Now it can be shown that the volumes of equal numbers of molecules in the arrangements A and B will be to one another as the height, H, of an equilateral triangle, to the height, h, of a regular tetrahedron whose edges are equal to the sides of the triangle, a length R (which will be equal to the diameter of a molecule). Then H = ¹⁄₂R√3, _h_ = R√²⁄₃. Then vol. in arrangement A : vol. in arr. B ∷ H : _h_ _i.e._ ∷ √3/2 : √²⁄₃ ∷ 1 : 0·943. That is, the volume changes in the ratio 1 to 0·943, the amorphous variety of gadolinite consisting of molecules in arrangement A, which go over to the closer packed arrangement B in the change to the crystalline form. More extended work has shown that this ingenious and interesting explanation is not of general application. Thus H. Rose[33] found that samarskite (_q.v._) exhibited the phenomenon of glowing, but that the specific gravity was actually less after the change than it was before, _i.e._ there was an increase of volume. Damour observed glowing in the case of zircon from Ceylon (_q.v._) with increase of density, the volume change being from 1 to 0·922, _i.e._ even greater than for gadolinite. Again, Hauser[34] observed in the case of his new rare earth mineral risörite a sudden change at a red heat, the mineral losing water, becoming very brittle, and increasing very considerably in specific gravity (the volume changing from 1 to 0·90 approximately), but without glowing. Ramsay and Travers[35] found that fergusonite (_q.v._) glowed strongly when heated to 500°-600°, with decrease of specific gravity (5·62 before to 5·37 after), evolution of all its helium, and very considerable evolution of heat; they suggested that helium was present in combination, in an endothermic compound decomposed by heat, but in view of the properties of helium, this hypothesis seems hardly tenable. [33] _J. pr. Chem._ 1858, ~73~, 391. [34] _Ber._ 1907, ~40~, 3118. [35] _Zeitsch. physikal. Chem._ 1898, ~25~, 568.