# Latitude and Longitude

The use of degrees, minutes, and seconds dates to the Babylonians, whose mathematics relied heavily on both 60 and 12.  This influence remains with us today for both time and circles.  Most of mathematics prefers radians to degrees, and in fact GIS software, like Excel or Matlab, actually will use radians for angular computations.

There are many conventions for how to record latitude and longitude, and they present  challenges for a computer.  How to record the minutes and seconds ('/'' or m/s or min/sec), and whether to record in decimal degrees, or decimal minutes, or decimal seconds means that coordinates are often ambiguous, if not to you then for the GIS program. To avoid problems, unless a program explicitly prompts or allows to use use minutes or second, you should always use decimal degrees; it is easy to use a spreadsheet to convert if necessary.

Latitude/longitude coordinates follow a regular Cartesian system starting from the Equator and the Prime Meridian.  Positive coordinates are to the right (east) and up (north). This means that the Western Hemisphere has negative longitudes.  If you create databases which do not plot on the map, you should check on a full world map to see if they are plotting in the wrong hemisphere, which is a common student problem when entering coordinates in the Western or Southern hemisphere..

The origin of the coordinate system is arbitrary for longitude, but tied to physical reality for latitude.  Latitude is defined from the locations of the geographic poles and the equator, which can be objectively measured for Earth or any other planet that rotates.  Celestial navigation can determine latitude with relative ease.  A host of parameters on earth depend on latitude: climate, vegetation, length of daylight; latitude is perhaps the single most useful thing to know about a place on earth.  Longitude, on the other hand, has no logical starting location, and is very hard to determine with celestial navigation.  Accurate longitude required very precise clocks, and was not easily calculated until the mid 18th century.

 French 1:250,000 map of 1901, showing the 0° meridian running through Paris. Eventually all mapmakers agreed to standardize on a prime meridian through Greenwich (in the 1880's), but even after that time, not all maps could be immediately redrawn. One interesting alternative to Greenwich was used in Austro-Hungarian empire maps in the 19th century.  This is a 1:200,000 scale 1906 map of Adrianople near the World War I battlefields of Gallipoli.  This measured longitude from Ferro, which goes back to Ptolemy.  Ferro is the smallest and westernmost of the Canary Islands (the edge of the known world for Ptolemy).   Making Ferro the starting point for longitude made all longitudes east (and positive).  If you have ever dealt with mapping around the Prime Meridian, the possibility of having both positive and negative longitudes in a single project area greatly complicates matters, and is the reason that the UTM projection uses a false easting (and false northing in the southern hemisphere).
 1778 Map of New Jersey (reprinted by USGS for the sesquicentennial in 1937).Longitude was measured from Philadelphia, although a table showed that Philadelphia was 75˚10' 0" west of London.

You may occasionally see only positive coordinates for longitude, from 0 to 360, which places the US in the 240-290 degree range.

Approximate conversions, degrees to metric.

Last revision 5/8/2019