We say that a system ∑ of equal spheres S1S2, … covers a proportion θ of n-dimensional space, if the limit, as the side of the cube C tends to infinity, of the ratio
of the volume of C covered by the spheres to the volume of C, exists and has the value θ. We say that such a system ∑ has density δ, if the corresponding ratio
has the limit δ as the side of the cube C tends to infinity. We confine our attention to systems ∑ for which both limits exist. It is clear that δ = θ, if no two spheres of the system overlap, i.e. if we have a. packing; and that, in general, the difference δ-θ is a measure of the amount of overlapping.