3 = 100/((_x_/5.1)+(100-_x_)/2.6) 3 = 1326/(510-2.5_x_) 204 = 7.5_x_ and _x_ = 27.2 If the percentage (P) and sp. g. (H) of one constituent and the sp. g. (M) of the mixture are known, the sp. g. of the other constituent may be calculated by the following formula, in which _x_ is the required sp. g.: _x_ = ((100-P)×M×H)/((100×H)-(P×M)) For example, "tailings" (sp. g. 3.0) containing 27.2 per cent. of pyrites (sp. g. 5.1) will contain (100-27.2), 72.8 per cent. of earthy matter having a mean sp. g. of _x_: _x_ = ((100-27.2)×3×5.1)/((100×5.1)-(27.2×3)) = 1113.84/428.4 = 2.6 The differences in sp. g. corresponding to differences in strength have been carefully determined and tabulated in the case of the stronger acids and of many other liquids. Such tables are given at the end of this book. _To Calculate the Weight of a Measured Volume of Mineral or Rock._--Multiply the cubic feet by 62.4 and then multiply by the sp. g. of the stuff, the answer gives the weight in pounds. For example, 100 cubic feet of quartz weighs 100×62.4×2.6 = 16,224 lbs. The weight of any mass of mineral of known extent and sp. g. is ascertained in this way. The following table gives the specific gravities of some of the commoner minerals. Barytes 4.5 Blende 4.0 Calcite 2.6 Cassiterite 6.9 Chalybite 3.8 Copper pyrites 4.2 Fluor 3.1 Galena 7.5 Hæmatite 5.0 Mispickel 6.2 Pyrites 5.0 Quartz 2.6 FOOTNOTES: [8] The difference of 20 or 30 milligrams is disregarded here because it detracts equally from the actual weight of the water and liquid to be determined. If the liquid is a heavy one the difference shows itself in the third or second place of decimals. The correction may be made by deducting from the weight of the flask 0.0012 grams for each gram of water it holds. PART II.--THE METALS. CHAPTER IX. SILVER, GOLD, CYANIDES, PLATINUM, MERCURY. SILVER. Silver is widely diffused, and has been found in most mining districts. It occurs native in sufficient quantity to constitute one of the chief ores of the metal. It also occurs combined with sulphur (as in argentite), with sulphur and antimony (as in stephanite or brittle silver ore, and in pyrargyrite or ruby silver), and with copper, sulphur, antimony, and arsenic, as in polybasite. Chloride of silver occurs native as horn silver or kerargyrite. Silver is found in the ores of other metals, such as fahlerz, which sometimes contains from two to ten per cent. of the metal, and galena, which is an important source of it; in fact, galena is never found entirely free from silver. It is present also in greater or less quantity in the ores of copper and zinc.