Valuable, however, as were Professor Miller's public services on these various commissions, his chief work was at the University. His teacher, Dr. William Whewell--afterward the Master of Trinity College--was his immediate predecessor in the Professorship of Mineralogy at Cambridge. This great scholar, whose encyclopaedic mind could not long be confined in so narrow a field, held the professorship only four years; but during this period he devoted himself with his usual enthusiasm to the study of crystallography, and he accomplished a most important work in attracting to the same study young Miller, who brought his mathematical training to its elucidation. It was the privilege of Professor Miller to accomplish a unique work, for the like of which a more advanced science, with its multiplicity of details, will offer few opportunities. The foundations of crystallography had been laid long before Miller's time. Hauey is usually regarded as the founder of the science; for he first discovered the importance of cleavage, and classed the known facts under a definite system. Taking cleavage as his guide, and assuming that the forms of cleavage were not only the _primitive forms_ of crystals as a whole, but also the forms of their _integrant molecules_, he endeavored to show that all secondary forms might be derived from a few primary forms, regarded as elements of nature, by means of _decrements_ of molecules at their edges. In like manner he showed that all the forms of a given mineral, like fluor-spar or calcite, might be built up from the integrant molecules by skillfully placing together the primitive forms. Hauey's dissection of crystals, in a manner which appeared to lead to their ultimate crystalline elements, gained for his system great popular attention and applause. The system was developed with great perspicuity and completeness in a work remarkable for the vivacity of its style and the felicity of its illustration. Moreover, a simple mathematical expression was given to the system, and the notation which Hauey invented to express the relation of the secondary to the primary forms, as modified and improved by Levy, is still used by the French mineralogists.