degree

   1. (° or deg)

   the standard unit of angle measure, equal to 1/360 circle, 60 minutes, 3600 seconds, or about 0.017 453 293 radian. So far as we know, this unit was introduced by the Greek geometer Hipparchus of Nicaea (ca. 180-ca. 125 BC), who developed the first trigonometric tables.

   2. (° or deg)

   a unit of distance sometimes used at sea, equal to 60 nautical miles, approximately 69.05 statute miles, or 111.12 kilometers. This distance is the average length of one degree of latitude (that is, the average distance between two lines of latitude 1° degree apart). Because the Earth is not exactly spherical, a degree of latitude actually varies from about 68.7 miles at the Equator to 69.4 miles at the poles. One degree of longitude is about 69.17 miles at the Equator (shrinking to nothing at the poles!).

   3. (° or deg)

   any of the various units of temperature (see below). In the U.S., the unmodified unit "degree" generally means the degree Fahrenheit; in other countries, it generally means the degree Celsius.

   4. (° or deg)

   a unit measuring the hardness of water. Water is called "hard" if it contains a high concentration of mineral salts, especially calcium carbonate. This concentration can be expressed clearly in parts per million (ppm) or in milligrams per liter (mg/L). But starting in the mid-19th century, several uses of "degree" for water hardness became well established. In the U.S. and Britain, hardness is measured in Clark degrees, named for the scientist who devised the first reliable test for water hardness. The Clark degree is defined as 1 part of calcium carbonate per 70 000 parts of water; this is about 14.3 parts per million (ppm), 17.1 mg/L, or 1 grain per gallon (gpg, another popular measure of hardness). The French, properly decimal as always, used a degree equal to exactly 10 ppm, while the German degree was equivalent to 17.8 ppm.

   5. (° or deg)

   various scientific quantities, especially specific gravity and viscosity, have been measured in "degrees" based on the readings of particular instruments. The degree scales of Baumé (see below) and Beck, and many others, have been used in measuring specific gravity, and the scales of Engler and MacMichael are common in the measurement of viscosity. Often these degree scales can't be converted in a simple way to the quantities being measured; one needs the conversion formula or table for the particular instrument. Some of this data can be found in scientific and engineering handbooks, especially older ones.

   6. (° or deg)

   the percentage of alcohol, by volume, present in a mixture. In winemaking, for example, a 13° wine is 13% alcohol by volume (13% v/v). This unit is also called the degree Gay-Lussac (° GL) after the French chemist Joseph-Louis Gay-Lussac (1778-1850).

   7. (deg)

   a unit used in mathematics to describe algebraic expressions. The degree of an expression having a single variable is the highest exponent (or power) to which that variable appears. If the expression has more than one variable, then the degree is the highest total exponent of the individual terms, where in each term the exponents of the different variables are added. Thus x²y⁴z³ is a term of degree 9.

   8. (°)

   the DIN speed rating for film; see DIN below.

   9. (deg)

(degree of consanguinity)

   a unit measuring consanguinity: the extent to which two persons are related to one another by common descent ("by blood," as the usual saying is). Essentially all cultures, societies, and nations have prohibited marriage between closely related individuals, and the determining factor is often the number of degrees of consanguinity between the two persons. If X is an ancestor of Y, the number of degrees of consanguinity between X and Y is the number of descents; thus parent and child are separated by 1 degree, grandparent and grandchild by 2 degrees, and so on. If persons X and Y are not linked by direct descent but do share a common ancestor A, the usual definition is that the number of degrees of consanguinity between X and Y is the total number of descents, counting up from X to A and then back down from A to Y. For example, siblings (brother and sister) are separated by 2 degrees, aunt and nephew by 3 degrees, and first cousins by 4 degrees. This calculation is backed by modern science, because we have learned that persons separated by n degrees of consanguinity share about 1/2^n-1 of their genes if they have two common ancestors or 1/2ⁿ if they have only one common ancestor.

   See also cousins.

   10. (°)

   a measure of curvature of railroad tracks or highways, used primarily in the U.S. When railroad tracks follow an arc of a circle, the angle of curvature is the angle (measured at the center of the circle) spanned by a chord of a standard length. In the U.S., the chord used is the U.S. chain of 100 feet (30.48 meters). In the metric world, a chord of 20 meters is sometimes used. On most U.S. rail lines curvatures are less than 6° (making the radius greater than 955 feet or 291 meters); on high speed lines they are less than 2° (making the radius greater than 2865 feet or 873 meters). For highways in the U.S., the angle of curvature is the angle (measured at the center of the circle) spanned by an arc 100 ft long.