Random Sequential Addition of Hard Spheres to a Volume

The configurations produced by placing spheres one at a time in a volume, subject to no overlap of the spheres but otherwise placing each at a point chosen at random, differ in a fundamental way from the configurations characteristic of a hard-sphere system of the same density which is in thermodynamic equilibrium. The difference is illustrated in four examples. The density at which the system becomes jammed is found in each case. The distribution of gaps produced by the random sequential placement of spheres on an infinite line is found for all densities up to that of jamming.