Let us remember that dramatic irony is when one or more characters and the audience know something that a principal character does not. Perhaps the most famous literary example of this is of course in Romeo and Juliet, when we know that Juliet is not dead but are forced to watch Romeo kill himself just before his true love awakes. Thus when we think of this definition of dramatic irony and apply it to this play, we can see the biggest dramatic irony comes as the two sisters, Cathleen and Nora, look through the bundle of clothes that was recovered from a drowned corpse whilst their mother is away and find that they belong to their brother, who has obviously drowned like his other brothers. However, because of Maurya's fear about her last remaining son going on the sea, they decide to keep this knowledge from her until Bartley's safe return:
Put these things away before she'll come in. Maybe it's easier she'll be after giving her blessing to Bartley, and we won't let on we've heard anything the time he's on the sea.
Of course, the irony heightens the tragedy, as Maurya is still plagued with the premonition that her last remaining son will die by the sea too, and we as the audience know that her other son has definitely been drowned the same way that she fears Bartey will die.