 If a sequence <formula> of tilings of a surface is conformal ( <formula> ) in the above sense , then there is a conformal structure on the surface and a constant <formula> depending only on <formula> in which the classical moduli and approximate moduli ( from <formula> for <formula> sufficiently large ) of any given annulus are <formula> <unk> , meaning that they lie in a single interval <formula> . 
