The reproducibility of glasses of 500 hard spheres is examined. Most amorphous packings are shown to tend to the limiting density z =0.870 +/- 0.008 (relative to the close packed crystal). When the fluid is compressed through the glass transition, in a molecular dynamics experiment, fast enough to avoid crystallites, the equation of state of the glasses, PV/NkT = 2.67/(1 - z/0.8754), and the statistical entropy, obtained by computing the configuration integral, are reproducible. The pressure bf the reproducible glasses does not diverge as fast as that of the crystal, with the result that the excess entropy of the glass (relative to the crystal) diverges. It is argued that the glass transition in hard spheres is a consequence of the geometry of the configuration space, and not simply a kinetic phenomenon.