"Buck Mulligan slung his towel stolewise round his neck." Even the narrative now assists Mulligan in his impersonations of a priest.
His ungirdled dressing gown and his untonsured hair may not cooperate in the act, but his towel does. A stole is the distinctive badge of priestly office, a strip of material several inches wide and perhaps seven or eight feet long. Putting on his holy vestments, the priest kisses the middle of the stole and then puts it around the back of his neck, with the two ends hanging down his chest. Mulligan is carrying his long towel in this way.