Section 57. Each application for a license as an engineer or fireman of a class specified herein shall be made upon a blank furnished by the department, signed and sworn to by the applicant, and shall show the total experience of the applicant. Each such application for a first class engineer's license, second class engineer's license or for a special license; for a third class, fourth class or portable class engineer's license or a steam fire engineer's license; for a first class or second class fireman's license shall be accompanied by an examination fee to be determined annually by the commissioner of administration under the provision of section three B of chapter seven. Each such application shall entitle the applicant to one examination only, except in case of an appeal under section sixty-six; provided, however, that no person shall make application hereunder for a license of any particular class oftener than once in 60 days. The fee for an examination on appeal shall be determined annually under the aforementioned chapter seven provision.