The vibrating square is the square where the invocation ritual is to be performed for entry into Moloch's Sanctum. It is always located on the penultimate dungeon level of Gehennom, which could be between levels 44 and 52. It is the lowest level that can be reached without performing the ritual; until the ritual is performed, there is no staircase leading down from that level. Only the Sanctum level has a higher dungeon level number.
The level with the vibrating square is in most other respects an ordinary maze level of Gehennom.
The only way to locate the vibrating square is to move over it, at which point you will get the message: "You feel a strange vibration under your feet." This will still occur even if you are mounted or levitating. There are no other special features of the square.
The vibrating square cannot appear near the edge of the screen nor the staircase, because there must always be room for the ring of fire traps and water to appear around it. Specifically, it will be at least five squares from the left and right sides of the map, at least four squares from the top or bottom, and not within a 10x10 square area centered on the upstair. It will also not be in a straight line with the upstair or on the same square as a trap, although it may be on the same square as a boulder or other item.
Many players will mark the vibrating square by leaving an object on it once they have located it. This is one of the leading uses for the mostly useless iron chain, but it is hardly necessary to find one for this purpose. Any object that most monsters will not want to pick up, or is protected by an engraved "Elbereth," will suffice, and the vibrating square itself never changes location. The general location of the square can also be permanently marked with a scroll of light, wand of light, or the spell from a spellbook of light.