For many of us, our familiarity with latitudes and longitudes comes largely from the straight lines on a Mercator map of the world, or the nearly straight lines on the edges of a USGS topographical map. However, since the Earth is roughly a sphere, latitude and longitude are actually a system of special coordinates used to assign a unique and spatially consistent coordinate pair to each point on the surface of the earth. Due to the spherical nature of these coordinates, the novice cartographer often experiences difficulty getting used to dealing with them.
      One of the first problems a novice cartographer may encounter is trying to keep straight which one is which. One memory gimmick is based on the work of the ancient Greek, Hippocrates-the scientist generally credited with inventing latitudes and longitudes. He referred to latitudes as climatica, or as the climate changes the latitude changes. Thus, if one associates the "at" in climate with the "at" in latitude, changes in latitude can be associated with changes in climate as one moves north and south. Similarly, you can relate time and longitude. As you proceed from one time zone to the next travelling east or west, the local time changes. Therefore one can associate "long," as in a long sermon, with longitude-the measure which determines the local time zone.
      Meridian, as an adjective, is defined by Webster as "pertaining to noon, especially the position of the sun at noon." With the aid of a chronometer which maintained time at Greenwich, early navigators determined their longitude position by simply noting Greenwich time at the local meridian, i.e., noon, as determined by the position of the sun. The difference between local noon or meridian noon and Greenwich time, was used to calculate the longitude of their current position. Lines of longitude are, therefore, often referred to as meridians, such as the Greenwich Prime Meridian.
      Assuming for a moment that the Earth is a sphere, lines of longitude are great circles. A great circle on a sphere is a line created by the intersection of the surface of the sphere with a flat plane which passes through the center of the sphere. In the case of longitude, the flat plane must also pass through both of the poles. As a result, all lines of longitude are great circles which intersect at both poles. Therefore, the distance between lines of longitude varies and shrinks from approximately 111,324 meters at the equator, to zero at both poles. A reasonably good approximation of the distance between two lines of longitude at any point can be had by multiplying the 111,324 by the cosine of the latitude at the point in question. Use the number 365,235 if you prefer to work in feet.
      Lines of latitude are not great circles. They are formed by the intersection of the Earth's surface with a flat plane parallel to the equator. Therefore, the plane of every line of latitude is parallel to the plane of every other line of latitude, with lines of latitude often referred to as parallels. The 38th parallel in Korea, or the 49th parallel, which is the border between much of the U.S. and Canada, are examples. Since they are parallel, the distance between any two lines of latitude remains constant regardless of the longitude. However, the distance between lines of latitude is not exactly the same. This is due to the definition of latitude and the fact that the Earth is closer to an ellipsoid than a sphere.
      Latitude is defined as the angle a line perpendicular to the surface of Earth makes with the plane of the equator. Due to the ellipsoidal nature of the Earth, the curvature of its surface is greater at the equator at the poles and, therefore, the distance between lines of latitude actually increases slightly as one moves from the equator toward either pole. The common perception that a degree of latitude is the same as a degree of longitude at the equator is therefore not exactly correct.
      At the equator, the distance between two lines of latitude is approximately 110,575 meters and increases to approximately 111,700 at the poles. The distance between lines of longitude at the equator, and the distance between any two lines of latitude, can be approximated by 111,000 meters, or 60 nautical miles. Note, the nautical mile is very close to being one minute of latitude-this is not by accident.
      Most all spatial measurements require a specific reference. In the case of latitude, this reference is the equator. The equator is a physical phenomena which is, conceptually, well defined. That is, it represents a great circle produced by a flat plane which passes through the center of the Earth and is perpendicular to the axis of rotation. However, no natural phenomenon exists for a reference point for longitude. Prior to 1884, there was no standard for referencing longitudes, and many different references were used.
      The ancient Greeks used a meridian passing through the island of Peno as their reference point. Ferro is one of the Canary Islands and was the western extent of what was the known world. Since then, meridians which passed through London, Paris, Rome, Oslo, and just about every other place (including Philadelphia) were used.
      At an 1884 conference appropriately referred to as the international Meridian Conference, the meridian used by the British Navy, the predominate naval organization of the world at the time, was adopted as the reference point for longitudes. This placed the meridian which passes through the Observatory of Greenwich as the standard reference for measuring longitude. Today, we refer to this as Greenwich Prime Meridian or simply Greenwich. There may be times that one might still encounter references to the Meridian of Paris which is 24'22.34" east of Greenwich.
      Latitude and longitude are usually given in degrees in that there are 360 degrees in a complete circle. The grad is another unit, commonly used in Europe, and there are 400 grads in a complete circle. Therefore, the latitude of the north pole can be given as 100 grads or 90 degrees.
      Most Computerized Aided Drawing systems (CAD) are based on the standard right handed Cartesian coordinate system. This system requires that 1) all units of X are the same, 2) all units of Y are the same, 3) every unit of X is the same as every unit of Y, 4) X coordinates increase to the right, and 5) Y coordinates increase up. Since the linear distance between lines of longitude varies with the latitude, and since the distance between lines of latitude vary with the latitude itself, using latitude and longitude values for X and Y coordinates in such a system (e.g., AutoCAD) produces rather odd looking maps. This does not mean that you can't use AutoCAD or other Computerized Aided Design systems to work with latitude and longitude numbers; it means that you must get used to the odd looking shape of things if you do.
      The right handed Cartesian coordinates system upon which CAD systems are based, requires that the X values increase to the right, and the Y values increase in the up direction. Observing the lines of longitude in the U.S., one sees that the numeric values assigned to them increase as one proceeds to the left. This is because the longitude is measured as being west of the Greenwich Meridian. This inconsistency can be resolved with a simple convention: Always use negative values for west longitude. A similar situation exists with south latitude. It is therefore customary to use positive values for east longitude and north latitude, while negative values are used for west longitude and south latitude.
      With these facts in mind, novice car-tographers should be able to comfortably deal with latitudes and longitudes. The terminology introduced here will also make dealing with other cartographic concepts, such as the projection, a bit easier as well.

About the Author:
Norman Olsen is president of Mentor Software Inc. in Thornton, Colo. He may be reached at 303-252-9090.

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