The Silent Monastery

In a remote monastery, $40$ monks live under a vow of total silence, and the monastery has no mirrors or reflective surfaces. Unknown to each monk individually, every one of the $40$ has an ink mark on his forehead. The order's rule is absolute: any monk who ever deduces with certainty that his own forehead is marked must depart at the next dawn. Each monk sees everyone else daily and all monks reason perfectly. One evening a visiting abbot addresses the assembled monks: \"At least one of you bears the mark.\" What happens, and on which day?