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Latitude and longitude comprises a grid system of lines encircling the globe and is used to determine the locations of points on the earth. Lines of * latitude*, also called

*parallels*, run east - west. Latitude lines always run parallel to each other, and hence, they are always an equal distance apart. Latitude lines never converge or cross.

Lines of latitude measure distance north or south of the equator. The latitude of a particular location is the distance, measured in degrees, between that place and the equator along a meridian, or line of longitude. The **equator **is 0^{o} latitude, and the North and South Poles are located at 90^{o} north and 90^{o} south latitude respectively. In other words, values for latitude range from a minimum of 0^{o} to a maximum of 90^{o}.

If the earth were a perfect sphere (which it isn't), the distance, or the length, of 1^{o} of latitude would be constant everywhere. In reality, the earth is slightly flattened at the poles, so the length of 1^{o} of latitude at the poles is slightly more than at the equator. At the equator, the length of 1^{o} of latitude is equal to 110.6 km (68.7 mi.) and at the poles, the length of 1^{o} of latitude is equal to 111.7 km (69.4 mi.). For our purposes, we will assume the length of one degree of latitude is 111 km.

Lines of **longitude**, also called *meridians*, run north - south. Meridians are farthest apart at the equator, and converge at the North and South Poles. Lines of longitude measure distance east or west of the prime meridian. The longitude of a particular location is the distance along a parallel, measured in degrees, between that place and the prime meridian. The prime meridian passes through the old Royal Observatory at Greenwich, England, and is sometimes referred to as the Greenwich meridian. Since meridians are farthest apart at the equator and converge at the poles, the distance in kilometers (or miles) of 1^{o} of longitude varies from a maximum at the equator, to a minimum at the poles. At the equator the approximate length of 1^{o} is approximately 111 km (69 mi.). At 60^{o} north and south latitudes, the length of 1^{o} of longitude is approximately 55.5 km (34.5 mi.), or half what it is at the equator.

The** prime meridian**, which runs through Greenwich, England, is referred to as 0^{o} longitude. The choice for Greenwich is completely arbitrary, and the prime meridian runs there only for historical reasons. Points are measured east or west of the prime meridian until one reaches the opposite side of the prime meridian, which is referred to as the International Date Line. This is considered 180^{o} longitude, and is the highest value which longitude can take. In other words, values for longitude range from a minimum of 0^{o} to a maximum of 180^{o}.

An infinite number of parallels or meridians can be drawn on a globe. Thus, parallels and meridians exist for any point on the earth. Generally, only selected parallels and meridians are marked on maps and globes, and these are usually spaced equal distances apart. Parallels and meridians always intersect each other at right angles. In order to locate a particular point on the earth, a latitude and a longitude measurement is necessary. As stated above, these measurements are in degrees, but sometimes measurements smaller than degrees are necessary. Traditionally, minutes and seconds were used. A degree contains sixty minutes, a minute contains sixty seconds. Montevideo, the capital of Uruguay, for instance, is at 34 degrees, 54 minutes and 4 seconds south of the equator, and 56 degrees, 9 minutes and 52 seconds west of the Prime Meridian. Decimal degrees are the more prevalent method used nowadays, where minutes and seconds are replaced by fractions of a degree. In that system, Montevideo is at 34.90 degrees south, and 56.16 degrees west.

## The Universal Transverse Mercator (UTM) Grid

Though a spherical coordinate system like latitude and longitude is convenient for large areas, it is cumbersome for small areas. The need for accurate measurements within small areas was realized with the increasing range of artillery during the First and Second World Wars. This spurred the development of rectangular coordinate grid systems as plane rectangular geometry formulas were simpler than spherical geometry formulas upon which latitude and longitude is derived from. The Universal Transverse Mercator (UTM) Grid is one such system.

The Universal Transverse Mercator Grid divides the world into 60 north-south zones, each covering a strip 6° wide in longitude between 84N and 80S. Poleward the Universal Stereographic grid (UPS) is used. These longitude zones are numbered (called the "zone number") from Zone 1, between 180° and 174° west longitude, progressing eastward to Zone 60, between 174° and 180° east longitude. Each longitude zone is subdivided into a latitude zone is 8 degrees high north and south of the equator, and lettered starting from "C" at 80° S, increasing up to "X" (called the "zone designator"). The letters "I" and "O" are omitted because of their similarity to the digits one (1) and zero(0). X spans 12° of latitude.

Each longitude zone is subdivided into an eastern and western half by drawing a line down the middle called the "central meridian". A point can be described by its distance east of the origin, called its "easting" value. The central meridian is assigned a false easting of 500,000 meters to insure positive coordinates. Any easting value greater than 500,000 meters indicates a point east of the central meridian. Any easting value less than 500,000 meters indicates a point west of the central meridian. A point's north-south origin depends on the hemisphere it is in. In the northern hemisphere, the origin is the equator and all distances north (or ‘northings’) are measured from the equator. In the southern hemisphere the origin is the south pole and all northings are measured from there. When writing UTM coordinates, the easting is always first and the northing is after it.

The UTM grid is printed on all U.S. Geological Survey (USGS) maps as blue tick marks in the margins, or as full grid lines. The spacing of the tick marks or grid lines depends on the scale of the map. Point A on the topopgraphic map is located at 599000 E., 4887000 N.