A more thorough explanation:

ad melius inquirendum

Ad melius inquirendum is a legal term that means "for making better inquiry." It refers to a writ that orders a coroner to hold a second inquest.

If new evidence comes to light after an initial inquest, a court may issue an ad melius inquirendum to ensure that a more thorough investigation is conducted. For example, if a witness comes forward with information that was not previously known, a second inquest may be necessary to determine the cause of death.