Section 81. If the board of aldermen of a city or the selectmen of a town and a company having a location in a way which said board of aldermen or said selectmen or the county commissioners of the county where said city or town lies have in writing requested the commonwealth to take charge of, make application to the department of highways, and with the application submit satisfactory plans, profiles and cross sections of said way, said department shall indicate on such plans, profiles and cross sections a location and grade for the tracks of said company. If said department considers said way suitable for a state highway, and said department and the company by vote of its directors agree as to the proportionate part of the cost of construction which shall be paid by the commonwealth and by the company, said department may pay, out of the appropriations for the construction and repair of state highways, said proportionate part of the damages sustained by a person whose property may be injured by the construction of such state highway, and of the cost of grading it to the lines established by said department. A way graded under this section shall remain a town way or a highway, subject to all laws relative thereto, until said way is taken charge of as a state highway by the commonwealth.