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On his first day of work at the Royal Airforce Establishment, metallurgist Dennis Scott meets eccentric scientist Theodore Honey, an American who has lived in England for many years. Scott is intrigued by Honey's assertion that the establishment's newest airplane design, the Reindeer, is flawed because after 1,440 hours of flight time, the plane's vibrations will cause the tail to fall off. After work, Scott offers Honey a ride home and meets his twelve-year-old daughter Elspeth, whose English mother died during a World War II bombing raid. Scott is aghast to discover that Honey, who views mathematics as a pure, abstract science, did not include his computations in his preliminary report, and that his daily testing of a Reindeer tail will not be completed before the Reindeer planes in service have exceeded the 1,440 hour mark. Scott reprimands Honey, pointing out that the formula might be important to the people aboard a Reindeer plane, but Honey responds that as a scientist, he cannot be concerned about people. Later, Scott investigates the crash of a prototype Reindeer and learns that the tail section was not found at the crash site in Labrador. Scott sends Honey to Labrador to locate the missing wreckage, and while boarding the plane, Honey does not notice that it is a Reindeer. On board, the nervous Honey is calmed by stewardess Marjorie Corder, who is amused to learn that the first-time flyer is an aviation scientist. Also aboard is glamorous film star Monica Teasdale, and when Honey discovers that the plane is a Reindeer and that it has been flying for 1,422 hours, he advises Monica and Marjorie that the men's bathroom is the safest place in the event of a crash. The pilot is baffled by Honey's frantic claims that the plane's tail will fall off, although Honey's sincerity convinces Monica and Marjorie. The plane lands safely at Gander, however, and while it is being re-fueled, the captain orders a thorough inspection. Convinced that Honey is crazy, the captain orders him detained, but Honey, who has realized that people are more important than mathematics, sabotoges the plane so that it cannot take off. Honey's instinctive reaction to the unseen danger convinces Monica that he was right, and after she and Marjorie return to London, both look after Elspeth. While Honey is delayed by the authorities in Gander, Monica visits the RAE's director, Sir John, and Scott to tell them that Honey is not crazy. Sir John and Scott are uncertain what to do, for if Honey's theory is correct, the RAE will be liable for authorizing an unsafe design, and the airline utilizing the Reindeers will lose a fortune. Scott accelerates Honey's laboratory test, much to the chagrin of Honey, who has returned to London. Scott convinces Honey of the necessity of the twenty-four-hour testing, however, and while Honey works at the laboratory, Marjorie continues to care for Elspeth. Both Monica and Marjorie have grown fond of Honey, but Monica, realizing that she could never fit into his world, leaves for America. While the test continues, Sir John prepares for an upcoming committee meeting, and Honey is interviewed by psychiatrists to determine if his actions in Gander were caused by mental illness. After 1,522 hours, the tail in Honey's laboratory has not failed, and he begins to wonder if his critics are right. Marjorie urges Honey to defend himself at the committee's review, but Honey, determined to hide in his laboratory and have no further interactions with people, asserts that he will say nothing. Marjorie reminds him that he cannot return to his past isolation, and that if he does not determine the truth about the Reindeers, flight attendants like her will be the ones to suffer. At the inquiry, the committee decides that they cannot ground Reindeers based on Honey's unsubstantiated theories, and Honey finally speaks out, asserting that he will sabotage Reindeer planes until his theories come to the public's attention and they refuse to fly on them. Honey then quits his job and returns home, where Marjorie praises him for defending his beliefs. Upon discovering that Honey is so disorganized that he has not cashed his paychecks, Marjorie declares that she will marry him and care for him and Elspeth. Happy, Honey returns to his office, and is packing his belongings when Scott and Sir John burst in to tell him that the Labrador crash site has been investigated, and the Reindeer's tail section was responsible for the wreck. Marjorie also arrives, and while they talk, the test Reindeer collapses. As Scott and Marjorie rejoice in Honey's vindication, the bemused scientist realizes that he forgot to incorporate temperature variations into his calculations.