In order to understand the relationships between time, history and arrative, this paper borrows the concept of "the arrow of time" from the Second Law of Thermodynamics to discuss the nature of time as found in both history and narrative. Questions addressed include: Within the irreversible context of "natural time" , how can the reversible arrows of historical times A and B be established? How can narrated time have "interruptibility"? What is the nature of "trans-narration" and how is narration transferred? What is meant by the terms "non-concomitance" and "pictorial co-representation "? These discussions develop, from the viewpoint of the nature of time, certain fundamental issues in the theory of historical narrative.