Gene wakes up, sees the dawn, and realizes he'd better haul booty back to campus if he wants to get there in time for his 10am exam. Still, he waits around for Finny to take another swim before they head back together.
Gene fails his test. It's the first test he's ever failed. Ouch.
Afterwards, while Gene is complaining about having failed his exam, Phineas teases him about wanting to be first in their class. Gene admits (to us) that, actually, yes, that is his goal.
That's when Gene suddenly "realizes" that Finny is trying to sabotage him. That must be why he insists that they jump out of the tree every night. He's trying to distract Gene from his work so that he won't be first in the class.
Interestingly, this makes Gene feel better.
After that, he becomes the greatest student ever. His competition for top dog is Chet Douglass, who is "crippled" by his intellectual curiosity. (As in, he does all this extra work outside of the class because he cares, whereas Gene can just focus on the grades.)
Finny, meanwhile, is still no star student. His biggest asset, remember, is his ability to talk himself out of situations – his charm and vitality. But these are useless to him on a written exam.
Gene figures, Finny is the best at athletics, so he himself should be the best at academics. Even better, Finny is a terrible student, while he (Gene) is a decent athlete – so he would come out on top in the end. Mwah-hah-hah.
Still, Gene finds himself "slipping back into affection" for Finny over the course of the summer, even though he's supposedly unearthed the guy's evil plan.
And then it's August. Gene continues to attend the secret tree-jumping society gig every night, because he doesn't want Finny to understand him as he understands Finny. (Oh, the machinations.)
One afternoon, the boys are in the library studying for a French exam the next day. Finny keeps distracting Gene, which is clearly part of the evil master plan. (Riiiight.)
After dinner, Gene is trying again to study when Finny comes in and announces that Leper has decided to jump. Leper is a pretty timid guy, so this would be a big deal.
Gene is, in an understatement, irate. He flips out at Finny about how watching Leper jump means Gene won't be able to study, will fail his French test, will not be head of the class, will not pass go, and, quite likely, will not collect 200 dollars.
Finny just shrugs and says, "What the hell, it's only a game." He tells Gene not to go.
This, of course, catches Gene by surprise.
Finny explains. He figured since athletics came easily to him, academics must come easily to Gene. He didn't know Gene had to study.
That does it. Gene says he's studied enough and goes with Finny across the playing fields toward the tree. On the way, he struggles with an intense "fear." Not of the tree, but of this new realization he's had. Finny hasn't been plotting against him at all. In fact, Finny is entirely pure of heart. Not only is Finny a better athlete and generally a more charismatic dude, but he's a better person than Gene. Gene can't deal with this.
When they get to the tree, Finny suggests that, to open the festivities, he and Gene should do a double jump – both jump off the tree together.
So the pair ascends, Finny first. He walks out onto the limb. Gene is behind him, holding firmly onto the trunk.
A brief interruption: Just read this paragraph in your text. The specific language is really important, and it will take you about, oh, 9.54 seconds. We'll wait.
So by now you should have read the passage in which Gene, while holding the trunk of the tree, "jounce[s] the branch." Finny looks at him "with extreme interest" as he falters and falls, landing with "a sickening, unnatural thud" on the ground below the tree.
Gene then jumps off the tree and into the water, his earlier "fear" now gone.