Aphylactic Projection- A term rarely used to qualify a projection as having neither the equal area or conformal characteristics.

Azimuth- The direction of one object from another, usually expressed as an angle in degrees relative to true north. Azimuths are usually measured in the clockwise direction, thus an azimuth of 90 degrees indicates that the second object is due east of the first.

Authalic- An adjective which has the same connotation as Equal Area.

Azimuthal Projection- A projection that accurately preserves the azimuth between certain objects. All projections introduce some distortion into the Cartesian results. To a certain degree, the mathematics chosen can eliminate certain types of distortion while introducing other types of distortion. An azimuthal projection preserves the azimuth between certain objects. Typically, such projections preserve only the azimuth of all points to a specific point, such as the origin of the coordinate system. In other words, on such a map, the direction from the origin to any other point on the map is shown accurately on the map.

Bearing- The direction of one object from another, usually expressed as an angle in degrees relative to a specific primary direction. Bearings differ from azimuths in that bearing values do not exceed 90 degrees.

Central Meridian- The longitude of the horizontal center of a coordinate system. This longitude value is often the longitude origin of the coordinate system. In the case of the Transverse Mercator projection, the central meridian is the great circle/geodesic at which the projection surface, i.e. the cylinder, touches, or is tangent to, the earth.

Conformal Projection- A projection that can accurately preserve the shape of mapped entities with the drawback of scalar and area distortion. All projections introduce some distortion into the Cartesian results; to a certain degree, however, the mathematics chosen to perform the transformation can reduce certain types of distortion while introducing other types of distortion. A conformal projection preserves the proper angles between connected line segments and therefore tends to preserve the shape of geographic objects better than other types of projections.

Conic Projection- A projection based on the geometry of the cone. You can imagine a conic projection as similar to placing a party hat on the earth. The plain conic touches the earth at a specific parallel referred to as the Standard Parallel. Mathematically, the cone is often recessed into the earth to reduce the aggregate distance between the earth and the cone over the specific geographic area of interest. Reducing this distance reduces the distortion. Since the cone enters and then leaves the earth, two standard parallels result.

Convergence Angle- The angle between the Y axis and true north on a map. This is often used as a measure of azimuthal distortion on a map; and it often varies from one position to another.

Coordinate System- An exact definition of a system of mathematics and geodetic constants that defines how a specific geographic location is converted to a set of two or three numbers, such as an x- and y-value (and possibly a z-value, also). In the cartographic context, most coordinate systems are Cartesian: the axes are orthogonal (perpendicular to each other) and the units are the same on all axes. The principal exception to this is the spherical coordinate system of latitudes and longitudes.

Cylindrical Projection- A projection based on the geometry of a cylinder. The spherical earth is mathematically projected onto a cylinder that surrounds the globe at a specific point. The traditional Mercator projection has the cylinder wrapped so that it is tangent to the earth at the equator. The Transverse Mercator projection places the cylinder tangent to the earth along the central meridian.

Datum- A datum is the combination of an ellipsoid, which specifies the size and shape of the earth, and a base point from which the latitude and longitude of all other points are referenced. Before satellites, lasers, and computer technology, establishing precise values for these points was impossible. More recently, many datums have been established and substantial amounts of data collected based on each. Data based on one datum will not necessarily overlay data based on another datum.

Ellipsoid- The mathematical shape that best describes the shape of the earth and yet is relatively simple to deal with mathematically. Ellipsoids are defined with two numbers. First, the equatorial radius must be specified. This is also referred to as the semi-major axis. Second, one of three numbers must be given: the polar radius (also known as the semi-minor axis), the eccentricity, or the flattening. Given the equatorial radius and the any one of the three secondary values, the remaining secondary values can be computed. A specific determination of the size of the earth is often referred to as an ellipsoid. For example, the phrase "Clarke ellipsoid of 1866" is frequently used to refer to the measurements of the size of the earth made by Clarke in 1866.

Ellipsoid Height- The height of an object above the reference ellipsoid in use. Nowadays, this term is generally used to qualify an elevation as being measured from the ellipsoid as opposed to the geoid. GPS systems calculate ellipsoidal height. The geoid height at that location must be subtracted to obtain what is commonly referred to as the elevation.

Equal Area Projection- A projection that accurately preserves the area of objects. All projections introduce some distortion into the Cartesian results; to a certain degree, however, the mathematics chosen can eliminate certain types of distortion while introducing other types of distortion. An equal area projection preserves the area of geodetic objects although the shape might be distorted. For example, a circle on the surface of the earth may be converted to an elliptical shape by an Equal Area projection, but the area covered by the ellipse will faithfully represent the area of the original circle. A coin placed on a map produced with an equal area projection covers the same amount of real area no matter where it is placed on the map.

Equidistant Projection- A projection that accurately preserves the distance between certain objects. All projections introduce some distortion into the Cartesian results; to a certain degree, however, the mathematics chosen can eliminate certain types of distortion while introducing other types of distortion. An equidistant projection preserves the distance between certain objects. For example, such projections can preserve the distance of all points to a specific point, such as the origin of the coordinate system; or preserve the correct distance between all points on the same meridian.

Equiareal Projection- A term rarely used to qualify a projection as having the equal area characteristic.

Equirectangular Projection- Another name used to refer to the Equidistant Cylindrical projection.

False Easting- An element of a coordinate system definition. False easting is the value added to all x-coordinates to create a coordinate system with no negative x-values in the geographic region for which it is designed. While all coordinate system definitions make provisions for a false easting, it is often set to zero to disable this feature.

False Northing- An element of a coordinate system definition. False northing is the value added to all y-coordinates to create a coordinate system with no negative y-values in the geographic region for which it is designed. While all coordinate system definitions make provisions for a false northing, it is often set to zero to disable this feature.

Geocentric Latitude- One of the many forms of latitude used when dealing with an ellipsoid. The geocentric latitude of a point is defined as the angle a line from the center of the earth through the point makes with the plane of the equator. Geocentric latitudes are used only in special applications. Generally, the unqualified term latitude refers to geographic, or geodetic, latitude.

Geodesic- The ellipsoidal equivalent of a great circle to the extent that the geodesic represents the shortest path between two points on the ellipsoid. The shape of a geodetic is not necessarily a circle or an ellipse; although it can be in special cases.

Geodesy- The study of the size and shape of the earth and the mathematics involved in accurately modeling the earth. Geodesy also studies such phenomena as the variations in the shape of an imaginary ocean covering the entire earth. The variations in it would be caused by the non-uniform nature of the earth.

Geodetic- Of or relating to the study of the shape and size of the earth. A geodetic coordinate is the specification of a precise location on the surface of the earth.

Geodetic Reference System- The true technical name for a datum. The combination of an ellipsoid, which specifies the size and shape of the earth, and a base point from which the latitude and longitude of all other points are referenced.

Geoid- The exact shape of sea level, as opposed to the ellipsoid mathematical model. The ellipsoid model is only an approximation required by the mathematical techniques of cartographers. The true shape of the earth (that is, the shape of the sea-level surface) varies from the ellipsoid model by as much as 80 meters above and 60 meters below the best fitting ellipsoid. This varying shape is caused by the non-homogeneous nature of the earth. When dealing with elevations, it is important to know if the elevation is referenced to the ellipsoid (a mathematical model of the size and shape of the earth) or to the geoid (the true representation of the size and shape of the earth).

Geoid Height- The height of the geoid above the ellipsoid in use. Nowadays, this usually refers to the height of the geoid above the WGS84 ellipsoid upon which the Global Positioning System is based.

Global Positioning System- A system based on satellites and sophisticates receivers capable of accurately measuring geodetic location of a receiver at any place in the world. Developed by the U. S. military, the Global Positioning System (GPS) is now widely used in surveying and navigational situations.

GPS- An acronym for Global Positioning System

GRS- An acronym for Geodetic Reference System

Great Circle- Circle produced by the intersection of a sphere and a flat plane which passes through the center of the sphere. Two points on the sphere which are not anti-podal uniquely define a great circle; and the shorter of the two arcs is the shortest path between the two points. The equator is a great circle, and on a sphere, all lines of longitude are great circles.

Grid Scale Factor- A measure of the scale distortion introduced by the projection at any given position on a map or in a Cartesian coordinate system. Technically, the scale distortion varies with the direction in which it is measured; producing an infinite number of grid scale factors at any point. However, for projections with the conformal characteristic, the scale distortion remains constant at a specific point regardless of the direction. Therefore, the term grid scale factor has useful meaning only for projections which are conformal. State plane coordinate systems and the UTM series of coordinate systems are based on conformal projections.

Homalographic- A term rarely used to qualify a projection as having the equal area characteristic.

Homolographic- A term rarely used to qualify a projection as having the equal area characteristic.

Latitude- The north/south component of the spherical coordinate system most widely used to record geodetic locations. Originally, when the earth was thought to be spherical, a degree of latitude represented one degree of arc on the surface of the earth, referenced to the center of the earth. Now that we know the earth to be ellipsoidal in shape, there are several types of latitude. The usual definition of latitude is the angle a line perpendicular to the surface of the ellipsoid (i.e. a plumb line) makes with the plane of the equator. This is also referred to as the geographic latitude or geodetic latitude. Whenever the unqualified term latitude is used, it is generally accepted that it refers to the geographic latitude. Normal conventions dictate that north latitudes be given in degrees, where positive numbers indicate north latitudes and negative numbers indicate south latitudes.

Longitude- The east/west component of the spherical coordinate system most widely used to record geodetic locations. Lines of longitude are great circles/geodesics, all of which pass through the north and south pole and intersect the equator. That is, all lines of longitude proceed in a true north/south direction. The imaginary lines of longitude are assigned values which represent, in degrees of arc, the distance of the line from the prime meridian. The line of longitude that passes through Greenwich, England is the most common prime meridian in use today.

Meridian. In a cartographic/geodetic context, a meridian is a line of longitude. Meridian originally meant midday; a sailing vessel would determine its longitude by recording the time shown by the ship's chronometer when the sun reached its meridian (midday or noon). Because the chronometer always showed the time at Greenwich (the prime or zero meridian), the difference between the local meridian time (noon) and Greenwich time was the vessel's longitude.

North American Datum of 1927 (NAD27)- A datum based on the Clarke ellipsoid of 1866, with a base station at Meades Ranch in Kansas. NAD27 used the latitude and longitude for Meades Ranch and the Clarke 1866 values to determine the latitude and longitude of over 50,000 surveying monuments throughout the contiguous United States and Alaska. These monuments served as starting points for more local surveying and mapping efforts. Over the years, stations were added to the network and there are now over 267,000 stations of varying quality. Use of this datum is gradually being replaced by the North American Datum of 1983.

North American Datum of 1983 (NAD83)- An earth-centered datum based on the Geodetic Reference System of 1980. The size and shape of the earth was determined through measurements made by satellites and other sophisticated electronic equipment; the measurements accurately represent the earth to within two meters. The datum is called earth-centered (or geocentric) because its reference point is the center of the earth, as opposed to a point on the earth's surface. In developing NAD83, the National Geodetic Service used data from NAD27. As a result, the latitude and longitude assigned to all 267,000 NAD27 monuments has changed by as much as 350 feet.

Origin Latitude- The latitude of the geodetic location at which the projection formulae produce zero values for the resulting Cartesian coordinates, before the false easting and false northing are applied. In certain cases, the origin latitude is implied by other elements of the coordinate system definition. The origin latitude of the Hotine Oblique Mercator, for example, is a point where the central great circle intersects the equator and it is calculated from the other elements of the coordinate system definition.

Origin Longitude- The longitude of the geodetic location at which the projection formulae produce zero values for the resulting Cartesian coordinates, before the false easting and false northing are applied. In many coordinate system definitions, the origin is implied by other elements of the definition. For example, the origin longitude of all coordinate systems based on the Transverse Mercator projection is the central meridian, simply because it is the nature of the projection. Coordinate systems based on any conic projection, however, require that you specify both an origin longitude and an origin latitude.

Orthometric Height- Another name for the elevation of an object. Essentially, the height of an object above the geoid.

Orthomorphic- An adjective which, when used in the context of naming or describing a projection, has the same meaning as conformal.

Parallel- In a cartographic/geodetic context, a parallel is a specific line of latitude. Lines of latitude are called parallels because they are parallel to all other lines of latitude.

Platte Carree Projection- Used to refer to the result of using the Equidistant Cylindrical Projection and setting the origin latitude and standard latitude to the equator. This term is also used to refer to the result of using latitudes and longitudes directly in Cartesian based systems such as CAD products. This is the effective result of using the Equidistant Cylindrical projection as described and setting the radius of the sphere equal to 57.29577951 (i.e. one radian in degrees).

Prime Meridian- The specific meridian (i.e. line of longitude) which is assigned the value of zero and to which all other meridians are referenced. While Greenwich is almost universally accepted as the prime meridian, several other meridians (such as the meridian of Paris) remain in use.

Projection- A mathematical development of one surface onto another. In the cartographic context, one surface is the earth and the other is a flat surface such as a map. The mathematics usually convert from the spherical coordinates of latitude and longitude to a Cartesian coordinate system. The projection is one element of a coordinate system definition.

Rectangular Projection- Another name used to refer to the Equidistant Cylindrical Projection.

Rhumb Line- A line or path on the ellipsoid which has constant azimuth. That is, a line or path which intersects all meridians at the same angle. A plane or ship which steers a specific course travels along a rhumb line.

Scale of the Central Meridian. See Scale Reduction Factor.

Scale Reduction Factor- The degree of distortion produced by a cylindrical projection can be reduced by shrinking the cylinder into the earth slightly. This reduces the greatest distance from the surface of the earth to the cylinder over the geographic region of interest, thus reducing the maximum degree of distortion. This also distributes the distortion more evenly across the map. Mathematically, this shrinkage is achieved by applying a scale factor to the cylinder. This scale factor is often called the scale reduction factor or the scale of the central meridian. This value is usually close to but less than one. In fact, it is usually set to the cosine of one quarter of the width of the geographic region being mapped. For example, a UTM zone is six degrees wide, therefore the scale reduction factor is set at the cosine of 1.5 degrees, or 0.9996.

Small Circle- The circle produced by the intersection of the sphere with a flat plane, where the plane does not contain the center of the sphere. Parallels of latitude, other than the equator, are special cases of small circles.

Standard Parallel- An element of conic projections indicating the latitudes where the projection cone enters and leaves the earth. For a coordinate system in the northern hemisphere, for example, the northern standard parallel indicates where the cone enters the earth, and the southern standard parallel indicates where the cone leaves the earth. It might help to imagine the conic projection as a conic party hat placed on top of the earth. Shrinking the cone into the earth reduces the maximum distortion introduced by the projection and the projection distortion is more evenly distributed over the region being mapped. The standard parallels, therefore, indicate the region being mapped, and also, because of the distance between the two, the degree to which the cone has been mathematically recessed into the earth. Some coordinate systems based on conic projections have a single standard parallel, indicating that the cone has not been recessed into the earth. To define such a coordinate system, it is common to enter the same value for the northern and southern standard parallels. The term standard parallel is also used with the normal aspect of several cylindrical projections. In this case, it usually indicates the latitude at which the projection surface, in this case the cylinder, intersects the earth.

Simple Cylindrical Projection- Another name for the Platte Carree projection.

State Plane Coordinate Systems- A complete system of coordinate systems by which Cartesian coordinates are assigned to all 50 states. The system consists of as many zones as are necessary to define coordinate systems where the scale distortion introduced by the projection is less than one part in 10,000. To achieve this objective, different states use different projections, and many states require more than one zone. For example, the state of Idaho, whose largest extent is north/south, uses the Transverse Mercator projection, and because of its size, requires three separate zones to achieve distortion less than one part in 10,000 within any zone.

Universal Transverse Mercator (UTM)- A series of 120 coordinate systems based on the Transverse Mercator projection originally developed by the U. S. Army for a world-wide mapping project. Sixty zones are used to map the northern hemisphere and the remaining 60 apply to the southern hemisphere. Each zone is six degrees wide and is numbered. Zone one covers longitudes of 180W through 174W. The remaining zones are numbered sequentially as they move east. All zones have their origin at the equator, use the meter as the system unit, and have a false easting of 500,000 meters and a false northing of zero. A scale reduction factor of 0.9996 is used on all zones. Zones for the Southern Hemisphere are identical to their northern counterpart except that the false northing is set to 10,000,000 to eliminate negative y-coordinates.

WGS- An acronym for World Geodetic System.

World Geodetic Reference System of 1984 (WGS-84)- The United States Defense Mapping Agency's Datum. This datum is a global datum based on electronic technology which is still to some degree classified. Data on the relationship of as many as 65 different datums to WGS-84 is available to the public. As a result, WGS-84 is becoming the base datum for the processing and conversion of data from one datum to any other datum. The Global Positioning System (GPS) is based on this datum. It should be noted that the difference between WGS-84 and NAD83 is small, and is generally considered to be insignificant.