After the drainway herein provided for shall be completed the person, firm, or corporation cutting or digging the same shall be entitled to recover of the landowners owning that part of the land with reference to which no contract for compensating those cutting or digging the drainway may have been made, an amount equal to the benefits to accrue to such lands by reason of the drainway, and shall be required by the clerk of the superior court to pay to any landowner the amount of damages in excess of benefits which may be done to the land to be determined in the manner hereinafter provided: Provided, that the recovery from any owner of the land shall be limited to the benefits to accrue to that land owned by such person, and situated in such swamp or lowlands or adjacent thereto; and provided further, that the amount to be so recovered as herein provided for until fully paid shall be and constitute a lien upon such land, the lien to be in force regardless of who may own the land at the time the amount to be recovered as compensation for digging or cutting the drainway shall be determined. (1917, c. 273, s. 2; C.S., s. 5285.)