Referring to a copy of a handbook of sailing terms "Ratline, one of a series of rope steps up the shrouds of a mast, 15 to 16 inches apart, by which men working aloft in square rigged ships reach the yards via the tops and crosstrees. Ratlines are normally made of 18-thread tarred rope with an eye in each end seized to the outermost shrouds, being secured to each intermediate shroud by a clove hitch".
In the drawing, the step (rat) lines looked to be about 1/3 the width of the shrouds. Scaling roughly from the drawing, the ratlines were pictured about 15mm apart, the with drawn was 0.5mm, so from the stated spacing of 15", about 1/2" thick.