That statue of King William appears in a funny story in James Joyce's story The Dead - the wealthy loyalists of Dublin liked to parade down Dame Street from City Hall and circle it and go onwards, but a hopefully upwardly-mobile uncle has harnessed up to his carriage his mill pony, which (as was its working custom) continued to go around and around once it was steered around the first time.
The reason poor Larry would turn white when he reached the statue was that it stood at the border of the land known as Hoggen Green, which stretched from Trinity College over to St Patrick's Cathedral, and where the city's main gibbet stood.