mass-luminosity relation, in astronomy, law stating that the luminosity of a star is proportional to some power of the mass of the star. More massive stars are in general more luminous. For stars on the main sequence of the Hertzsprung-Russell diagram, it is found empirically that the luminosity varies as the 3.5 power of the mass. This means that if the mass is doubled, the luminosity increases more than tenfold. The law can be derived theoretically and was confirmed by independently measuring the masses of many visual binary stars, all at approximately the same distance. A more exact formulation of the law takes into account the chemical composition of the star. One important use of the mass-luminosity relation is in estimating the mass of a star of known luminosity that is not in a binary system.

mass transit, public transportation systems designed to move large numbers of passengers.

Types and Advantages

Mass transit refers to municipal or regional public shared transportation, such as buses, streetcars, and ferries, open to all on a nonreserved basis. An important form of mass transit is rapid transit, such as subways and surface light rail systems, designed for commuting between urban and suburban (or exurban) centers. Mass transit can be divided into fixed route systems (often involving rails), such as streetcars and subway trains, and nonfixed route transit (along surface streets or water), such as buses and ferries, but does not usually include airplanes, taxis, or long-distance rail with more formal ticketing procedures. Mass transit systems offer considerable savings in labor, materials, and energy over private transit systems. Since far fewer operators are required per passenger transported, they can be better trained and more strictly licensed and supervised.

When utilized to any reasonable fraction of their capacity, mass transit vehicles carry a far higher passenger load per unit of weight and volume than do private vehicles. They also offer fuel savings, not only because of the relative reduction in weight transported, but also because they are large enough to carry more efficient engines. Further, if emphasis is given to mass transit in the planning of future ground transportation systems, smaller rights of way will be possible, lessening the amount of landscape that must be paved over for highways and roads. Although mass transit offers many savings, it does require some sacrifices in personal convenience. These are the necessity to travel on a fixed rather than an individually selected schedule and to enter and disembark from the system only at certain designated locations. The obvious goal for a mass transit system is to have as few unused passenger accommodations as possible.

See also rapid transit.

History

The history of mass transportation is intimately connected to industrialization, urbanization, and the separation of residence from workplace. By the beginning of the 20th cent., London, New York, Boston, Paris, Budapest, and other major cities had fixed-rail subway systems (sometimes elevated); by the 1920s buses were common. In the United States, patronage of mass transit grew steadily from 1900 (six billion passengers per year) to 1927 (over 17 billion), but plummeted during the Great Depression. Patronage grew again during War II, peaking in 1946 at 23 billion riders, but then dropped steadily every year until the mild renaissance of public transit in the early 1970s.

The total number of riders in 1970 was less than that of 1910. The reasons for these declines are complex and often political. Los Angeles, for example, had over 1,000 miles of trolley and interurban lines before 1930; this system was taken over by a private company, dismantled, and replaced with noisy, polluting, and comparatively slow buses. Since few people chose to ride them, costs rose, thereby cutting the number of passengers further. To reduce costs, private companies eliminated outlying branches and smaller stations. These trends, along with inexpensive gasoline, suburban and highway development, the deterioration of older subway lines, and the greater freedom cars offered, helped turn the United States into a car culture.

However, as the public has grown increasingly concerned over the impact of cars on the environment and the quality of life in urban areas, there is growing support for the development of more efficient and comfortable mass transit systems. Models for such systems were developed in Europe and Japan. Trains in the Paris Metro, for example, operate on rubber tires and can reach speeds of 48 mph (77 km). Smaller cities are watching developments in Edmonton, Canada, which built a 4.5-mi (7.2-km) rapid transit system of lightweight trains at a cost of $65 million instead of adding five new freeways at ten times the cost.

In the United States, efforts to upgrade mass transit systems have experienced mixed results. The trend has been away from private ownership; by 1990 over 90% of North American mass transit was publicly owned and managed. The BART (Bay Area Rapid Transit) system serving San Francisco and neighboring cities maintained service during the 1989 earthquake, but it has never attracted the number of riders originally anticipated. Washington, D.C.'s Metro system (144 million riders in 1988) included a wider area of service and more efficient schedules. Currently buses account for 60% of mass transit rides in the United States; innovations such as articulated buses and reserved lanes on highways are balanced by the problems of noise, air pollution, and traffic. The issue of mass transit has come full circle; it is once again a central social and political issue.

mass spectrograph, device used to separate electrically charged particles according to their masses; a form of the instrument known as a mass spectrometer is often used to measure the masses of isotopes of elements. J. J. Thomson and F. W. Aston showed (c.1900) that magnetic and electric fields can be used to deflect streams of charged particles traveling in a vacuum, and that the degree of bending depends on the masses and electric charges of the particles. In the mass spectrograph the particles, in the form of ions, pass through deflecting fields (produced by carefully designed magnetic pole pieces and electrodes) and are detected by photographic plates. The beam of ions first passes through a velocity selector, consisting of a combination of electric and magnetic fields that eliminates all particles except those of a given velocity. The remaining ion beam then enters an evacuated chamber where a magnetic field bends it into a semicircular path ending at the photographic plate. The radius of this path depends upon the mass of the particles (all other factors, such as velocity and charge, being equal). Thus, if in the original stream isotopes of various masses are present, the position of the blackened spots on the plate makes possible a calculation of the isotope masses. The mass spectrograph is widely used in chemical analysis and in the detection of impurities.

mass production: see production.

mass number, often represented by the symbol A, the total number of nucleons (neutrons and protons) in the nucleus of an atom. All atoms of a chemical element have the same atomic number (number of protons in the nucleus) but may have different mass numbers (from having different numbers of neutrons in the nucleus). Atoms of an element with the same mass number make up an isotope of the element. Different isotopes of the same element cannot have the same mass number, but isotopes of different elements often do have the same mass number, e.g., carbon-14 (6 protons and 8 neutrons) and nitrogen-14 (7 protons and 7 neutrons).

mass extinction, the extinction of a large percentage of the earth's species, opening ecological niches for other species to fill. There have been at least ten such events. The five greatest were those of the final Ordovician period (approximately 435 million years ago), the late Devonian period (357 million years ago), the final Permian period (250 million years ago), the late Triassic period (198 million years ago), and the final Cretaceous period (65 million years ago). The most devastating was that at the end of the Permian period, when an estimated 95% of marine species and 8 of 27 insect orders were lost. The best-known mass extinction is that at the end of the Cretaceous period, when the dinosaurs and many other plants and animals disappeared and up to 75% of all marine genera were lost. The most recent mass extinction was that of the late Eocene epoch, approximately 54 million years ago. Understanding and definition of these events have changed rapidly as information from more and more complete fossil samplings is compiled in larger and more comprehensive databases and as computer modeling of such events becomes more sophisticated.

Theories regarding the causes of mass extinctions abound and are the subject of intense study and debate. In general it is believed that the extinctions resulted from drastic environmental changes that followed events such as meteorite or comet impacts or massive volcanic eruptions. For example, the final Permian extinctions have been linked to huge volcanic eruptions in what is now Siberia. These eruptions, which continued for up to 800,000 years (a relatively short period of time by geological standards), spewed out dust and droplets that blocked the sun, causing global cooling that trapped sea water in the polar ice caps. The levels of inland seas and oceans lowered significantly, eliminating or changing marine habitats. Alternatively, it has been suggested that carbon dioxide and other gases released by the volcanic eruptions may have raised temperatures by 20-50°F; (10-30°C;) in an extreme greenhouse effect and disrupted ocean circulation patterns, or that the gases produced acid rain and depleted the ozone layer, creating conditions inhospitable to many species. Other theorized causes for the Permian extinctions include the effects of the breakup of the supercontinent Pangaea (which include the huge volcanic eruptions), a large meteor impact, and a supernova that exploded near enough to the earth to bathe it in radioactivity that destroyed the ozone layer.

The most popular theory of the final Cretaceous extinction is that one or more asteroids or comets hit the earth, lifting massive amounts of debris and sulfur in the air and blocking the sunlight from reaching the earth's surface. In 1980 Walter Alvarez of the Univ. of California at Berkeley found a layer of iridium in sediments that dated from the time of the final Cretaceous extinction. Iridium is rare on earth, but is concentrated in meteors and comets. In 1991 the Chicxulub crater was discovered on the Yucatán peninsula in Mexico. Some 180 km (112 mi) wide, it is wide enough to have been created by the 10-km (6-mi) diameter asteroid thought necessary to cause the environmental upheaval required to precipitate a mass extinction. Large amounts of sulfur found in the Chicxulub soil lend credence to the hypothesis that sulfuric acid dispersed into the atmosphere after the collision creating a dense haze that could have cooled the earth by 20 to 30°F; (10-17°C;). Some scientists believe global wildfires that incinerated as much as one quarter of the earth's vegetation followed the impact. There is also evidence of other asteroid collisions at about the same time.

Another theory concerning the cause of the final Cretaceous extinction is that it resulted from the huge volcanic eruptions that created the lava flows of the Deccan Traps in what is now India. One model has put these theories together (both for the Permian and Cretaceous extinctions), hypothesizing that shock waves from the impact of a large asteroid moved through the earth, shaking the earth's crust and triggering or intensifying the volcanic events.

In addition to eradicating large percentages of both land and sea creatures, mass extinctions also opened new ecological niches, permitting surviving species to thrive in new habitats and encouraging diversity. The extinctions, however, did not conform to the usual evolutionary rules regarding who survives; the only factor that appears to have improved a family of organisms' chance of survival was widespread geographic colonization at the time of the event.

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.

critical mass: see chain reaction.

center of mass, the point at which all the mass of a body may be considered to be concentrated in analyzing its motion. The center of mass of a sphere of uniform density coincides with the center of the sphere. The center of mass of a body need not be within the body itself; the center of mass of a ring or a hollow cylinder is located in the enclosed space, not in the object itself. Under the action of a constant force of gravity, a body suspended or balanced at its center of mass will be stable; there will be no net moment acting on it. Sometimes a problem may be analyzed from the point of view of the center of mass of an entire system of objects, such as several colliding elementary particles or a multiple-star system. For example, the complex motions of the earth and moon about the sun become somewhat simpler when viewed from the common center of mass of the earth-moon system, located about 1,000 mi (1,600 km) below the earth's surface. It is this point that is moving in an elliptical orbit around the sun rather than the center of mass of the earth alone.

atomic mass unit or amu, in chemistry and physics, unit defined as exactly 1/12 the mass of an atom of carbon-12, the isotope of carbon with six protons and six neutrons in its nucleus. One amu is equal to approximately 1.66 × 10^-24 grams.

atomic mass, the mass of a single atom, usually expressed in atomic mass units (amu). Most of the mass of an atom is concentrated in the protons and neutrons contained in the nucleus. Each proton or neutron weighs about 1 amu, and thus the atomic mass is always very close to the mass number (total number of protons and neutrons in the nucleus). Atoms of an isotope of an element all have the same atomic mass. Atomic masses are usually determined by mass spectrography (see mass spectrograph). They have been determined with great relative accuracy, but their absolute value is less certain.

air mass, large body of air within the earth's atmosphere in which temperature and humidity, although varying at different heights, remain similar throughout the body at any one height. Air masses form over parts of the earth's surface called source regions, which are large bodies of water or landmasses with relatively uniform topography, often ranging hundreds of thousands of square miles in area. When a body of air remains over a source region for days or weeks, it reaches an equilibrium with the surface. Radiation and convection exchanges between the surface and the air determines the air mass characteristics. Air masses formed over oceans generally contain more moisture than continental ones; air masses formed in polar latitudes are colder than those from the tropics. As an air mass moves away from its source region, it brings its particular weather conditions to areas over which it travels. At the same time, its characteristic properties are slowly modified by exposure to new environments. The boundaries between air masses, called fronts, are, typically, zones of rapid transition from cold to warm or from dry to moist air. Turbulence at the boundary often breeds low-pressure storms.

Mass, religious service of the Roman Catholic Church, which has as its central act the performance of the sacrament of the Eucharist. It is based on the ancient Latin liturgy of the city of Rome, now used in most, but not all, Roman Catholic churches. The term Mass [Lat. missa,=dismissed] probably derives from the practice of dismissing the catechumens—those not yet initiated into the mystery of the Eucharist—before the offertory and from the words Ite, missa est [Go, you are dismissed] spoken to the faithful at the end of the Mass. The term is also used among Anglo-Catholics; in the Eastern churches the Mass is generally called the Holy Liturgy or the Offering. For non-Roman liturgies, see liturgy.

The Role of the Catholic Mass

In the Roman Catholic Church, except for the altogether distinct Ambrosian rite (see Ambrose, Saint) and for some variant forms among religious orders, especially that of the Dominicans, the service is the same everywhere, under regulation of the Holy See. The language of the liturgy is typically terse. The celebrant, who must be a priest, follows a prescribed missal and wears certain vestments. Mass is said at an altar containing relics; two candles must be burning. A congregation is not essential, but solitary Mass is discouraged. A High (solemn) Mass requires a priest, deacon, and choir. Low Mass, much more common, is the same service said by one priest. Normally at Low Mass a server or acolyte, traditionally called an altar boy but now often a girl, helps the celebrant. Most of the text is invariable, or "ordinary," but certain parts, called "proper," change with the occasion or day. Mass may be offered with a special intention, as in thanksgiving or for peace. A requiem is a proper Mass for the dead. Most priests say Mass daily. Sunday Mass is an important sociocultural factor in Roman Catholic life. All members are required to attend Mass on Sunday as a minimum participation in public worship.

The Service

The Mass begins with an entrance hymn, a greeting, and a brief penetential rite that includes the Kyrie eleison, the Gloria in excelsis (not always), a collect or collects, the proper epistle, an anthem and the proper Gospel (usually chanted and with all standing), and a homily on the texts. This ends the part of the Mass known in primitive times as the Mass of the Catechumens.

Mass continues with the creed (sometimes), the offertory (anthem with offering of bread and wine), offering of incense (sometimes), washing of the celebrant's hands, and proper prayers called "secrets." Then there is a chanted or spoken dialogue and proper preface of thanksgiving, ending in the Sanctus. That opens the long eucharistic prayer, or canon. It begins with prayers for the living. The consecration of the bread and wine follows; then the celebrant raises Host and chalice above his head for all to see and adore. The canon ends with prayers for the dead and a doxology, which is the solemn climax of the eucharistic prayer.

After the canon the Mass consists of the Lord's Prayer, a prayer amplifying the supplication "Deliver us from evil," the symbolic breaking of the Host and putting a piece into the cup, the kiss of peace (shared by the members of the congregation), the Agnus Dei, the communion, the ablution of vessels, the communion anthem, postcommunion prayers, the dismissal, and the blessing. There are ceremonial adjuncts such as processions, blessings, censings, and in some places, the ringing of a handbell at the consecration.

Music in the Mass

Of the portions of the Mass that may be sung, some are chanted solo at the altar with choral response; there are also nine hymns for the choir. Four of these are proper and related in theme, with texts usually from the Psalms: introit, anthem after the epistle (alleluia, gradual, tract, or sequence), offertory, and communion. The five ordinary choral pieces are Kyrie eleison, Gloria in excelsis, Credo (see creed), Sanctus, and Agnus Dei. Plainsong is prescribed for all texts, but latitude is permitted the choir. A musical setting for the five ordinary hymns, called a Mass, has been a major musical form. The principal period of Mass composition lasted from 1400 to 1700. It came to an end with shift of interest to instrumental music, although later composers did use the form. Among the many composers who produced Masses are Josquin des Prés, Palestrina, Monteverdi, Bach, Haydn, Mozart, Beethoven, Verdi, and Stravinsky.

Changes in the Mass

The basic structure of the Mass is largely unchanged since the 6th cent. In the Counter Reformation the forms were restricted and local variants eliminated. As a result of the Constitution on the Sacred Liturgy of the Second Vatican Council, the Roman Mass liturgy has undergone extensive reformation. The revisions include the use of the vernacular languages in the place of Latin, an emphasis on congregational singing, latitude for modifications that may be introduced by local bishops, additional eucharistic prayers, and communion in both bread and wine.

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.

Learn more about weapon of mass destruction (WMD) with a free trial on Britannica.com.

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.

Learn more about requiem mass with a free trial on Britannica.com.

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.

Learn more about atomic weight with a free trial on Britannica.com.

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).

Learn more about Einstein's mass-energy relation with a free trial on Britannica.com.

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.

Learn more about mass movement with a free trial on Britannica.com.

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.

Learn more about mass transit with a free trial on Britannica.com.

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.

Learn more about mass spectrometry with a free trial on Britannica.com.

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.

Learn more about mass production with a free trial on Britannica.com.

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.

Learn more about mass action, law of with a free trial on Britannica.com.

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.

Learn more about mass with a free trial on Britannica.com.

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.

Learn more about critical mass with a free trial on Britannica.com.

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.

Learn more about air mass with a free trial on Britannica.com.