# Lecture: The Geographic Grid (Latitude)

```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 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
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
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. 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
Airport).
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.
F. How latitude can be determined if you have no idea where you are (an
1. If you're going to get lost, it'll be a lot easier on you if you
plan to get lost on a clear night in the Northern Hemisphere.
a. If you do get lost under these ideal conditions, you can use the
b. The North Star is almost perfectly located above the North Pole.
c. Uhhhhh, how do you find it?
i. Well, pack a compass (and a working flashlight) after
learning how to use it:  That will at least get you pointed
in the right general area of the sky.
ii. To find Polaris, you need to find the Big Dipper.
a. The Big Dipper is a constellation, or traditional
grouping of stars.  Actually, it's an asterism (or group
of stars within another constellation, in this case,
URSA MAJOR, the Great Bear).  This group of stars is
named for a dipper.  Whuzzat? you ask?  In the olden
days, before coffee and juice bars, when you got
thirsty, you went to the village well.  You pulled up a
bucket of (hopefully) fresh water and used the attached
cup with a long hook-handle to slurp it up (this was
before we worried about disease-causing organisms).
b. The ancients thought that this group of stars kind of
looked like the communal dipper, hence the name
(eeeeeuuuw!).
c. It's a group of seven stars, four of them arranged in a
trapezoid that kind of looks like a cup, with another
three trailing off in a curve that sort of looks like
the long, curved handle of a dipper.  It can be oriented
every which way, depending on the time of the year and
the time of night.  You're looking for a group of stars
that looks like this no matter how it's tilted:

d. Once you've found it, you identify the two "pointer
stars," that is, the two stars on the outside of the
cup, the side away from the handle.  These two are Merak
on the bottom and Dubhe on the upper lip of the cup.
You draw an imaginary line straight up from Merak and
Dubhe above the cup until you spot a rather ordinary
star some distance up:  This unpreposessing star is
Polaris.

d. What do you do with it once you've found it?  What you do is you
measure the angle that the North Star makes with the northern
horizon below it, in degrees of arc.  That measurement is your
(north) latitude.
i. More elegantly put, L = N, where L = latitude and N = North
Star angle.
ii. So, if Polaris makes an angle of 12° with the northern
horizon, you're at 12°N; if it makes an angle of
78°, you're probably pretty chilly, being at 78°N.

e. So, how do you make that measurement?  Well, you have a crude
option and a fancy option here.
i. Crude version: Use your hands.
a. If you stick your arms straight out in front of you and
distance from the tip of your thumb to the tip of your
b. If you ball your hand up into a fist, it's about 10°
c. This works for people with little hands (because they
tend to have shorter arms) and for folks with big hands
(because they tend to have longer arms).  Cool, eh?
d. So, count how many totally stretched out hands, one
touching on top of the other, it would take you to span
the way to Polaris.  Multiply the number of stretched
out hands by 20°  To refine it, use your fists to
get within another 10° of precision (and your
fingers are maybe 2 or 3 degrees or thereabouts).
ii. Fancy version:  Use a sextant.
a. A sextant is a gizmo used to measure angles from you to
a celestial object and to the horizon.
b. It usually looks like a wedge (of brass or bronze in the
olden days, more likely cheesy plastic now) one sixth of
a circle in size, with a movable arm attached to the top
of the wedge, a mirror rigged up on this arm, a bunch of
degrees of arc measured along the bottom skirt of the
wedge, a mirror on one side that is aligned with the
horizon, and an eyepiece on the opposite side.

c. You line the sight up with the horizon and then fiddle
with the arm until you get Polaris or whatever throwing
its reflection from the arm's mirror into the mirror on
the horizon sight and into your eyeballs.  This may take
a while!  Once you have it, you turn the thing over so
you can see the reading on the bottom of the sextant.
2. What if it's not a clear night?  Tough.
3. What if it is a clear night but you're in the Southern Hemisphere?
a. In that case, you can't see the North Star:  It's beyond the
northern horizon out of sight.
b. What you do is use a small constellation, the Southern Cross
(Crux Australis or just Crux to its friends) near the South
Celestial Pole to serve the same function.
i. The South Celestial Pole is that point in the sky above the
South Pole (in the Northern Hemisphere, Polaris is pretty
closely aligned with the Northern Celestial Pole).
ii. The Southern Cross is a tiny constellation (actually, an
asterism) of five apparent stars in a brightly starred
part of the sky.  The asterism is a part of the
constellation, Centaurus, which is embedded in the Milky
Way.  So, locating it may take a while.  The four outer
ones form a perfect little cross (Alpha at the foot, Beta
as the left arm, Delta as the right arm, and Gamma as the
head), while the fifth, much dimmer one (Epsilon) is
offset below Alpha and Delta. Anyhow, you locate the long
axis of the little constellation (Alpha and Gamma) and
extend an imaginary line down from Gamma through Alpha
about 30° below the center of the cross (that is, one
open hand and one fist).  Have fun sighting on that blank
spot in the sky!

iii. No, I'm not going to make you memorize the five stars and
what you do with them!
4. It's a little more difficult if you somehow get lost on a clear or
mostly clear day in whatever hemisphere.
a. If you do this, you are confronted with a few problems that make
i. The sun is at a right angle to your latitude -- more or
less -- because latitude is measured from 0° at the
equator and 90° N or S at the poles.  That is, on the
21st of September, if you're at the equator, the sun is
directly overheard.  Sun angle is, therefore, 90°, but
you certainly aren't at 90° N or S!  If you were
instead at the North Pole, the sun would be right on the
horizon at noon, making an angle of 0° but you sure as
heck aren't at 0°!
ii. The second problem has to do with that "more or less" bit:
The sun changes its declination through the course of the
year, from 23½°N to 23½°S.  That is
47° of confusion, folks!
iii. I suppose a third problem (to make your list of all
possible paranoias complete) is if you have a cheapskate
sextant:  You could burn your retina sighting on the sun (a
good sextant has a series of filters you can flip down
between the mirrors to prevent just this problem).
b. Luckily for you, someone long ago came up with a formula that
takes care of the first two problems at least!  Here's that
equation:

L = 90° - S ± D
Where S = Sun angle reading
D = Declination

first.  Right?
c. Here's how you use that equation.
i. Write L = 90° (builds confidence -- you're halfway
through, right?)
ii. Check to see that it is noon and the sun's at the highest
point in the sky (it's either overhead or to the north or
the south) and it casts the shortest shadows it will all
day.
iii. If it is noon, dust off your trusty sextant and take the
sun angle (now, if we were real navigators, we would be
able to handle the non-noon situation, but we're just
apprentice navigators, so let's not worry about that).
iv. Subtract it from 90° (gosh, you're ¾ through!)
v. Tentatively identify the hemisphere you think you may be
in.  Guess that hemisphere!  Are you in the Northern
Hemisphere or is it the Southern Hemisphere?  Assume for
this lecture that you are in the hemisphere OPPOSITE the
horizon you used to sight the sun.  For example, if you got
a sun angle reading of 20° from the southern horizon,
chances are very good that you are in the Northern
Hemisphere.
California, in a subtropical paradise, as the tourist
literature would put it.  Even so, we never see the sun
get quite overhead at noon.  It is always a little bit
to our south, closer to the southern horizon than the
northern one.
b. If you were in New Zealand instead, the sun would always
pass to your NORTH (how's that for a weird thought?):
They are in the Southern Hemisphere.
c. So use this rule-of-thumb to guess that hemisphere for
the purposes of this class:  Assume you're in the
hemisphere opposite the horizon you used to sight the
sun with.
vi. Now, determine the sun's declination for the date you got
lost (assuming you can even remember that!).  You can
a. Look it up in a declination chart.
b. Probably better, you could look it up in an analemma.
c. You could even count the number of days between today
and the beginning of the year (January 1st = 1) and then
plug in the declination equation:
D = 23.44 * sin [360/365 * (284 + N)]
Where D = declination
N = the number of days from January the first to
today.
vii. Now, ask yourself the burning question:  Is the declination
in the same hemisphere you THINK you're in?  (Here in Long
Beach, we're in the Northern Hemisphere and, during the
summer, the sun's declination is, too; comes winter, we're
in opposite hemispheres.)
a. If the answer is yes, and the sun's declination is in
the same hemisphere you think you're in, then ADD the
declination to the rest of the formula (+ D).  And you
are happily done.  Don't forget to put the proper
suffix, N or S, after the latitude determination.
b. If the answer is no, and the sun is NOT in the same
hemisphere you think you're in, SUBTRACT the declination
from the rest of the equation (- D) and put in the N or
S suffix.  Bet you think that's all there is.  You're
1. Look at that answer.  Did you get a nice, normal
number, or did you get a negative number (e.g.,
-7°S)?
2. If the number is nice and normal, you are done and
outta here. Yesssssss!
3. If the number is negative, you have a problem.
Specifically, you are not in the hemisphere you
thought you were in.  You didn't do anything wrong.
What happened is you turned up somewhere in the
tropics and the sun was farther from the equator than
you were.  Not to worry.  Whatever you do, do NOT go
mess up the whole process if you did that).  What you
do is just drop the negative sign and change the
hemisphere suffix (N or S).  That's all -- and you
are finally done.  If this bothers you, think about
the meaning of a nonsense location, such as -7°S.
What is that location, really?  Imagine a normal
7°S, then a 6 (closer to the equator),then a 5,
4, 3, 2, 1, and then a 0 for the equator.
Continuing, a -1°S is just past the equator 1
little degree.  In other words, it's 1° into the
other hemisphere: 1°N!  Keep going, and you see
that -7°S is just an eccentric way of writing
7°N.
G. Well, that's about enough of latitude for a while.  There will be a
lab based on it, but that will come after you've read the longitude
lecture, which is next.

```

Document and © maintained by Dr. Rodrigue
First placed on web: 09/08/00
Last revised: 02/04/04