FILLMORE, on the same day, took the oath of the Presidential office in presence of both Houses of Congress, and thus quietly, quickly, and peaceably was effected a transfer of all the Executive powers of this great nation--a transfer never effected without difficulty, and often causing commotion, turmoil, and bloodshed in the less free and more conservative nations of the Old World. In the preceding pages of this Magazine will be found a condensed outline of the life of the late President, which obviates the necessity of further reference in this place. His decease was celebrated by public obsequies in all the principal cities of the Union, and has awakened a universal and intense sentiment of regretful grief. Immediately upon the death of President TAYLOR the members of his Cabinet tendered their resignations to President FILLMORE, but at his request, and for the safety of the public service, they retained their offices for a few days, to give him the desired opportunity for care and inquiry in selecting their successors. That selection was made as soon as practicable, and on the 15th the President made the following nominations, which were at once confirmed by the Senate, which had previously and by a unanimous vote, chosen SENATOR WILLIAM R. KING, of Alabama, to preside over its deliberations: _Secretary of State_ DANIEL WEBSTER, Mass. _Secretary of the Treasury_ THOMAS CORWIN, Ohio. _Secretary of the Interior_ JAMES A. PEARCE, Md. _Secretary of War_ EDWARD BATES, Missouri. _Secretary of the Navy_ WILLIAM A. GRAHAM, N. C. _Attorney General_ JOHN J. CRITTENDEN, Ky. _Postmaster General_ NATHAN K. HALL, N. York. It is understood that Mr. PEARCE declines the secretaryship of the Interior, but no official nomination has yet been made to fill his place. No business of public importance has been transacted in Congress. In the SENATE the Compromise Bill, reported by Mr. CLAY from the Committee of Thirteen, continues under debate. Mr. WEBSTER, on the 17th ult., made a very eloquent speech in its support, declaring himself earnestly in favor of admitting California, of providing a Territorial government for New Mexico, without the anti-slavery proviso, which he deems superfluous, and of settling the question of boundary between Texas and New Mexico. He said he should have preferred to act upon these measures separately, but he was willing to vote for them as conjoined in the bill. Speeches were also made by several Senators against the bill, and some amendments, offered to obviate objections entertained to it in various quarters, were rejected. No decisive action has been had upon it up to the time of putting these pages to press.