Geography 140
Introduction to Physical Geography

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°

                   [ 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. 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 
        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 
        introduction to basic navigation).
        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 
              North Star, Polaris, as your navigation aid.
           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 
                   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:

                      [ Big Dipper ] 

                   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.

                   [ Polaris angle ] 

           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 
                      then spread your hands as widely as you can, the 
                      distance from the tip of your thumb to the tip of your 
                      little finger is about 20° 
                   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.

                      [ variation on a sextant ] 

                   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!

                   [ Crux Australis ]

              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 
              sun navigation a lot worse than Polaris navigation.
                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 

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

              Bet you're shaking your head at the elegance of this solution, 
              slapping your forehead wondering why you didn't just hit on it 
              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 
              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 
                   a. Think about this a minute.  We are in sunny Southern 
                      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 
              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 
                      sadly deluded.
                      1. Look at that answer.  Did you get a nice, normal 
                         number, or did you get a negative number (e.g., 
                      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 
                         back to step five and change your answer (you would 
                         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 
     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