Definitions

# mass

[mas]
mass, in physics, the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weight, which is the measure of the force of gravity (see gravitation) acting on a body. Under ordinary conditions the mass of a body can be considered to be constant; its weight, however, is not constant, since the force of gravity varies from place to place. There are two ways of referring to mass, depending on the law of physics defining it: gravitational mass and inertial mass. The gravitational mass of a body may be determined by comparing the body on a beam balance with a set of standard masses; in this way the gravitational factor is eliminated. The inertial mass of a body is a measure of the body's resistance to acceleration by some external force. One body has twice as much inertial mass as another body if it offers twice as much force in opposition to the same acceleration. All evidence seems to indicate that the gravitational and inertial masses of a body are equal, as demanded by Einstein's equivalence principle of relativity; so that at the same location equal (inertial) masses have equal weights. Because the numerical value for the mass of a body is the same anywhere in the world, it is used as a basis of reference for many physical measurements, such as density and heat capacity. According to the special theory of relativity, mass is not strictly constant but increases with the speed according to the formula m=m0/1-v2/c2, where m0 is the rest mass of the body, v is its speed, and c is the speed of light in vacuum. This increase in mass, however, does not become appreciable until very great speeds are reached. The rest mass of a body is its mass at zero velocity. The special theory of relativity also leads to the Einstein mass-energy relation, E=mc2, where E is the energy, and m and c are the (relativistic) mass and the speed of light, respectively. Because of this equivalence of mass and energy, the law of conservation of energy was extended to include mass as a form of energy.

Weapon with the capacity to inflict death and destruction indiscriminately and on a massive scale. The term has been in currency since at least 1937, when it was used to describe massed formations of bomber aircraft. Today WMDs are nuclear, biological, or chemical weapons—frequently referred to collectively as NBC weapons. Efforts to control the spread of WMDs are enshrined in international agreements such as the Nuclear Non-proliferation Treaty of 1968, the Biological Weapons Convention of 1972, and the Chemical Weapons Convention of 1993. See nuclear weapon; chemical warfare; biological warfare.

Musical setting of the mass for the dead. (Requiem, Latin for “rest,” is the first word of the mass.) The requiem's text differs from the standard mass Ordinary in omitting its joyous sections and keeping only the Kyrie, Sanctus, and Agnus Dei, which are combined with other sections, including the sequence Dies irae (“Day of Wrath”). The first surviving polyphonic setting is by Johannes Ockeghem; celebrated later requiems include those of Wolfgang Amadeus Mozart, Hector Berlioz, Giuseppe Verdi, Gabriel Fauré, Johannes Brahms, and Benjamin Britten.

Ratio of the average mass of a chemical element's atoms to 112 the mass of an atom of the carbon-12 isotope. The original standard of atomic weight, established in the 19th century, was hydrogen, with a value of 1. From circa 1900 until 1961, the reference standard was oxygen, with a value of 16, and the unit of atomic mass was defined as 116 the mass of an oxygen atom. Oxygen, however, contains small amounts of two isotopes that are heavier than the most abundant one, and 16 is actually a weighted average of the masses of the three isotopes of oxygen. Therefore, the standard was changed to one based on carbon-12. The new scale required only minimal changes to the values that had been used for chemical atomic weights.

Relationship between mass (math.m) and energy (math.E) in Albert Einstein's special theory of relativity, expressed math.E = math.mmath.c2, where math.c equals 186,000 mi/second (300,000 km/second), the speed of light. Whereas mass and energy were viewed as distinct in earlier physical theories, in special relativity a body's mass can be converted into energy in accordance with Einstein's formula. Such a release of energy decreases the body's mass (see conservation law).

or mass wasting

Bulk movements of soil and rock debris down slopes, or the sinking of confined areas of the Earth's ground surface. The term mass wasting refers only to gravity-driven processes that move large masses of earthen material from one place to another. The term mass movement includes the sinking of confined areas.

Transportation systems, usually publicly but sometimes privately owned and operated, designed to move large numbers of people in various types of vehicles in cities, suburbs, and large metropolitan areas. Modern mass transit is an outgrowth of industrialization and urbanization. In the 1830s early mass transit in New York City included horse-drawn buses, which were soon replaced by fixed-rail horse-drawn trolleys. By 1900 motorized buses had appeared in Europe and America. With the advent of electricity, streetcars and subways were introduced in many large cities. In the 20th century the automobile's increasing popularity undermined mass transit development; fixed-rail streetcar systems were widely removed to provide space for cars. Concern over air pollution has revived interest in light-rail transit and has led to regional mass transit systems.

or mass spectroscopy

Analytic technique by which chemical substances are identified by sorting gaseous ions by mass using electric and magnetic fields. A mass spectrometer uses electrical means to detect the sorted ions, while a mass spectrograph uses photographic or other nonelectrical means; either device is a mass spectroscope. The process is widely used to measure masses and relative abundances of different isotopes, to analyze products of a separation by liquid or gas chromatography, to test vacuum integrity in high-vacuum equipment, and to measure the geological age of minerals.

Application of the principles of specialization, division of labour, and standardization of parts to the manufacturing of goods on a large scale. Modern mass-production methods have led to such improvements in the cost, quality, quantity, and variety of goods available that the largest global population in history is now sustained at the highest general standard of living ever. The requirements for mass production of a particular product include the existence of a market large enough to justify a large investment; a product design that can use standardized parts (see interchangeable parts) and processes; a physical layout that minimizes materials handling; division of labour into simple, short, repetitive steps (see time-and-motion study); continuous flow of work; and tools designed specifically for the tasks to be performed. Seealso assembly line.

Fundamental law of chemical kinetics (the study of rates of chemical reactions), formulated in 1864–79 by the Norwegian scientists Cato M. Guldberg (1836–1902) and Peter Waage (1833–1900). The law states that the reaction rate of any simple chemical reaction is proportional to the product of the molar concentrations of the reacting substances, each raised to the power corresponding to the number of molecules of that substance in the reaction.

Celebration of the Eucharist in the Roman Catholic church. It is considered a sacramental reenactment of the death and resurrection of Jesus as well as a true sacrifice in which the body and blood of Jesus (the bread and wine) are offered to God. It is also seen as a sacred meal that unifies and nourishes the community of believers. The mass includes readings from Scripture, a sermon, an offertory, a eucharistic prayer, and communion. The rite was greatly changed after the Second Vatican Council, notably in the adoption of vernacular languages in place of Latin. Seealso sacrament, transubstantiation.

Minimum amount of a given fissionable material necessary to achieve a self-sustaining nuclear chain reaction under specified conditions. Critical mass depends on several factors, including the kind of fissionable material used, its concentration and purity, and the composition and geometry of the surrounding reaction system.

In meteorology, a large body of air having nearly uniform conditions of temperature and humidity at any given altitude. Such a mass has distinct boundaries and may extend hundreds or thousands of miles horizontally and sometimes as high as the top of the troposphere. An air mass forms whenever the atmosphere remains in contact with a large, relatively uniform land or sea surface long enough to acquire its temperature and moisture properties. The Earth's major air masses all originate in polar or subtropical latitudes. The middle latitudes constitute essentially a zone of modification, interaction, and mixing of the polar and tropical air masses.

The carat is a unit of mass used for measuring gems and pearls. Currently a carat is defined as exactly 200 mg (0.007,055 oz, 3.086 grains). This definition, known as the metric carat, was adopted in 1907 at the Fourth General Conference on Weights and Measures, and soon afterwards in many countries around the world. It is universally used today. The carat is divisible into one hundred points of two milligrams each.

For diamonds, a paragon is a flawless stone of at least 100 carats (20 g). The ANSI X.12 EDI standard abbreviation for the carat is CD.

The word came to English from French, derived from the Greek kerátion (κεράτιον), “fruit of the carob”, via Arabic qīrāṭ (قيراط) and Italian carato. The Latin word for carat is siliqua. In past centuries, different countries each had their own carat unit, all roughly equivalent to the mass of a carob seed. These units were often used for weighing gold.

Carob seeds were used as weights on precision scales because of their reputation for having a uniform weight. However, a 2006 study found carob seeds to have as much variation in their weights as do other seeds, though it seems that it is easier than with other seeds to recognize particularly large or small specimens and remove them. Thus, the carob seed was used as a weight not because it was naturally more uniform in weight, but because it could be more easily standardized.

## Historical definitions in the United Kingdom

In the United Kingdom, before 1888, the Board of Trade carat was exactly $3,tfrac\left\{1647\right\}\left\{9691\right\}$ grains; after 1887, the Board of Trade carat was exactly $3,tfrac\left\{17\right\}\left\{101\right\}$ grains. Despite it being a non-metric unit, a number of metric countries used this unit for its limited range of application.

The Board of Trade carat was divisible into four diamond grains, but measurements were typically made in multiples of $tfrac\left\{1\right\}\left\{64\right\}$ carat.

### Pound carat and ounce carat

There were also two varieties of refiners’ carats once used in the United Kingdom — the pound carat and the ounce carat. The pound troy was divisible into 24 pound carats of 240 grains troy each; the pound carat was divisible into four pound grains of 60 grains troy each; and the pound grain was divisible into four pound quarters of 15 grains troy each. Similarly, the ounce troy was divisible into 24 ounce carats of 20 grains troy each; the ounce carat was divisible into four ounce grains of 5 grains troy each; and the ounce grain was divisible into four ounce quarters of 1¼ grains troy each.

## The carat of the Romans and Greeks

The solidus (carat) was also a Roman weight unit. There is literary evidence that the weight of 72 coins of the type called solidus was exactly a Roman pound, and that the weight of a solidus was 24 siliquae. The weight of a Roman pound is generally believed to have been 327.45 g or possibly up to 5 g grams less. Therefore the metric equivalent of 1 solidus was approximately 189 mg. The Greeks had a similar unit of the same value.

## The carat in Byzantine Egypt

A carob based weight unit was also used in Egypt in the Byzantine and early Arab periods. In this region, glass weights were used for weighing coins. From these the weight of the Egypt carat has been reconstructed as 196 mg. This is consistent with the average weights of carob seeds in the region.

## The Syrian and Arabic carat in Mohammad's time

According to literary sources, the Arabic carat was only 2% less than the Syrian carat. Based on coins and glass weights their weight was reconstructed as approximately 212 mg. This is consistent with literary information that a solidus weighed slightly less than 22 carats.