The rate of subcores in cosmic-ray air showers has been measured near sea level with a close-packed 35 m2 array of spark chambers at Leeds. A large transition effect was observed from wood beams in the original roof. After the first year, the spark chambers were affixed directly to a new Styrofoam sandwich roof of thickness 20 cm (2.2 g cm-*) in order to minimise transition effects. The measured rate is 0.038 f 0.01 per shower of size N > IO5 particles for subcores of size n25 2 50, where nz5 is the net number of subcore particles within a circle of radius 25 cm. The dependence on subcore size goes approximately as n2534. The higher rates of subcores reported in other experiments are probably due to transition effects. Ifp, is calculated by assuming subcore production by no's, we find no cases ofpt > 5 GeVic. The problem of abstracting realistic information from the subcore data in order to test theories of high-energy interactions at lo" eV is treated. Simulation results that predict significant improvement in data acquisition at higher altitudes are presented.