If the board of county commissioners finds that the bond provided for in section 6155.01 of the Revised Code has been filed and notice given as required by section 6155.03 of the Revised Code, it shall hear and determine the petition and view the premises along the proposed improvement and the lands of the petitioners and others affected by the milldam. If it finds that such improvement and removal of the milldam will be conducive to the public health, convenience, or welfare, it shall report its finding in writing and order the county auditor to enter it on the journal of the board.