Euripedes
Adolphus is morally against making weapons of war. Ironically, he accepts the inheritance to manufacture Undershaft weapons.
Lady Britomart
Lady Britomart wants nothing to do with her former husband in terms of relations with him. Ironically, she is willing to do whatever is necessary to fight for his wealth and provision not solely for her children but for herself.
Ruling Class
Charles Lomax has been born into the aristocratic class of England. He is one of the elite in society. Ironically, he proves his dimness in the real world when he lights a match near live ammunition being tested and then tells the technician to calm himself.
Character
Stephen tells his father that he will not fight for the Undershaft inheritance. That he is a man of character who would never creates arms for war. Ironically, once he sees his father's factory he congratulates his dad and speaks of the great character he now understands this business to have.
Marriage
Barbara is a woman who is firmly against what her father does, thus when Adolphus chooses the Undershaft inheritance the expectation is she will leave Cusins. Ironically, she chooses to marry him as she sees that her power to save has been increased exponentially by the inheritance given to her through marrying Adolphus.