Final answer:
The important story event that occurs between Samuel and Captain Smith on pp. 44-45 of Blood on the River is the condemned man's realization that he still has a chance to escape. This event falls in the rising action of the story and develops the plot by presenting an opportunity for the condemned man to try and escape.
Step-by-step explanation:
The important story event that occurs between Samuel and Captain Smith on pp. 44-45 of Blood on the River is the condemned man's realization that he still has a chance to escape. As he stands on a plank on the bridge, he hears a recurring metallic sound that turns out to be the ticking of his watch. This event falls in the rising action of the story, as it increases the tension and develops the plot by presenting an opportunity for the condemned man to try and escape.