The story starts with Neddy and Lucinda Merrill being at their friends' house - Donald and Helen Westerhazy. It's midsummer Sunday and everyone around Ned is saying that they drank too much the previous night. Suddenly Ned decides to take up a journey from the Westerhazy's to his own house, which is about 8 miles away. He is resolved to be a groundbreaker and swim in his neighbours' pools along the way and thus become an across-county swimmer. Ned decides to call this 'river' of pools he is going to swim the Lucinda River.
The protagonist starts with the Graham's pool. Unfortunately for him Mrs. Graham wants to hang out with him. He obliges her for a few minutes but is saved by arriving guests and continues on his journey home. He goes through Mrs. Hammer's pool, who doesn't recognize him and through the Lears' pool, who hear him splash in it through the open window.
Next is the Bunker's pool where Enid Bunker greets him warmly and Ned meet a lot of friends happy to see him. After a short stay he goes to the Levys' pool and realizes that hey are gone. While he is at their place, a storm begins and he waits it out in their gazebo. Then, cold and tired, he goes to the Welches only to see with great disappointment that their pool is drained and they have put their house for sale. He is confused and tries to remember their last dinner invitation.
Along the way many bystanders make fun of him and even throw beer cans but he takes swimming the Lucinda River as a pilgrimage and continues with the same resolution.
Next he goes to the Recreational Center in the village of Lancaster and swims the pool, disgusted by the chlorine water. He doens't have an identification disk and has to leave.
He goes to the Halloran estate. They are an old friendly couple who hang out naked at their pool. Neddy takes off his trunks as well when he goes to swim their pool. They are nice to him and Mrs. Halloran expresses sympathy for his misfortunes but Ned seems to be unaware what she is talking about and dismisses her statement. Then he goes to the Hallorans' daugter and her husband - Helen and Eric Sachs. He asks for a drink but it turns out that hey have had no alcohol in the house since Eric's operation 3 years ago. Ned is baffled that he doesn't remember such a serious event. He wonders how much his selective memory has suppressed and hidden from his conscience.
Afterwards he goes to the Biswagers searching for a drink. They have been very friendly to him in the past and he is sure that they will gladly have him. Grace Biswager is displease to see him and continues to talk behind his back about him being broke. At their place Ned orders a drink from a bartender but the man is very rude to him and the protagonist is even more confused about his social and financial situation. To pick his spirits up he decides to visit his old mistress Shirley Adams. He is unable to remember when exactly they had an affair. Shirley is not happy to see him and refuses to give him a drink because she has male company. She tells him that she won't give himmoney if he is there for that. Ned is surprised because she was very upset when he broke it off with her.He swims her pool and leaves.
He swims a few more pools unable to stop thinking about the rudeness of the people he met along the way. Finally, he reaches his house but wonders why it's dark. No one seems to be in. He knocks and shouts but no one is there. He then sees through the window that the house is empty.