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
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
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
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.
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
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
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
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
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!
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 90°N and 90°S.
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°
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. 34°N (here in
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
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. 33°49'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:
33.75°N is not traditionally acceptable. What would be
acceptable is 33°45'N or 33¾°N.
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.
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°
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. 118°W
b. long. 118°09'W
c. long. 118°09'06"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.