The morning after their night of passionate lovemaking, Rearden is angry. He regards sex as a low impulse of the flesh, and he feels contemptuous of Dagny (and especially himself) for craving "obscene" pleasures. Dagny rejects his scorn, because she regards sex with Rearden as noble — something to be proud of. She tells him joyously that she makes no other claims on him but this: When he seeks to satisfy this "lowest" of his bodily urges, he must bring his urges to her.
James Taggart meets an innocent shop girl who is star-struck by his fame. Cherryl Brooks came from a poor family and moved to New York because she wanted more from life. She admires achievement and believes that Jim — along with Dagny and Rearden — is responsible for the success of the John Galt Line. Taggart takes a perverse pleasure in her misguided hero worship. Around this time, Taggart's flunky, Wesley Mouch, is appointed Top Coordinator of the Bureau of Economic Planning and National Resources.
Dagny and Rearden take a vacation together, driving through the countryside. In Wisconsin, they visit the former site of the Twentieth Century Motor Company, looking for machine tools. In the research lab of the factory, they find the abandoned remnant of a motor that was designed to take static electricity from the atmosphere and convert it into usable energy. They're shaken to find a motor that would have revolutionized industrial production lying rejected on a scrap heap. Dagny and Rearden are determined to find the inventor.
The differences between the ways Rearden and Dagny view sex are indicative of an underlying philosophical difference. Rearden recognizes that the mind and its achievements are noble, but he believes that the desires of the body are low and base. Although he's generally a rational man, he holds what Rand portrays as an irrational viewpoint regarding the relative value of mind and body. Many philosophies and religions teach that only the mind or soul is pure; the body and its urges are ignoble. Dagny utterly rejects this mind-body dichotomy. She realizes that she's specifically attracted to Rearden because of the enormity of his achievements. She loves and desires him because of his intellectual and moral greatness. She also realizes that Rearden is similarly attracted to her because of her own accomplishments, although Rearden himself doesn't yet recognize this truth. Dagny repudiates the split between mind and body because she recognizes that, for a rational man, the desires of the body flow logically from the understanding and evaluations of the mind.
The beginning of the romance between James Taggart and Cherryl Brooks is motivated by opposite premises. Cherryl is a hero worshipper who sincerely admires great achievement and who mistakenly believes that Taggart is one of the great men responsible for the triumph of the John Galt Line. Taggart, on the other hand, is a nihilist, a person who hates achievements and the great people who create them. He attempts to defeat Dagny and Rearden because of their ability, and he hates Francisco d'Anconia because of his genius. The great men are too powerful for him to destroy, but he can take his revenge on the little hero worshipper who admires them. This is his motivation for his relationship with Cherryl.
The discovery of the motor is a major turning point in the novel's plot. Prior to the discovery, Dagny's primary goal was to build the John Galt Line (which is now, once again, the Rio Norte Line of Taggart Transcontinental). Now, she shifts her energies to discovering the secret of the motor. Dagny understands that this invention will do much more than save her railroad; it will transform every aspect of man's life on earth in a more powerful way than the invention of the electric light. Therefore, she's understandably desperate to find the inventor. In addition, the discovery of the motor adds to the mystery that lies at the center of the novel's plot. How could such an extraordinary device be left unrecognized on a scrap heap? Dagny is determined to find the answer, as well as the inventor.