Whenever a road is of general utility and of public convenience and constitutes the only or principal means of communication between one town or village and another town or village in the same county, the board of supervisors may determine, by a two-thirds vote of its membership, that the public convenience and necessity demand the acquisition and reconstruction of such road. Thereafter, by a resolution passed by a two-thirds vote of its membership, the board may determine to, and after such determination may proceed to, acquire and reconstruct such road although it is not of the width required by Section 906. The board shall charge the expense of such acquisition and reconstruction to the county general fund, the road fund of the county, or the district fund of each district benefited, or to any two or more of such funds in such proportions as the board considers just and equitable.