Christie uses an idiom, “nose to the grindstone,” in her description of Dr. Armstrong’s exhaustion during his long drive to Soldier Island:
He was tired after his long motor drive. His eyeballs ached. Driving west you were driving against the sun. Yes, he was very tired. The sea and perfect peace—that was what he needed. He would like, really, to take a long holiday. But he couldn’t afford to do that. He could afford it financially, of course, but he couldn’t afford to drop out. You were soon forgotten nowadays. No, now that he had arrived, he must keep his nose to the grindstone.
Dr. Armstrong runs a successful medical practice that keeps him very busy, contributing to his exhausted state. Though he has been called to Soldier Island for a medical consultation, he nevertheless feels that this will be a relaxing change of pace for him. He believes that he cannot “afford” to “take a long holiday” as this will cause patients to forget about his medical office, and so he feels that “he must keep his nose to the grindstone.” Here, Armstrong uses an old-fashioned idiom that refers to a “grindstone,” a tool for sharpening and polishing objects and materials. His use of the idiom, which means "to force oneself to work hard," reflects his strong preoccupation with his profession.