The Board of Revision of Assessments shall consist of the Mayor, the Director of Law and the Director of Finance and Public Record. The Mayor shall be the President of the Board and the Director of Finance and Public Record shall be the Secretary thereof. It shall meet at such times and places as is provided by its rules and shall hear all claims and objections as to the character of all improvements to be paid for in part or in whole by special assessments, the necessity therefor, and the equity of the assessments as provided in the assessment report. A majority of those constituting the Board of Revision of Assessments shall have power to determine all complaints and objections submitted to it, and as to each improvement the Board shall, after such hearing amend, equalize, and adjust the assessment report, and shall report its findings as to the necessity for the improvements and any amendments it directs in the assessments to the Council.