In part 3 of the story, Peyton Farquhar is described as the rope drops to hang him as swinging
through unthinkable arcs of oscillation, like a vast pendulum.
This physically depicts what he looks like moving with the rope around his neck. It also symbolizes the oscillation, or back-and-forth movement, of his experiences at the end of his life. On the one hand, he feels the dread of his impending death, symbolized by the maddening ticking of his watch. But on the other hand, he also enters into a mental state in which he is able to have a detailed fantasy about escaping and arriving back home. He swings from his grim reality to his fantasy and back again over the course of the story.
On a deeper level, the image of the pendulum swinging may also be seen as describing Peyton's life as a whole: he is simultaneously a gentleman with kindly gray eyes and a sordid slave-owner, a courteous gentleman farmer with a gracious manner and someone who subscribes to the "villainous dictum" that "all is fair in love and war."
There are also his devotion, heart and soul, to the Southern cause and his mysterious "circumstances" that prevent him from joining the "gallant" Southern forces. Readers get the impression that Farquhar has been swinging throughout the war between supporting the idea of the glorious cause and hedging his bets so that he doesn't get caught up too wholly in its "disastrous" consequences—until he does.