Hard water
Water's hardness is determined by the concentration of multivalent cations in the water. Multivalent cations are positively charged metal complexes with a charge greater than 1+. Usually, the cations have the charge of 2+. Common cations found in hard water include Ca and Mg. These ions enter a water supply by leaching from minerals within an aquifer. Common calcium-containing minerals are calcite and gypsum. A common magnesium mineral is dolomite (which also contains calcium). Rainwater and distilled water are soft, because they contain few ions.
Friedrich Mohs
As part of this task, he started classifying minerals by their physical characteristics, instead of their chemical composition, as had been done traditionally. This emphasis on physical characteristics was at odds with the prevailing chemical systematics. However, both Theophrastus and Pliny the Elder had compared the relative hardness of minerals known to them in the ancient world, including diamond and quartz. They knew that diamond could scratch quartz, so showing it to be harder. This became the basis of the hardness scale developed by Mohs. The hardest mineral, diamond was given a value of 10 and softer minerals such as talc were given the very low value of 1 (unity). Other minerals were given intermediate values, depending on their ability to scratch another mineral in the scale. Thus gypsum was given the value 2 because it will scratch talc crystals, and calcite the value 3 because it will scratch gypsum. Minerals are also now classified by chemical characteristics, but the physical properties are still useful in field examination.