It follows from the atomic theory that the number of atoms in equal weights of any two solid substances, is in the inverse ratio to the weights of these atoms. Now since the bodies that have the greatest specific gravities are the heaviest, if the specific gravities and atomic weights of equal bulks of two simple substances be known, the relative number of atoms they contain may be found. For the density divided by the atomic weight of the one, is to the density divided by the atomic weight of the other, as the number of atoms in the first to the number of atoms in the second. By the preceding law it is found that in equal bulks of the three metals, sodium, platinum, and potassium, platinum contains five times as many atoms as sodium, and ten times as many as potassium. When substances which have strong analogous qualities are compared in this manner, the results are either equality, or a simple ratio. It has already been mentioned that the protoxides of iron, copper, zinc, nickel and manganese, have the same form, and contain the same quantity of oxygen, but differ in the respective metals that are combined with it; and by the preceding law it appears that equal bulks of these isomorphous bodies contain also the same number of atoms. Mr. Hermann Kopp has proved that the atomic weight of a substance divided by the specific gravity, that is to say, its atomic volume, is the same for all isomorphic bodies simple and compound, and as a general law that the atoms of isomorphous substances are not only the same in form, but equal in dimensions. It follows, therefore, that any one of the preceding metals might be substituted for any other in the respective protoxides, and on that account, according to the modern theory, they are the chemical equivalents of each other, for that expression is used now in a different sense from what it formerly had. Chemical equivalency between two or more substances consists in their capacity for being exchanged one for the other. Direct or indirect substitution forms the basis of the modern doctrine of chemical equivalents. Substances which are capable of replacing one another in compounds, and which are endowed with qualities mutually analogous, are said to be isomeric. Many isomeric compounds are formed of the same materials, in the same proportions, and yet differ essentially both in their physical and chemical properties; whence M. Daniel observes, that a specific and definite arrangement of the constituent molecules in space appears to be no less essential to the individual constitution of bodies than a certain proportion between their heterogeneous ingredients.