All the guests leave the table except Lord Mayfield and Sir George, to discuss a new aircraft that will give Britain supremacy over the skies. Lord Mayfield invites Mrs. Vanderlyn, a spy, to tempt her with the plans for the new fighter jet. Everyone goes to bed except Lord Mayfield and Sir George. Mr. Carlile heads to the safe to retrieve plans for the new aircraft where he collides with Mrs. Vanderlyn searching for her handbag. Lord Mayfield spots a figure leaving the study by the French window. In the study, Lord Mayfield quickly discovers that the plans for the fighter jet are missing. Mr. Carlile says he definitely left the plans on the table. However, he was distracted by a scream which turned out to be Mrs. Vanderlyn's maid, claiming she saw a ghost.
Poirot is called in the middle of the night. He examines the grass outside the study but finds not footprints. Therefore he concludes that the theft of the plans was done by someone inside the house. He questions everyone and discovers that the maid did not see a ghost; she was startled by Reggie who snuck up on her to steal a kiss. Lady Julia believes her son stole the plans as he is short on money and was unaccounted for at one point in the day. She promises Poirot that the plan swill be returned in 12 hours if no further action is taken.
Poirot explains that Mrs. Macatta was snoring in her room, Mrs. Vanderlyn called for the maid from upstairs and Sir George was with Lord Mayfield on the terrace. But what about Mr. Carlile and Lord Mayfield? Mr. Carlile had access to the safe and therefore could have taken a sketch of the drawings at any time. Poirot is convinced Lord Mayfield pocketed the drawings. Lord Mayfield, not wanting to reveal that he was involved with a belligerent foreign power a few years before, was blackmailed into handing the plans over to Mrs. Vanderlyn.