Ba_{2}O_{2} 5·7 52 - 10 La_{2}O_{3} 6·5 50 + 1 Ce_{2}O_{4} 6·74 50 + 2 Ta_{2}O_{5} 7·5 59 + 4·6 W_{2}O_{6} 6·8 68 + 8·2 Hg_{2}O_{2} 11·1 39 + 4·5 Pb_{2}O_{4} 8·9 53 + 4·2 Th_{2}O_{4} 9·86 54 + 2 As the volumes of the chlorides, organo-metallic and all other corresponding compounds, also vary in a like periodic succession with a change of elements, it is evidently possible to indicate the properties of substances yet uninvestigated by experimental means, and even those of yet undiscovered elements. It was possible by following this method to foretell, on the basis of the periodic law, many of the properties of scandium, gallium, and germanium, which were verified with great accuracy after these metals had been discovered.[23] The periodic law, therefore, has not only embraced the mutual relations of the elements and expressed their analogy, but has also to a certain extent subjected to law the doctrine of the types of the compounds formed by the elements: it has enabled us to see a regularity in the variation of all chemical and physical properties of elements and compounds, and has rendered it possible to foretell the properties of elements and compounds yet uninvestigated by experimental means; thus it has prepared the ground for the building up of atomic and molecular mechanics.[24] [23] As an example we will take indium oxide, In_{2}O_{3}. Its sp. gr. and sp. vol. should be the mean of those of cadmium oxide, Cd_{2}O_{2}, and stannic oxide, Sn_{2}O_{4}, as indium stands between cadmium and tin. Thus in the seventies it was already evident that the volume of indium oxide should be about 38, and its sp. gr. about 7·2, which was confirmed by the determinations of Nilson and Pettersson (7·179) made in 1880. [24] As the distance between, and the volumes of, the molecules and atoms of solids and liquids certainly enter into the data for the solution of the problems of molecular mechanics, which as yet have only been worked out to any extent for the gaseous state, the study of the specific gravity of solids, and especially of liquids, has long had an extensive literature. With respect to solids, however, a great difficulty is met with, owing to the specific gravity varying not only with a change of isomeric state (for example, for silica in the form of quartz = 2·65, and in tridymite = 2·2) but also directly under mechanical pressure (for example, in a crystalline, cast, and forged metal), and even with the extent to which they are powdered, &c., which influences are imperceptible in liquids. Compare Chapter XIV., Note 55^{bis}.