In the first section of the story, a man is contemplating family and his surroundings during the waning moments prior to his death sentence. Here, he perceives time subjectively. For him, during these moments, time has slowed down:
A piece of dancing driftwood caught his attention and his eyes followed it down the current. How slowly it appeared to move! What a sluggish stream!
As he continued to wait, time progressively grew slower and he was aware of this. He began to hear a "sharp, distinct, metallic percussion" sound. At first he didn't know what it was. It was regular and sounded like a "death knell." This regular sound was his watch. He senses time slowing down:
He awaited each stroke with impatience and—he knew not why—apprehension. The intervals of silence grew progressively longer, the delays became maddening.
The spaces of silence between the "regular" ticks of his watch become increasingly slower. In his intense state of mind, he perceives time moving at a much slower pace. This new perception also sets up the remainder of the story which occurs during the brief moments between his (Farquhar's) position on the bridge and his eventual death.
Part II takes the reader back in time before the man is captured. Part III recounts the thoughts that run through the man's mind just before he is hung. In Part III, the rope snaps and he falls into the water. The narrator waits until the end of the story to reveal that this was a daydream so, at this point, the reader believes that Farquhar has indeed escaped the hanging. He falls, loses consciousness and when he wakes up, he feels like a long time has passed, "ages later, it seemed to him."
As he swims away, he dives down to avoid the gunshots. "As he rose to the surface, gasping for breath, he saw that he had been a long time under water; he was perceptibly farther downstream—nearer to safety."
After reaching land, Farquhar travels all day and all night to get home. Yet all this occurs in his mind during the moments before he is hung from the bridge. Possibly, the interpretation is that it is a daydream of hope during his last moments; it could also be a psychological reaction, distorting time to forestall his own death. Bierce's descriptions of time and his nonlinear structure give the reader an experience of this distortion/slowing of time.