§1. This paper is one of a series, planned by Prof. S. Chapman and one of the present authors in collaboration with the object of calculating theoretically the properties of the carbonate and nitrate crystals. A necessary preliminary to such an investigation is the calculation of the electrostatic potential energy of an infinite array of electrical charges distributed according to the scheme determined by X-ray analysis. This calculation has been made by Prof. Chapman and his collaborators, and the results have just been published. The results of this investigation were, however, communicated to us before publication, for which we offer grateful acknowledgment. The results of this paper have similarly been conveyed to Prof. Chapman, who with Mr. Topping is using them in a theoretical determination of some of the physical properties of the carbonates and nitrates.