Rebuilding of the north west tower in 1837 is the most recent substantial change to the cathedral fabric. Originally built in romanesque style 1070-81, a steeple was added to the original tower in 1317 by Prior Henry Eastry, but a severe storm led to removal of the steeple in 1704. Further dilapidation left the tower unstable, and during 1832-1837 it was entirely re-faced to create a twin tower to match the south west tower.
The name Arundel tower arose from the set of four bells, known as the Arundel ring, which was given by Archbishop Arundel in the 15th century. Formerly hung in the Bell Harry tower, they were removed to the north west tower in the 1440s.
What's of interest:
the original tower with spire as depicted in Somner's The Antiquities of Canterbury (Image 1)
the spire-less tower as it appeared between 1704 and 1832 - the drawing is dated 1832 and appears in Lang-Sims' Canterbury Cathedral (Image 2)
the tower as it appears today (Image 3)
Sources: Bell (2009: Lang-Sims (1979); Somner (1703)