From the INTRODUCTORY. IN any discussion of the constitution of the Atom the phenomenon of crystallization must have an important place, and it may be justly said that no theories of atomic or molecular constitution, which ignore the facts connected with the crystallization of the Elements, can be considered as resting on a sound basis. When an elementary substance is in a gaseous condition enclosed in a vacuum tube and subjected to forces relatively of great magnitude, there must necessarily be great difficulty in separating the phenomena produced by these conditions and by the rapid movements (both rotational and translatory) of the atom, from those characteristics that belong exclusively to the atom itself. If these characteristics are studied then the atoms are in a state of approximate rest, they afford a much more satisfactory field for investigation, and more reliable results may be expected. The following statement of facts in connection with the crystallization of elementary substances is submitted. (1). A large proportion of the Elements are known to assume a crystalline structure when in the solid state, and of those which are not so known, many are capable of forming crystalline space-lattices when in combination with other Elements.