The electrostatic energy of a polar crystal (i.e. a crystal with a net dipole p u c in the unit cell) is conditionally convergent, i.e. depends on the order of the summation. For example, if the dipole-dipole interactions of a central unit cell with unit cells located on an ever-increasing cube, the energy converges to a different value than if the interaction energies had been summed spherically. Roughly speaking, this conditional convergence arises because (1) the number of interacting dipoles on a shell of radius R grows like R 2 ; (2) the strength of a single dipole-dipole interaction falls like 1 / R 3 ; and (3) the mathematical summation ∑ ∑ n = 1 ∞ ∞ 1 n diverges.