The jurisdiction and control of the Highway Bridge across the Potomac River, including appropriations and employees, shall be under the Mayor of the District of Columbia. The Highway Bridge shall be for highway traffic. The entire cost of paving, repairs, or replacements incident to track repairs, replacements, or changes made at a time when the bridge is not being paved, and one-half the cost of other paving, repaving, or maintenance of paving between its track and for 2 feet outside the outer rails, and the excess cost of construction and maintenance of the bridge due to the existence or installation of its tracks thereon shall be paid by the street railway company or companies using the same under such regulations as the Mayor of the District of Columbia shall prescribe; provided, that all street railroads chartered or that may hereafter be chartered by Congress shall have the right to cross said bridge upon terms mutually agreed upon with the Washington, Alexandria, and Mount Vernon Railway Company or in case of disagreement, upon terms determined by the United States District Court for the District of Columbia which is authorized and directed to give hearing to the interested parties and to fix the terms of joint trackage.