And Then There Were None

Eight people, all total strangers to each other, are invited to a small, isolated island off the coast of Devon, England, by a Mr. and Mrs. Owen. They settle in at a mansion tended by two newly hired servants, Thomas and Ethel Rogers, but their hosts are absent. When the guests sit down to dinner, they notice the centerpiece, ten figurines of Indians in a circle. Afterward, Thomas Rogers puts on a gramophone record, from which a voice accuses them all of murder:

General Sir John Mandrake (C. Aubrey Smith), of ordering his wife's lover, a lieutenant, to his death
Emily Brent (Judith Anderson), of the death of her young nephew
Dr. Edward G. Armstrong (Walter Huston), of drunkenness which resulted in a patient dying
Prince Nikita Starloff (Mischa Auer), of killing a couple
Vera Claythorne (June Duprez), of murdering her sister's fiance
Judge Francis J. Quinncannon (Barry Fitzgerald), of being responsible for the hanging of an innocent man
Philip Lombard (Louis Hayward), of killing 21 East African tribesmen
William H. Blore (Roland Young), of perjury, resulting in an innocent man's death
Thomas (Richard Haydn) and Ethel Rogers (Queenie Leonard), of the demise of their previous employer, an invalid.
It turns out that none of the ten knows or has even seen "U. N. Owen," as he signed his instructions to Rogers; they suddenly realize it stands for "unknown." The guests decide to leave, but Rogers informs them that the boat will not return until Monday, and it is only Friday.
Starloff admits to running down a couple while speeding. Then he takes a drink and dies from poison. The next morning, the guests learn that Mrs. Rogers has died in her sleep. Quinncannon reports that Rogers found one figurine broken after Starloff's demise. Now another is missing. With two deaths matching the Ten Little Indians nursery rhyme, they search the island for "Mr. Owen" without success. After General Mandrake is stabbed in the back, the judge arrives at the only explanation: Owen must be one of them.
Another day passes. Everyone votes secretly for whom they suspect. Only Rogers receives two votes, and is sent to spend the night in the woodshed. After locking the dining room, they give Rogers the key. The next morning, however, they find him dead, his head split open with an axe. Miss Claythorne persuades Miss Brent to reveal that she had her nephew placed in a reformatory, where he hanged himself. Later that day, Miss Brent's body is found with a hypodermic needle nearby. Armstrong discovers that his is missing. Lombard admits he had a revolver, but it is lost as well.
At dinner, Quinncannon confesses he sentenced an innocent man to death to ruin the defending counsel's reputation. Armstrong then admits to operating while drunk, with fatal results. Blore grudgingly discloses that he perjured himself to put an innocent man in prison, where he died. Lombard merely states that the accusation against him is true. When it is Miss Claythorne's turn, she excuses herself to get her coat. The others hear her shriek and rush to her. In the confusion, a single gunshot is heard. They find her shaken after being brushed by seaweed hanging from the ceiling. They eventually find Lombard's gun, and Quinncannon dead from a shot to the head.
Miss Claythorne insists she is innocent, but Armstrong contends that only a person who had not committed a crime would want to mete out "justice", and locks her in her room. Later that night, she wakes to find Lombard outside her window. After he gives her his gun, she lets him inside. He persuades her to admit that it was her sister who killed her own fiancÃ©, and that Miss Claythorne helped her cover up the crime and unofficially took the blame. They hear someone going downstairs. Upon investigation, they realize that Armstrong is missing.
The next morning, Blore goes outside to look for Armstrong and is struck by stonework toppled from the floor above. Lombard takes binoculars found beside the body and sees what Blore hadâa corpse on the beach. It is Armstrong. Miss Claythorne pulls out the gun, now certain that Lombard is the killer. He tells her that his real name is Charles Morley, and that the real Lombard was his friend and had committed suicide. Morley has a flash of insight and urges Vera to shoot him.
Miss Claythorne fires and Morley drops. Returning to the mansion, she finds a noose hanging in the parlor and discovers who Owen is: Quinncannon, very much alive. The judge tells her that all his life he had searched for perfect justice. After learning that he was terminally ill, he concocted this plan. He persuaded Armstrong to fake his (Quinncannon's) death, supposedly to help catch Owen, then murdered Armstrong. He tells Miss Claythorne that she can either hang herself or be sent to the gallows (as the only possible perpetrator). He drinks poisoned whiskey, but then sees Morley alive before he succumbs. Miss Claythorne had missed intentionally.

Question: Where does Miss Claythorne convince Miss Britt to reveal she had her nephew placed?
Answer: Reformatory