The correct answer is C) bell book. The bell book is the official record of engine speeds and maneuvers made by the vessel when entering or leaving a port. It is used to document the engine orders given by the captain and the corresponding engine speeds maintained by the engineer. This record is important for verifying the vessel's navigation and compliance with regulations. The other options are incorrect because: A) The deck rough log is a general log of events and observations on the deck, not specifically focused on engine speeds. B) The engine rough log is a more informal record kept by the engineering department, not the official log. D) The Official Logbook is a comprehensive record of the vessel's voyage, crew, and activities, but does not specifically focus on engine speeds during port entry/departure.