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.
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.