Thin flat unshaped stones were used to form more of a rustic cope stone border either side of the footpath of Springdale Bridge. String lines are used to determine the general curve of the top of the copes over the bridge.
Whereas fatter squarer pre-shaped ones were formally fit on the parapet of Crown Bridge.
String lines are used to get keep the stones flush with the sides of the bridge.
Generally string lines are useful at all times on bridges in order to keep everything flush and plumb. Most of my bridges don't have a batter because the dynamics of the arch gives a bridge enough strength not to have to depend on battering the sides (leaning the sides in slightly) the way you would a narrower free-standing dry stone wall.