By his studies, however, Haüy was able to determine that whenever substances of the same composition crystallized, even though the external form of the crystals seemed to be different, all of them were found to have the same internal nucleus. Whenever the mineral under observation was chemically different from another, then the nucleus also had a distinctive character; and so there came the law that all substances of the same kind crystallized in the same way, notwithstanding apparent differences. Indeed, one of the first results of this law was the recognition of the fact that when the crystalline forms of two minerals were essentially different, then, no matter how similar they might be, there was sure to be some chemical difference. This enabled Haüy to make certain prophecies with regard to the composition of minerals. A number of different kinds of crystals had been classed together under the name of {180} heavyspar. Some of these could not, by the splitting process, be made to produce _nuclei_ of similar forms, and the angles of the crystals were quite different. Haüy insisted that, in spite of close resemblances, there was an essential distinction in the chemical composition of these two different crystalline formations; and before long careful investigation showed that, while many of the specimens called heavyspar contain barium, some of them contain a new substance--strontium--which had been very little studied heretofore. This principle did not prove to be absolute in its application; but the amount of truth in it attracted attention to the subject of crystallography because of the help which that science would afford in the easy recognition of the general chemical composition of mineral substances. The most important part of Haüy's work was the annunciation of the law of symmetry. He emphasized the fact that the forms of crystals are not irregular or capricious, but are very constant and definite, and founded on absolutely fixed and ascertainable laws. He even showed that, while from certain crystalline nuclei sundry secondary forms may be derived, there are other forms that cannot by any possibility occur. Any change of crystalline form noticed in his experiments led to a corresponding change along all similar parts of the crystal. The angles, the edges, the faces, were modified in the same way, at the same time. All these elements of mensuration within the crystal Haüy thought could be indicated by rational coefficients. {181}