Who is designated to replace a man on post?

The correct choice is the Supernumerary, as this term refers specifically to a replacement for a guard or sentry who is unable to fulfill their duties while on post. The role of the Supernumerary includes being ready to step in at a moment's notice to maintain security and ensure that there are no gaps in coverage on duty.

In contrast, the Corporal of the Guard, the Officer of the Day, and the Sergeant of the Guard have specific responsibilities that involve oversight and command rather than direct replacement of personnel. For example, the Corporal of the Guard usually manages the daily operations of the guard and may supervise the Supernumerary, but does not directly step in for someone on post. The Officer of the Day is responsible for the overall duties of the day and ensures proper protocol is followed, while the Sergeant of the Guard is tasked with training and enforcing discipline among the guards. None of these roles are designated specifically for the act of replacing a guard on post in the same manner that a Supernumerary is.