  Accurate measurements of the lateral distribution of extensive air showers
produced by cosmic rays of energy greater than $10^{17}$ eV were made in the
1970s by Linsley. At the time, the state of knowledge about the best hadronic
interaction model to use to describe such data prevented conclusions about the
cosmic ray mass from being drawn. We have used a modern model, {\sc qgsjet98},
to infer the primary mass from these data, using the very careful records left
by Linsley. We find that at a median energy of $10^{18}$ eV, the data are well
described by an iron-dominated composition (88 $\pm$ 6(stat) $\pm$ 18 (syst))%.
We discuss the systematic errors in this estimate that arise from model
uncertainties and from the range of energies used in the work of Linsley. These
data are used with the permission of the late John Linsley to whom this work is
dedicated.
