Croom and his young son, Augustus Coverly. The group marches out of the room to meet the hunters and continue debating the transformation of the Croom estate, leaving Septimus and Thomasina alone again. Innocently, she draws a picture of a hermit in Noakes's hermitage and hands Septimus a note from Mrs. Chater, which he reads then inserts into the pages of ‘‘The Couch of Eros.’’ (Both the drawing and the note also become essential clues later in the play.) Act I, scene 2
The next scene takes place nearly two centuries later, at the present day Sidley Park. The room remains the same but its inhabitants change. Hannah Jarvis, an author in her late thirties, is visiting the estate, which still belongs to the Croom family. She has written one bestselling book already and is conducting research for her next work, which she thinks will focus on the breakdown of the Romantic Imagination in the early-nineteenth century.

Hannah's hosts are the current children of the Croom family, who wander in and out of the room throughout the scene, preparing the house for a big costume garden party. The children are Valentine Coverly, an Oxford postgraduate student conducting mathematical research on the number of grouse reported killed in the family's game books over the years; Chloe Coverly, the Crooms' eighteen-year-old daughter; and Gus Coverly, the fifteen-year-old, apparently mute, youngest son.

The mysteries which are at the root of Arcadia's plot develop with the arrival of Bernard Nightingale, a Sussex professor who has come seeking information about Lord Byron. Bernard has stumbled across Septimus's copy of ‘‘The Couch of Eros’’ and discovered the notes and inscription inside. Because the book was found in Byron's personal library, Bernard has taken a few creative— and erroneous—mental leaps. He has developed the theory that Lord Byron, who was visiting the Croom estate at the same time as Chater in 1809, killed the hapless would-be poet in a duel and fled the country. A mistake of sorts is also at the root of Hannah's work. Finding Thomasina's drawing of the ‘‘hermit’’ in Noakes's landscape sketches, Hannah assumed the figure was a real person, who died on the estate in 1834. She is making the ‘‘Sidley hermit’’ the metaphorical centerpiece for her book about the decline of Romanticism in England.

Hannah and Bernard get off to a rocky start when she discovers that the pompous professor is actually the same man who wrote an insulting review of her first book. Two heads appear better than one, however, as they each have information to offer that helps them piece together the clues of their separate puzzles. They declare a truce and spend the day ransacking the estate's library for proof of their theories. At the same time, Chloe expresses an interest in Bernard and tells Hannah she plans to ask him to the party that evening; and young Gus seems to have developed a similar crush on Hannah. At the end of the scene, the silent boy presents her with an apple, freshly picked from the orchard.

Act I, scene 3
The scene changes to the past. It is 1809 once more, a day after the previous skirmish between Septimus and Chater. Thomasina is once again studying in the great garden room, attempting to translate a poem from Latin into English. Septimus is writing his review of Chater's "Couch of Eros.'' Again Jellaby delivers a note from Chater, which Septimus chooses to ignore. Thomasina reveals that her mother, Lady Croom, is angry with Lord Croom for allowing Noakes to destroy the garden and has become interested in their houseguest, Lord Byron.

Thomasina continues to insist, over Septimus's objections, that the universe can be reduced to a mathematical formula. In order to prove it, she offers to plot the leaf off an apple (the same piece of fruit, left on the set from the previous scene, that Gus gave to Hannah) and deduce its equation.

Chater storms in with Captain Brice, once again demanding a duel with Septimus. He has heard about Septimus's scathing review of his previous work,"The Maid of Turkey,'' and is convinced the tutor means to insult him again when he writes about his new book. Before the men can take steps to settle the matter, Lady Croom appears and borrows Septimus's copy of ‘‘The Couch of Eros’’ to give to Lord Byron. Byron wishes to satirize Chater and his awful poetry in the next edition of his English Bards and Scotch Reviewers. (An important plot development: This is how Chater's book ends up in Byron's library for Bernard to find generations later.) Lady Croom remarks with some concern that Byron intends to leave Sidley Park and go adventuring through Europe, right in the middle of the Napoleonic wars.

Lady Croom rushes off with ‘‘The Couch of Eros,’’ leaving the quarrelsome men alone again. This time Septimus agrees to duel. He will meet Chater behind the boathouse at five o'clock the next morning, followed by Chater's subsequent duel with Captain Brice five minutes later (the naval officer has also been dallying with Mrs. Chater). Afterward, Hodge rails angrily: he will leave the country, Byron can remain behind to tutor Thomasina, and everybody will be happy.

Act I, scene 4
Present day Sidley Park: Hannah and Valentine are poring over books in the garden room. Hannah is examining Septimus's math primer, while Valentine leafs through Thomasina's lesson book. They have discovered a note Thomasina wrote in the margin of the primer, similar to Fermat' s last theorem, that suggests her intent to explain nature through numbers. The graphs in her lesson book, Valentine explains, are primitive iterated algorithms, created using the same mathematical theory Valentine is applying to his study of the grouse population in the game books. He is surprised by the find, since iterated algorithms weren't widely known until computers made them practical, late in the twentieth century.

Bernard sputters into the room, excited about a recent find. He has discovered a copy of Byron's English Bards and Scotch Reviewers with a penciled inscription insulting Chater's poetry. To Bernard, this is proof positive that Byron killed Chater. Hannah adds fuel to the fire by telling him about a discovery of her own. She ran across a letter from Lady Croom to her husband that describes the marriage of Captain Brice to Mrs. Chater, again suggesting that Mr. Chater had been recently killed. More crucial, if misleading, information comes from Valentine, who affirms that Lord Byron was indeed a guest at Sidley Park; the game books he has been studying record that Byron shot a hare there in 1809.

Bernard rushes off in search of the records, while Valentine leads Hannah to a new revelation in her own work. He notes that it would take innumerable pencils, stacks of paper, and years and years of concentrated time for someone to complete the iterated algorithm that was started in Thomasina's lesson book. To do so, Valentine wryly remarks, someone would have to be insane. Hannah's thoughtful look suggests she is putting some new pieces together—linking the Sidley hermit to Thomasina's discovery.

Act II, scene 5
Bernard's theory about Lord Byron has rocketed from speculation to spectacular find in a single afternoon. Armed with the "facts" he has been provided by Hannah, Valentine, and the books in the Coverlys' library, he has already prepared a lecture he plans to read at the Byron Society, prior to publishing his version of history in pursuit of wealth and academic fame. He reads the lecture to the smitten Chloe, who listens adoringly; to Valentine, who listens semi-attentively while feeding his turtle; and to Hannah, who punctuates his address with continuous objections to his findings. In the end, she warns him, ‘‘You'll end up with so much fame you won't leave the house without a paper bag over your head.’’

In the course of arguing about his research, Bernard manages to offend everyone in the house except Hannah, who knows his insults and intellectual bullying are only tools of rhetoric—he uses them to win points, not to seriously hurt people. Bernard packs up his research and heads off to town in a cab, promising to return that evening to accompany Chloe to the costume party. On his way out he drops another piece of Hannah's puzzle in her hands: a small book, written in 1832, that describes the hermit of Sidley Park and his pet tortoise, Plautus. She adds this to a letter she found, announcing the death of the hermit at the age of twenty-seven, and is more convinced than ever that the hermit and Septimus Hodge are one and the same, but she has yet to find the final clue that will prove it.

Act II, scene 6
The briefest scene of the play describes how the events of 1809 came to a climax in the middle of the night at Sidley Park. It is early in the morning, just before dawn, and Septimus returns from the boat-house, where he was supposed to have dueled Chater but instead shot only a rabbit. He is met by Jellaby, who explains that Mrs. Chater was caught leaving Byron's room the night before, and in the tumult that followed, Captain Brice, the Chaters, and Lord Byron all left the estate. Lady Croom interrupts the gossip, sending Jellaby off to work. She is infuriated at Septimus for leaving behind two letters to be read in the event of his death. One was a love letter, addressed to her, the other a note of encouragement from teacher to student, addressed to Thomasina.

It turns out that Septimus's real passion all along has been for Lady Croom—Mrs. Chater was merely a diversion. For her part, the Lady has always been fond of Septimus and merely toyed with Lord Byron. She reveals that her brother, Captain Brice, has enlisted the help of Mr. Chater to serve as an amateur botanist on an expedition to the Indies. His ulterior motive, of course, is to be near Mrs. Chater. Septimus and Lady Croom agree to put the events of the past few days behind them. To please her, Septimus even burns a letter he received from Lord Byron without reading it. Grateful for his discretion, Lady Croom invites Septimus to come to her room later that morning. When she is gone, the young tutor burns the two letters he wrote as well, leaving no clues for future detectives like Bernard and Hannah.

Act II, scene 7
The final scene of the play combines the past and present on stage at the same time. In the present, it is the night of the costume garden party, hosted by the Coverlys. Chloe, Valentine, and Gus are all dressed in Regency clothes, typical of Byron's era. Bernard's "discovery" has landed him in all the newspapers, while Hannah still struggles with her hermit. Valentine has fed Thomasina's equations into a computer, taken them a few million steps further than she was able, and produced beautiful pictures out of simple numbers. While looking over Valentine's shoulder at his computer-generated model, Hannah reveals the most startling surprise of the play: Thomasina died in a fire at Sidley Park the night before her seventeenth birthday.

While Valentine and Hannah continue their work in silence, Thomasina and her little brother, Augustus, run onstage. A few years have elapsed in the nineteenth century setting. It is now 1812, and Thomasina is sixteen and nearing her birthday. Septimus joins the children for the daily lesson, which Augustus chooses to abandon. Left alone, Thomasina insists that Septimus should make good on his promise to teach her how to waltz. The piano has been playing in the next room throughout the scene. At the keys (though unseen) is Count Zelinsky, Lady Croom' s new piano tuner and, apparently, her new lover. When she whisks into the room Septimus treats her coldly. She ignores his jealousy and remarks on her new dahlias, which Captain Brice recently brought back from his expedition to the Indies, where Mr. Chater died of a monkey bite and Mrs. Chater subsequently became Mrs. Brice.

Switching to present-day action, Bernard appears for his date with Chloe and is hounded immediately by Hannah, who has found the last, and fatal, piece of his puzzle. In one of Lady Croom's garden books, Hannah ran across an entry describing the dahlias and Chater's unfortunate accident in the Indies. Since he was killed picking flowers by a monkey, he obviously could not have been killed in a duel by Lord Byron. Bernard finally realizes he should not have rushed to judgment and that his newfound fame will soon be over when Hannah reports her find in the press. Life, for the moment, goes on, and Chloe assembles a costume for Bernard to wear to the party. A few hours pass and it is evening. In the offstage room, the Count is playing piano for Lady Croom. Septimus is studying Thomasina's work when she appears in her nightgown for her waltzing lesson. The work she has drawn in her lesson book, it turns out, is a diagram of heat exchange. It suggests what hadn't been discovered yet by scientists: that heat could not work backwards. The second law of thermodynamics, as described by Thomasina, meant the universe must someday wind down, grow cold, and die. Disturbed by the implications, Septimus takes his young pupil in his arms and begins to dance.

While Septimus and Thomasina waltz, and stop to kiss, the action in the present day continues around them. Bernard suddenly rushes in, adjusting his clothes, followed by Chloe. They explain to Valentine and Hannah that Chloe's mother caught them together in the hermitage. A little embarrassed but not very repentant, Bernard dresses himself and prepares his escape, leaving a crestfallen Chloe behind. On his way out the door Hannah tells him she thinks she knows who the hermit of Sidley Park was but still lacks proof. Still his impetuous self, Bernard advises her: "Publish!"

Septimus and Thomasina stop their dancing. He returns her lesson, lights her candle, and tells her she should go off to bed, being careful of the candle's flame. Too in love to leave, she asks for another dance. As they twirl around again, Gus enters with a folio for Hannah. It contains a drawing of Septimus and Plautus, the final piece of her puzzle, linking the tutor to the hermitage. In a gesture of gratitude, she dances, awkwardly, with Gus. The final haunting image of the play is of the past and present dancing together.