1. Said boards may repair, grade, gravel, macadamize, pave or otherwise improve to the distance of fifteen miles from any line of such special road district, any highway outside of such district if the same be a prolongation of an improved street or highway in said district and if liberal contributions toward such improvements be made in money, material or labor by the inhabitants interested in such improvements or the county commission or any special road district organized under the laws of this state, or the state highway board, or the United States government, or by any one or more of the foregoing.

2. Or in lieu of doing such work in the improvement of such roads such boards may, under the same conditions as would authorize them to do such construction work under this section, contribute toward the repair, grading, graveling, macadamizing, paving or otherwise improving any such highway such an amount as the said board of commissioners of the special road district may determine, providing the other contributions from any one or more of the sources herein mentioned are liberal contributions toward such improvements and together with the contribution of such board will be sufficient to make and complete such improvement; and provided, also, that such work shall be done under plans and specifications and estimate of cost prepared by some competent engineer and approved by such board of commissioners and such contribution of such board shall be paid from time to time only as the work is done or the improvement constructed in compliance with said plans and specifications and on certificate of some competent engineer designated by such board of commissioners and the payments on the work completed shall be in the same proportion as the total contribution of said board bears to the estimated cost of the entire job, and said certificate of the engineer shall show the work completed and the proportional amount of contribution to be paid thereon.