you. While I am very anxious that any great disaster or capture of our men in great numbers shall be avoided, I know that these points are less likely to escape your attention than they would be mine. “If there be any thing wanting which is in my power to give, do not fail to let me know it. And now, with a brave army and a just cause, may God sustain you! “Yours, very truly, A. LINCOLN.” To which the General, from Culpepper Court House, Va., on the 1st of May, thus replied: “TO THE PRESIDENT:--Your very kind letter is just received. The confidence you express for the future and satisfaction for the past, in my military administration, is acknowledged with pride. It shall be my earnest endeavor that you and the country shall not be disappointed. “From my first entrance into the volunteer service of the country to the present day, I have never had cause of complaint, have never expressed or implied a complaint against the Administration, or the Secretary of War, for throwing any embarrassment in the way of my vigorously prosecuting what appeared to be my duty. “Indeed, since the promotion which placed me in command of all the armies, and in view of the great responsibility and importance of success, I have been astonished at the readiness with which every thing asked for has been yielded, without even an explanation being asked. Should my success be less than I desire and expect, the least I can say is, the fault is not with you. “Very truly, your obedient servant, “U. S. GRANT, Lieutenant-General.”