At a seaside resort, the young dentist, Valentine, extracts a tooth from his first patient, the voluble Dolly, who has just arrived with her family from Madeira. Her equally voluble twin brother, Philip, appears, and at once they invite the dentist to lunch. They are joined at the dentist's office by their mother, the famous Mrs. Clandon, authoress of social-reform treatises; and by their elder sister, Gloria, who is her mother's haughty disciple. Valentine promptly falls in love with Gloria, though she initially seems to have no interest in him.
Believing she has no need of a husband and her children have no need of a father, Mrs. Clandon, though presses by Valentine and the children, refuses to tell her children who their father is (she separated from him when the children were very young, and they haven't seen him since); and she leaves. At that time, Valentine's landlord, the ill-tempered Fergus Crampton appears, wanting an aching a tooth pulled. Valentine bets the six weeks rent that he owes Crampton that he can extract the tooth without Crampton feeling it. Crampton agrees, and Valentine pulls off the feat, surreptitiously using a bit of anesthetic. The twins immediately invite Crampton to also join them for lunch.
Later in the day, on the terrace of the resort hotel, Mrs. Clandon and her three children meet with her solicitor, Finch McComas, before lunch. McComas is an old friend of Mrs. Clandon and at one time a suitor, but is now simply her efficient solicitor. Mrs. Clandon has invited him to lunch to tell her children about their long-lost father. However, they quickly learn of the coincidence that Valentine's landlord, Crampton, is none other than the father they can't remember. Their dismay at such a discovery is somewhat allayed when they learn he is wealthy. At that time Valentine and Crampton arrive, and Crampton is greatly upset by the unexpected meeting with his family. The luncheon party threatens repeatedly to blow up, and is saved only by Walter Boon, the "perfect waiter," who diplomatically smoothes everyone's feelings and tells them of his son, a distinguished attorney for the queen. After lunch, Gloria infuriates Crampton with her cold rationality, but is herself completely thrown off balance by Valentine's "sensible and scientific" courting methods.
Later in the day, the wild-spirited twins explain to their mother that Gloria's recent emotional and out-of-character behavior is due to her having fallen in love. Valentine adds that he has won Gloria by using "thoroughly modern" scientific methods in the "duel of sex." However, when Gloria hears that Valentine has loved other women, she furiously rejects him. McComas, in the meantime, reports that Crampton is demanding custody of the twins and observes that, though Crampton is uncouth, he is a kind man who has been unfairly dealt with in the separation deal. He further convinces Mrs. Clandon to agree to arbitration by the waiter's attorney-son, who is soon to visit.
That evening, during a masked ball, the visiting attorney expertly brings about a friendly reconciliation between the members of the family—and between Valentine and Gloria. It appears that Gloria, too, has had a number of romantic relationships, a fact that shocks and enrages Valentine but also opens the way their peacemaking and engagement. As all dance the evening away, Valentine, "the defeated Duellist of Sex," ruefully observes that he feels like "a married man already." The waiter, Walter, comfort him about marriage: though his wife, like Gloria, "was of a commanding and masterful disposition," his marriage turned out very well. "I'd do it again, I assure you," he tells Valentine. "You never can tell, sir."