After outlining briefly the quantitative methods of Delesse, Rosiwal, Johannsen, Shand, and Wentworth, as carried out on mineral surfaces or thin-sections, the paper deals with some new variations of the Rosiwal method. These are based on the fundamental principle that accuracy of quantitative determination is increased by enlarging the scale of measurement or estimation. To this end small cross-sectioned grids, so arranged that one square of the grid corresponds to i per cent of the total area, are superimposed on photomicrographs or lantern slides. Quantitative determinations are then made either by areal estimation or lineal measurement. To increase the scale of measurement still farther, determinations are also made on the images of lantern slides, as projected by the lantern on the screen. The accuracy of these three new methods is checked successfully against a photographic variation of the Delesse method. A more rapid method for approximate determinations is also evolved by setting up a series of quantitative photographic standards, by comparison with which determinations may be made on any section. These standards are given for five of the common structures in ores. Finally there are indicated a few of the directions in which such quantitative methods may be used.