Senate Rule I - Appointment of a senator to the chair

111th Congress
1. In the absence of the Vice President, the Senate shall choose a President pro tempore, who shall hold the office and execute the duties thereof during the pleasure of the Senate and until another is elected or his term of office as a Senator expires.

2. In the absence of the Vice President, and pending the election of a President pro tempore, the Acting President pro tempore or the Secretary of the Senate, or in his absence the Assistant Secretary, shall perform the duties of the Chair.

3. The President pro tempore shall have the right to name in open Senate or, if absent, in writing, a Senator to perform the duties of the Chair, including the signing of duly enrolled bills and joint resolutions but such substitution shall not extend beyond an adjournment, except by unanimous consent; and the Senator so named shall have the right to name in open session, or, if absent, in writing, a Senator to perform the duties of the Chair, but not to extend beyond an adjournment, except by unanimous consent.

110th Congress
1. In the absence of the Vice President, the Senate shall choose a President pro tempore, who shall hold the office and execute the duties thereof during the pleasure of the Senate and until another is elected or his term of office as a Senator expires.

2. In the absence of the Vice President, and pending the election of a President pro tempore, the Acting President pro tempore or the Secretary of the Senate, or in his absence the Assistant Secretary, shall perform the duties of the Chair.

3. The President pro tempore shall have the right to name in open Senate or, if absent, in writing, a Senator to perform the duties of the Chair, including the signing of duly enrolled bills and joint resolutions but such substitution shall not extend beyond an adjournment, except by unanimous consent; and the Senator so named shall have the right to name in open session, or, if absent, in writing, a Senator to perform the duties of the Chair, but not to extend beyond an adjournment, except by unanimous consent.

Resources

 * Rules of the 109th U.S. Senate

Articles

 * "Rule I," U.S. Senate - Committee on Rules and Administration, 2005.