The secretary of the district shall, within 10 days after the filing of such supplemental petition or petitions, make like examination of the same and certify to the result of such examination as herein before provided.

If his certificate shall show any such petition, or such petition as amended, to be insufficient, it shall be filed by him with the board of the district and kept as a public record, without prejudice, however, to the filing of a new petition to the same effect, but if, by the certificate of the secretary, such petition, or petition as amended, is shown to be sufficient, the secretary shall present the same to the board without delay.