Eve is hinting at Roger spending the night in her sleeper car.
“Yes, I know exactly what you mean,” says Roger.
Eve reaches for a cigarette. Roger pulls out his personalized matchbook, with the initials “R.O.T.” stamped on the front and back.
Thornhill notices Eve looking at his matchbook cover. “That was my trademark,” explains Roger. “Rot!”
“Roger O. Thornhill,” says Eve. “What does the O stand for?”
“Nothing,” replies Roger, smiling.
Roger leans forward with a lit match. Eve steadies his hand with her own as she lights her cigarette, blowing a puff of smoke toward the ceiling. Thornhill starts to move his hand back, but Eve pulls the match toward her mouth, blowing it out in a long breath.
Roger looks extremely pleased with the gesture. Eve smiles.
“I’d invite you to my bedroom, if I had a bedroom,” says Roger.
“A roomette?” asks Eve.
“Nohing,” says Roger. “Not even a ticket. I’ve been playing hide-and-seek with the Pullman conductor ever since the train left New York.”