When a gas or hard nonattracting spheres is compressed it can go over into a densely packed random arrangement or a regular arrangement which becomes close packed at high densities. To these arrangements correspond two branches of the equation of state (pv/kT vs v). Though it is not possible to get an exact expression for the equation of state, the curves are fairly well determined by the application of certain general considerations concerning the entropy, by a general form for the random branch of the equation of state, and by some interpolations; certain geometrical factors having to do with the spherical shape of the particles are of some importance. Curves so obtained are compared with the results of some published machine calculations. The possibility of a first-order transition between the two branches is considered, and the position of such a transition, if it occurs, is roughly located.