Leaning on the "parapet" that surrounds the roof of the tower, Stephen looks down on "the mailboat clearing the harbourmouth of Kingstown." Later, Haines looks over the bay, "empty save for the smokeplume of the mailboat vague on the bright skyline." The mailboats were oceangoing ships that carried the mail between Ireland and England twice every day. Later in the novel, we learn that Joseph Patrick Nannetti is taking the mailboat to Wales on June 16, to catch a train to London.
Receiving the day's mail by express rail cars from Dublin, the mailboats carried it to the port of Holyhead in NW Wales for distribution throughout the sister island. Gifford identifies their daily departures as 8:15 AM and 8:15 PM. When Stephen sees the boat passing the harbormouth, the time must be about 8:20.
In Cyclops, Bloom learns from Joe Hynes that Nannetti, the newspaper printer and M.P., is "going off by the mailboat . . . tonight" to ask questions on the following day about an action pending in Parliament. In Nausicaa he thinks, "Nannetti's gone. Mailboat. Near Holyhead by now." Gifford notes that "the run to Holyhead . . . took about two and a half hours in 1904," but it does not seem possible that nearly so much time has elapsed since the boat's departure at 8:15, so Bloom's estimate may be mistaken. (Gifford also notes that, according to the Evening Telegraph, the actual Nannetti was asking his questions in Parliament on June 16, not June 17.)