Section 41. Term of office; vacancies

The term of office of each member of
  such board shall be three years, from the first day of January following
  his appointment. Vacancies occurring by expiration of a  term  shall  be
  filled  by  the  mayor  for  a  full  term. Vacancies by death, removal,
  inability to act, resignation or removal from the  city  of  any  member
  shall  be  filled  by him for the unexpired term. The chief inspector of
  plumbing and drainage and the  engineer  in  charge  of  sewers  or  the
  officers  holding  equivalent  positions  or  acting  in like capacities
  designated or appointed by the mayor as herein  provided,  shall  be  ex
  officio  members  of  such examining board, and when they shall cease to
  hold their offices by reason  or  on  account  of  which  they  were  so
  designated  or  appointed,  their  successors shall act on the examining
  board in their stead.