Fluctuations of the number of low-energy muons in fixed-size cosmic ray showers are calculated using scaling and realistic nuclear break-up models. The measured fluctuations are found to be consistent with at least two primary compositions near 10¹⁵-10¹⁷ eV. These are a composition composed of approximately=90% heavy nuclei such as iron and a composition of nearly pure protons. The composition of predominantly heavy nuclei resembles that required if a scaling model is to yield the muon abundance and rapid development of air showers observed in this energy region.