According to a nearby information board:

A “necessary” is a privy, or outhouse. In front of you is the vault of the only necessary known to have existed at Fort Montgomery. When it was finished in April 1776 it was described as “a large necessary, for soldiers”. It is hard to imagine that this one small building served the needs of hundreds of soldiers, so it is possible that there were other necessaries within the fort that have not yet been identified.

In privies, archaeologists usually find large quantities of discarded material like bottles and broken dishes as well as things that were inadvertently lost like coins and buttons. However, relatively little was found at the bottom of Fort Montgomery’s necessary. One possible explanation is that soldiers may have avoided using this necessary to keep it in readiness in case the fort was ever besieged.