Applying the law of isomorphism in a similar manner, Berzelius was enabled to fix the atomic weights of copper, cadmium, zinc, nickel, cobalt, iron, manganese, chromium, sulphur, selenium, and chlorine, the numbers accepted to-day differing only in the decimal places, in accordance with the more accurate results acquired by the advance of experimental and quantitative analytical methods. But with regard to several other elements, owing to inadequate data, Berzelius made serious mistakes, showing how very great is the necessity for care and for ample experimental data and accurate measurements, before the principle of isomorphism can be applied with safety. Given these, and we have one of the most valuable of all the aids known to us in choosing the correct atomic weight of an element from among two or three possible alternatives. We are only on absolutely sure ground when we are dealing not only with a series of compounds consisting of the same number of atoms, but when also the interchangeable elements are the intimately related members of a family group, such as we have since become familiar with in the vertical groups of elements in the periodic table of Mendeléeff. Before leaving Stockholm Mitscherlich showed, from experiments on the crystallisation of mixtures of the different sulphates with which he had been working, that isomorphous substances intermix in crystals in all proportions, and that they also replace one another in minerals in indefinite proportions, a fact which has of recent years been wonderfully exemplified in the cases of the hornblende (amphibole) and augite (pyroxene) groups. In November 1821 Mitscherlich closed these memorable labours at Stockholm and returned to Berlin, where he acted as extraordinary professor of the university until 1825, when he was elected professor in ordinary. His investigations for a time were largely connected with minerals, but on July 6th, 1826, he presented a further most important crystallographic paper to the Berlin Academy, in which he announced his discovery of the fact that one of the best known chemical elements, sulphur, is capable of crystallising in two distinct forms. The ordinary crystals found about Etna and Vesuvius and in other volcanic regions agree with those deposited from solution in carbon bisulphide in exhibiting rhombic symmetry. But Mitscherlich found that when sulphur is fused and allowed to cool until partially solidified, and the still liquid portion is then poured out of the crucible, the walls of the latter are found to be lined with long monoclinic prisms. These have already been illustrated in Fig. 2, Plate I., in Chapter I.