Irony of Helping by Telling the Truth
Archie's father and children are aware that Archie intends to divorce Phoebe so as to marry a young woman about twenty years of age, whose family is supposed to be putting up money to continue the show. This of course would destroy Billy's wife Phoebe and have serious financial implications for Frank, who as a boiler-stoker does not make a lot of money and perhaps cannot quite live independently.
Instead of berating Archie the way Jean does, Billy goes to the young woman's parents and informs them that Archie is already married, with three adult children. That ends any talk of marriage, but what Billy does not know is that Archie has made significant financial commitments on the strength of the promised money from his future parents-in-law. Thus, the act he intended to save Phoebe puts her in even more trouble than before: if Archie goes to jail, she will be penniless.
Irony of Alienation
Asserting that he feels nothing and is "dead inside", Archie does as much damage as possible to his family by behaving inconsiderately. He has flagrant adulterous affairs and is verbally abusive to his wife, elderly father, and children. By pushing hard against the rest of the world and particularly the more successful elements such as his brother Bill, Archie guarantees he is without support when actual tragedy strikes and he loses both his soldier son Mick and his elderly father.
Irony of Independence
Despite being very financially dependent on others, Archie asserts his right to do what he wants (generally with their resources) until the very last scene. The more desperate his financial situation becomes, the more he clings to his independence. Ironically, the failing music-hall business is dragging him down with it.
Irony of Job as Identity
Like his father Billy, Archie identifies himself primarily through his occupation. In fact, many of the characters in the story are identified that way. Frank is "just" a common laborer, and Brother Bill is stereotyped as an unfeeling attorney. Although Billy achieved a great deal of success through his skill, talent, and luck (he was born in a good generation for stage entertainers and got through World War I unscathed), Archie has not been so lucky. The live music-hall business is in decline, and his jokes fail to entertain and impress the dwindling crowds. Identifying himself as a performer and showman, and refusing to consider other means of employment, condemns Archie to a life of hardship.
Irony of British power
Initially, the Rice family believes Mick will be returned safely home because his captors would not dare to harm him for fear of what Britain might do in retaliation. However it is because of Britain's international reputation that Mick is killed: he is murdered to send a message to the British government, and by extension the British people, that they are not in charge of the world anymore.
