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.