The first part of this paper deals with the application of a new microhardness tester, called Durimet, manufactured by E. Leitz, Ltd., Wetzlar, for determining Vickers hardness by making four-sided diamond shaped pyramidal indentation in the polished mineral surface. The length of the resulting diagonal is precisely measured by means of a measuring ocular.The general construction of the apparatus, and the working procedure are briefly described. Results obtained from testing the polished surfaces of about fifty different mineral species, and the correlation of the results obtained with Talmage's Scale of Hardness are given in detail. The "Durimet" seems to be of valuable aid in helping to determine metallic opaque minerals, from their polished surfaces, particularly in small inclusions or discrete grains too small to be examined by Talmage's method. Furthermore, the instrument can also be used for determining Knoop hardness as well as scratch hardness simply by changing the diamond that produces the indentation.The second part of the paper shows relationships between hardness and the textures encountered in the study of polished mineral surfaces. Among the most important relationships are the following:(1) Ore minerals of the metallic elements belonging to the same group in Mendeleeff's Periodic Table are generally of the same class of hardness.(2) Ex-solution textures, graphic intergrowths, and graphic replacement textures are generally shown by minerals belonging to the same grade of hardness.(3) Soft minerals commonly replace hard ones, whereas minerals of the same hardness commonly replace each other. Rarely hard minerals replace softer minerals.(4) In most ores the harder minerals seem to have crystallized earlier than the softer ones.