Service by publication is typically used in cases where:

Service by publication is a legal process used when a party cannot be located through normal means of service, such as personal delivery or certified mail. This method allows a plaintiff to notify a defendant of legal proceedings when the defendant's whereabouts are unknown, making it impractical to serve them directly. The requirement for service by publication is typically outlined in the rules of civil procedure and often necessitates that the plaintiff demonstrate due diligence in attempting to locate the defendant.

In the context of the other options, while a defendant being in hiding could warrant service by publication, it does not capture the broader application of the mechanism, which is specifically aimed at instances where normal service methods fail. High public interest may highlight the case, but it does not dictate the necessity for service by publication. Circumstantial evidence pertains to the nature of the evidence presented in the case rather than directly influencing how a defendant should be served. Thus, the correct answer reflects the fundamental purpose of service by publication as a last resort when standard service efforts have proven unsuccessful.