All casual vacancies among the members (other than ex-officio members) of any authority or other body of the University shall be filled, as soon as conveniently may be, by the person or body who appointed, elected or co-opted the member whose place has become vacant and the person appointed, elected or co-opted to a casual vacancy shall be a member of such authority or body for the residue of the term for which the person whose place he fills would have been a member.