If there shall be practical difficulties or unnecessary hardships in carrying out a rule or regulation of the board of appeals, the board may, after a public hearing, make a variation from such requirements if the spirit of the rule and laws shall be observed. Any person affected by such rules, or his agent or attorney, may petition the board for such variations, stating the ground therefor. The board shall fix a date for hearing on such petition and give reasonable notice thereof to the petitioner. A properly indexed record of all variations made shall be kept by the clerk of the board of appeals in the office of the Department of Labor and shall be open to public inspection.