Advance very gradually (4)
(Other definitions for inch that I've seen before include "Move slowly, in small steps" , "Twenty five point four millimetres" , "Creep towards < island" , "Move by slow degrees" , "One point 63380 th of a mile" .)
(Other definitions for edge that I've seen before include "Border - meeting place" , "Brim" , "Move furtively; intense quality" , "Border or cutting side of knife" , "Verge" .)