Section 4. Such boards may connect any public park or way, under their control, with any part of the city or town for which they are appointed by taking over any connecting ways, or part thereof leading to such park, and may accept and add to such park any way or part thereof, adjoining and parallel with any boundary line of the same; but the consent of the public authorities having control of such way, and the written consent of a majority of the owners of land abutting thereon, shall first be obtained. They shall have the same power and control over such ways as they have over parks, and a town may invest them with the control, improvement and maintenance of any of the ways thereof for the purpose of carrying out this section. If any such way or part thereof shall pass from the control of any such board, the power and authority over the same shall revert to the public authorities having control of ways in the town in which such way is located.