Latitude and Longitude: The Geographic Grid (Introduction)

  I. Introduction to the Geographic Grid
     A. In order to measure accurately the position of any place on the 
        surface of the earth, a grid system has been set up.  It pinpoints 
        location by using two coordinates:  latitude and longitude.
     B. It is purely a human invention, but it is tied to two fixed points 
        established by earth motions:  the poles, or ends of the earth's 
        rotational axis.
        1. Longitude represents east-west location, and it is shown on a map 
           or globe by a series of north-south running lines that all come 
           together at the North Pole and at the South Pole and are the widest 
           apart at the equator -- these lines of longitude are called 

           Figure 1 -- meridians of longitude

          [ globe showing meridians ]

        2. Latitude represents north-south location, and it is shown on a map 
           or globe by a series of east-west running lines that parallel the 
           equator, which marks the midpoint between the two poles all around 
           the earth's circumference -- these lines of latitude are called 

           Figure 2 -- parallels of latitude

          [ globe showing parallels ]

        3. Be aware of the potential for confusing yourself:
           a. Longitude = E/W location, but it is shown by a series of N/S 
              running lines called meridians.
           b. Latitude = N/S location, but it is shown by a series of E/W 
              running lines called parallels.
        4. If you look at Figure 1 more closely, notice that meridians connect 
           all places on Earth having the same longitude (or E/W location): If 
           you mark a whole bunch of places having the same longitude with 
           dots and then connect the dots, you create N/S running lines, or 
        5. Looking at Figure 2 above, notice that parallels connect all places 
           on Earth having the same latitude (or N/S location):  If you mark 
           several places having the same latitude with a series of dots and 
           then connect all the dots, you create E/W running lines, or 
           parallels (that are all "parallel" with the equator).
     C. There is an infinite number of these latitude and longitude lines, 
        because every place on Earth is at the intersection of a particular 
        parallel and a particular meridian.
     D. Maps and globes, however, generally only show a few selected (and 
        mathematically convenient) parallels and meridians, e.g., by tens or 
        fifteens or thirties.  Otherwise, a map or globe would be one big mess 
        of dark ink!

 II. Great and Small Circles
     A. The geographic grid is built of intersecting great and small circles 
        with with half-great circles.
        1. Definitions: 
           a. A great circle is created whenever a sphere is divided exactly 
              in half by a plane (imaginary flat surface) passed right through 
              its center.  The intersection of the plane with the surface of 
              the sphere is the largest possible circle you could manage to 
              draw on that sphere's surface.  

              Figure 3 -- different ways of creating great circles

              [ exploded globes showing great circles ]

           b. A small circle is any circle produced by planes passing through 
              a sphere anywhere except through its exact center.  It will of 
              necessity be smaller than a great circle, hence the clever name.

              Figure 4 -- a small circle 

              [ exploded globe showing a small circle ]

        2. Relevance to latitude and longitude
           a. The equator is a great circle drawn along a latitude of 0
           b. The North Pole and the South Pole are single points at 90 N 
              or S
           c. All other parallels are small circles drawn parallel to the 
              equator; viewed from above one of the poles, they create a 
              bull's eye pattern in that hemisphere with the pole at the 
              center (see Figure 2.
           d. All meridians are half-sections of great circles, all of them 
              coming together at both the North Pole and the South Pole (see 
              Figure 1.
     B. Properties of great circles:
        1. They always result when a plane passes through the exact center of 
           a sphere, regardless of the plane's orientation when it enters the 
        2. A great circle is the largest possible circle that can be drawn on 
           the surface of a sphere.
        3. An infinite number of great circles can be drawn on any sphere.
        4. One and only one great circle can be found that will pass through 
           two specified points on the surface of a sphere, unless those two 
           points happen to be exactly opposite one another (antipodes, 
           pronounced "ant-TIP-id-dees"; the singular is antipode, pronounced 
           "ANTIE-pode").  An infinite number of great circles can be drawn 
           through antipodes.  For example, the North Pole and the South Pole 
           are antipodal and you can draw an infinite number of meridians 
           (which are sections of great circles) through them.
        5. The arc of a great circle is the shortest surface distance between 
           any two points on a sphere:  It's the analogy of the old adage 
           about a straight line being the shortest distance between two 
           points (on a plane, that is).
        6. Intersecting great circles always cut one another exactly in half.
     C. Practical uses of great circles:
        1. They can be used to find the shortest route for a ship, airplane, 
           or, less happily, a missile that must cross great distances.  
        2. You can find the great circle route between two places on a globe 
           by stretching a string or rubber-band between any those two 
           locations on the globe:  It'll settle on the great circle.
        3. When you sample headings for a variety of places on the great 
           circle route and then transfer the resulting line segments onto a 
           flat map, like a wall map, you'll produce a weird-looking path that 
           forms an arc between the two places (instead of a straight line).  
           a. The reason it looks so bizarre is that a globe is a three-
              dimensional sphere, but a map is a flat two-dimensional 
              representation of that sphere:  It is necessarily distorted, so 
              your shortest route looks like a long, circuitous route on the 
              distorted flat map.
           b. That's why, if you've ever flown from someplace like London to 
              Los Angeles or from, say, Tokyo to New York, they fly you over 
              northern Canada and its Arctic climes!
           c. You might want to experiment with this with a globe and a flat 
              atlas map to convince yourself of it.  Or you can just trust me!
 III. Latitude
     A. Latitude is distance north or south of the equator.
     B. The latitude of any given place is its distance, measured in degrees 
        of arc, from the equator.
     C. Latitude is reckoned in both directions from the equator, so the 
        equator is numbered 0 and the poles 90N and 90S.
        1. The reason that 90 is the top number possible for latitude is 
           that, by starting at the equator (the midpoint between the two 
           poles), we measure one fourth of a circle to get to each pole.
           a. A circle is 360 of arc.
           b. 360 divided by 4 is 90

                   [ 1/4 circle ] 
        2. Except for the equator, the suffix "N" or "S" must appear after the 
           number given for the latitude:  It definitely helps to know which 
           hemisphere we're talking about (as your ship is sinking), since the 
           numbering is the same in each hemisphere.         
     D. Subdividing latitude:
        1. A degree of latitude is approximately 110 km of linear distance 
           (~69 mi. or so):  If that's as much precision as you need, you 
           would write your latitude as, for example, lat. 34N (here in 
           Long Beach)
        2. If you need more precision, you can include minutes of arc. 
           a. Minutes of arc are similar to minutes of time in that one minute 
              of latitude is 1/60th of a degree, and there are 60 minutes of 
              arc in 1 degree.
           b. Just as with time, a minute of arc is represented by an 
              apostrophe: '.
           c. One minute of latitude is equal to about 1.83 km of linear 
              distance (that would be roughly 1.15 mi.).
           d. Refining a latitude reading to the minute level, then, would be 
              written like this one: lat. 3349'N.
        3. If you really need even more precision (that ship is going down 
           fast and you see some fins circling in the water), you can break a 
           minute of arc down, just as with time, into seconds of arc.
           a. One second of arc is 1/60th of a minute; there are 60 seconds of 
              arc in a minute 
           b. Put another way, one second of arc is 1/3600th of a degree, and 
              that means there are 3600 seconds in a degree (kind of like 
              there are 3600 seconds in an hour).
           c. Seconds of arc, like seconds of time, are represented by a 
              quotation mark: ".
           d. One second of arc is about 0.031 km (or 0.019 mi.), which is 
              very roughly 30 m or 100 ft.
           e. Taking a latitude reading down to the second level would be 
              shown as something like: lat. 33 49' 04" N (Long Beach 
        4. Latitude is represented in degrees, minutes, and seconds, a system 
           of measure by sixes that goes back to the ancient Chaldeans and 
           Babylonians.  It's the same system we use to reckon time.  You are 
           not supposed to subdivide latitude (or longitude) in decimal units:  
           33.75N is not traditionally acceptable.  What would be 
           acceptable is 3345'N or 33N.  
     E. How latitude is represented on a globe or map:
        1. Cartographers use parallels to depict that part of the geographic 
           grid that refers to latitude.
        2. Parallels (with three exceptions) are entire small circles, 
           produced by passing planes through the earth parallel to the 
           equator at a particular latitude.
        3. The exceptions are:
           a. The equator itself, which is an entire great circle;
           b. The north and south poles, which are each single points.
        4. Other characteristics of parallels:
           a. Parallels are always parallel to each other (except, of course, 
              the two poles)
           b. All parallels are true east-west lines (except the poles), used 
              to represent north-south latitude with respect to the equator.
           c. Parallels always cross lines of longitude at right angles 
              (except the poles).
           d. An infinite number of parallels can, theoretically, be drawn on 
              the globe, which means all locations on Earth lie on a parallel.
 IV. Longitude
     A. Longitude is distance east or west of a base line or prime meridian 
     B. The longitude of any given place is its distance, measured in degrees 
        of arc, from this base line.
     C. Picking a base line from which to begin numbering longitude was not 
        the easy matter that it was with latitude.
        1. Latitude uses the midpoint between the two poles, the equator, as a 
           base line, and this is a pretty obvious line given by the rotation 
           of the earth.
        2. There is no such naturally obvious base line for longitude, and so 
           each country figured that the meridian of its capital should merit 
           the honor.  This led to years of international bickering and 
           cartographic confusion. Some cities that have been used for prime 
           meridians include Munich, Warsaw, Brussels, Rio de Janeiro, 
           Copenhagen, Amsterdam, Lisbon, Paris, Madrid, Rome, Stockholm, and, 
           of course, Washington, DC.
        3. These excesses of patriotism, of course, made communications among 
           ships at sea difficult and even on board a single ship with its 
           often multicultural crews kidnapped from various ports!
        4. In 1871, the International Geographical Congress met to resolve the 
           issue and recommended that the meridian passing through the old 
           (1675) Royal Observatory in Greenwich, England (a borough of 
           London) should be the common zero.  The proposal didn't get too 
           far, given all the national pride problems that kept erupting.
        5. The IGC met again in 1875 and, again, things weren't proceeding too 
           well.  The French did suggest that they might be willing to 
           relinquish their demand for Paris as the Prime Meridian if everyone 
           else agreed to sign onto the metric system, which had been 
           developed during the French Revolution.  This did pave the way for 
           a break in the logjam, though. 
        6. In 1884, the British agreed to adopt the metric system in exchange 
           for the honor of having the Prime Meridian passing through a London 
           suburb.  So, the Greenwich Meridian was finally passed at the 
           International Meridian Conference held in Washington, DC, and 
           attended by delegates for 41 nations (Santo Domingo was the sole no 
           vote, and France and Brazil abstained).
           a. Greenwich probably won because the USA had already decided to 
              use it rather than Washington, DC.
           b. Also, at the time, 72% of the entire world's trade was carried 
              on ships that used the Greenwich Meridian:  This was the age of 
              empire, and Britain had colonies all over the world ("the sun 
              never sets on the British Empire") and was, therefore, in a 
              position to strongarm the rest of the world into giving its own 
              Royal Observatory the honor.  
           c. Despite the imperialism involved in this choice, it worked out 
              fairly well internationally:
                i. The antipodal meridian to the Greenwich Meridian makes a 
                   mathematically convenient International Date Line (more on 
                   that in another lecture) of 180
               ii. The antipodal meridian to Greenwich's is out in the middle 
                   of the Pacific Ocean, where the date issue can 
                   inconvenience the fewest people in the sparsely settled 
                   mid-Pacific. Not that the British gave a hoot about that, 
                   but it worked out rather well in the end.
           d. Greenwich, incidentally, is pronounced "GREN-itch," not "Green-
              witch" (go figure)
     D. Anyhow, latitude is reckoned in both directions from the Greenwich 
        Meridian, so this base line is numbered 0 and the antipodal line 
        is numbered 180.
        1. The reason that 180 is the top number possible for longitude 
           is that, by starting at the base line (an arbitrary choice of a 
           meridian, which is one half of a great circle stretching from the 
           North Pole to the South Pole), we measure one half of a circle to 
           get to the antipodal meridian (the other half of the same great 
           circle that the prime meridian is on).
           a. A circle is 360 of arc.
           b. 360 divided by 2 is 180

                   [ 1/4 circle ] 

        2. Except for the prime meridian and the antipodal meridian (most of 
           which is the International Date Line), the suffix "E" or "W" must 
           appear after the number given for the longitude:  It definitely 
           helps to know which hemisphere we're talking about, since the 
           numbering is the same in each hemisphere.         
     E. Subdividing longitude:
        1. There are no linear equivalents for degrees, minutes, and seconds 
           of longitude that are applicable all over the world, the way there 
           are for latitude.  This is because the meridians of longitude are 
           spread out the farthest at the equator (where a degree of longitude 
           would be about 110 km on the ground) but they converge as you 
           approach the poles:  By 60 N or S, one degree of longitude is 
           down to about 55 km on the ground and, at the poles, it's zero.
        2. So, other than that caveat, we use the same units of arc for 
           pinpointing longitude as we do for latitude:  degrees, minutes, and 
           a. long. 118W
           b. long. 11809'W
           c. long. 11809'06"W (Long Beach Airport again)
           d. Some nice geotrivia for you:  If you would like to know the
              latitude and longitude of any American city, you can click here.
     F. How longitude is represented on a globe or map:
        1. Cartographers use meridians to depict that part of the geographic 
           grid that refers to longitude.
        2. All meridians are half sections of great circles.
        3. Meridians are spaced the farthest apart at the equator and converge 
           closer and closer together until they actually touch at each pole.  
           At the equator, then, a degree of longitude is roughly 110 km wide 
           but this drops to about 55 km by 60 N or S, and down to 0 
           at each pole.
        4. Other characteristics of meridians:
           a. All meridians are true north-south lines used to represent east-
              west longitude with respect to the Prime Meridian.
           c. Meridians always cross lines of latitude at right angles (except 
              the poles, which are points of latitude).
           d. An infinite number of meridians can, theoretically, be drawn on 
              the globe, which means all locations on Earth lie on a meridian.