The terms and times of payment of the bonds so issued shall be fixed by the board of directors of the improvement district, and such bonds shall be signed by the county mayor and countersigned by the clerk of the county, each of the officers signing officially, and shall be verified either by the county seal or seal of the county clerk. Such bonds shall be issued for the benefit of the district numbered on the bonds, and each district shall be numbered by the county court and recorded by the county clerk in the drainage record, the record showing specifically the lands embraced in that district and upon which the assessment has not been previously paid in full.