FINDING THE ISLE'S LATITUDE
"Hark to the Lassie and Ye'll find Y'r way!"
|"Lulu, what do these clues tell us about latitude?!"|
|"First of all, Lou, you have to remember what lines of latitude are! They're circles on the earth's surface that are perpendicular to the earth's north-south axis! "|
|"And they're numbered from 0° at the equator to 90° N and 90° S at the poles!"|
|"Right! But you have to understand what those numbers mean! They're meaured in degrees, right!? That means they're angles!"|
|"Angles between what?"|
|"The angle formed by a line that goes from a place on the surface of the earth (B) to the center of the earth (C) and a line from the center of the earth (C) to the equator (0°)! For example, in the diagram, the angle BC0° - which in this case is 22°. And it's a north latitude because it's north of the equator!"|
|"And how ya going to find that angle? Start digging holes to the center of the earth??!"|
| "Like yeh, Lou! Don't be an idiot!"|
"Have you ever noticed, Lou, that the world looks like you're in the middle of a hemisphere? The sky is a dome above your head, and it's like the land about you is a vast circle extending to the horizon?!"
|"But what's really going on is quite different. Here you can see me (the tiny green blob) standing on the sphere of the earth, looking about me in all directions! I can only see the close part of the earth's surface; places further off are hidden by the curve of the earth! The part I can see is roughly a circle and is bounded by the horizon!" |
|"Actually, the last diagram is very distorted! I am much too large compared to the size of the Earth! This diagram is a bit closer to the way it is! You can see that the tiny section of the curve of the earth that is shown is very close to a straight line! In fact, we we won't go wrong if we pretend that it really is a straight line! The limits of my vision (my horizon) is indicated by the two red arrowheads and the letters 'H'. Notice that the line to the center of the earth is perpendicular to the straight line!" |
| "Here's another view of the situation! I've made myself nice and large! I'm standing on the surface of the Earth at B. I'm having a good time, basking in the sun's rays (S)! Line H-H represents the way the earth looks to me - more or less flat, extending out in all directions to my horizon! Once again, line H-H is perpendicular to the line that goes to the center of the earth (line BC)! BC is a radius of the earth!"|
"I don't know it yet, but I'm standing at latitude 22° N!"
| "Here I've moved slightly to the side to let you see what's going on! I've also extended line CB to R. If I were standing at B, R would be directly over my head! Notice my latitude angle, BC0°!"
"Now watch this, Lou! At noon on the equinox, at the equator (0°) the sun is directly overhead! So, at that moment, the sun's rays are coming in to the Earth parallel to line C0°!"
"Now where I am, the sun at noon is not directly overhead! It makes an angle, RBS with overhead! Notice that angle RBS is equal to angle BC0°! That is, the angle that CBR (the blue line) makes with the sun's rays (yellow line SB) is equal to my latitude angle, BC0°! So, at noon where I am, the sun is not overhead - it is 22° away from overhead!"
|"So all you need to do to get your latitude - assuming it's the equinox and it's noon, which clues 1 and 3 tell us it is - is measure the angle between the sun and the vertical! Sounds easy!"|
|"In practice, Lou, it's easier to get the angle the sun makes with the horizon using a sextant and subtract that angle from 90°! Angle SBH is the angle we want! 90° minus 68° = 22°!"|
|"All this theory is great! But we're not at the Island so we can't measure the elevation of the sun!!"|
|"You're right, Lou! But there's two other clues! Clues number 4 and 5!"|
|"OK! I'll hold a stick upright, perpendicular to the ground! Its length is BC! The length of its shadow is AB! Line CA, from the end of the shadow to the top of the stick, points to the sun! So the angle we want, the angle between the horizontal and the sun, is angle CAB!"|
|"Right, Lulu! But there are two possibilities....!"|
|"Right, Lou! But look at clue number 4....!"|
|"WE GOT IT!!"|
If ye think ye have the latitude now, check it out below!
INSTRUCTIONS: Enter each answer in the appropriate box and then click the button to the right of it to find out if the answer is correct. Make sure not to enter letters or other symbols when numbers or numerical values are asked for. If letters are asked for, always enter them as capital letters.
"When ye've figured out the latitude, return to the treasure trail!"
©David J. Leveson