If it shall be necessary to acquire a right-of-way or an outlet over and through land affected by the improvements, then and in such event the power of eminent domain is hereby conferred, and such land may be condemned. The right of condemnation hereby conferred shall be invoked by application to the court of probate of the county in which the lands over which said right-of-way or outlet is desired are situated, and the same proceedings shall be had as in other cases of condemnation of lands for public uses as provided in this code, and such damages as may be awarded shall be paid by the other landowners in proportion to the assessments approved by the county commission against the benefits accruing to their lands by virtue of the improvements established in said subdistrict.