Physical properties of materials and systems are often described as intensive and extensive properties. This classification relates to the dependency of the properties upon the size or extent of the system or object in question. The distinction is based on the concept that smaller, non-interacting identical subdivisions of the system may be identified so that the property of interest does or does not change when the system is divided or combined. An intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, refractive index, density, and hardness of an object. When a diamond is cut, the pieces maintain their intrinsic hardness (until their size reaches a few atoms thick). By contrast, an extensive property is one that is additive for independent, noninteracting subsystems. The property is proportional to the amount of material in the system. For example, both the mass and the volume of a diamond are directly proportional to the amount that is left after cutting it from the raw mineral. Mass and volume are extensive properties, but hardness is intensive. The ratio of two extensive properties is scale-invariant, and is therefore an intensive property. For example, when gravity may be assumed constant, the ratio of the extensive properties mass and volume, the density, is an intensive property. This terminology of intensive and extensive properties was introduced by Richard C. Tolman in 1917.