There are many remaining mysteries as to how the ancient Egyptians constructed their royal pyramid tombs. For example: how did they get all those tons and tons of large stone blocks up the sides? Two things we know for sure: the methods had to be simple and low-tech, and that they had plenty of time to think up their clever ideas.
Before we start considering a possible method they might have used to orient their pyramids so precisely to the compass directions, let's try to gain some inspiration from the discovery of how they made the foundation surfaces for the pyramids so precisely flat and level. Remember we are not talking about a small area as the base of the largest pyramid covered nearly 13 acres (about 750 feet on a side). Go outside and see just how much that is - several city blocks, if you live in a city. No, this was not a small "building" even by today's standards!
What the Egyptians did was clear away the sand down to the bedrock, and then they hacked away at the rock to make a level, flat surface. But how did they know that they had made a "level" surface? Simple and low-tech, of course! It was discovered that there is a shallow groove completely around the bases of all the pyramids. When these grooves were cleaned out of all the wind-blown sand, and water was dumped in, the water level was "level" all the way around the pyramid. Thus the flat surface of the foundation was carved away until every portion of it was exactly the same distance above the water level. Simple! Low-tech! Neat, hey? (Soon, as the pyrammid blocks were stacked higheer and hiiiiiiigher, they needed to make upper layers level also. How they may have done that is discussed later.)
So now let's think about how they so precisely oriented each of their pyramids so that one side faced exactly east, another exactly south, and so on. And remember that the magnetic compass wasn't invented yet for another several thousand years (it wouldn't have helped them much since magnetic compasses usually don't point exactly north-south), and they didn't have any global positioning satellites (they'd have to wait for an additional thousand years!). You might want to suggest that they used Polaris, the North Star. But the precession of earth's axis would have meant that Polaris was not close to north at that time. Besides, even if it were, Egypt is so close to the equator that Polaris would have been lost in the haze at the horizon.
What these ancient peoples did have was a rather thorough understanding of the sun. Afterall, the sun was their chief god, and ancient priests and other scholars studied with great care the sun and its daily voyages across the sky. But how can the sun tell us the compass directions? (Do I hear you saying: "It's gotta be simple and low-tech"?)
In the following, you will not have to wear ancient Egyptian clothing as in the picture, nor will you have to use an ankh staff or use rocks on the desert floor.
What is an "Eratosthenes"?
Things you need:
- A flat, level area, perferably made of concrete, such as your driveway. It should be in a place that is sunny all day. You will want to use a carpenter's level to make sure it is close to being truly level. Set the carpenter's level down on the driveway and see if the bubble is near the center of the glass tube. Turn the level 90-degrees to see if it is level that way also.
- Your "ankh" staff - actually you don't need the loop on top - just any permanent stick will do! (As said: low-tech!) Because you are not likely to have a stick permanently in place in your driveway, you will need to make one that can be put in place, used, and then taken away easily. If you make one such as shown in the picture to the right, you can set this down in the same place day after day and take your solar ("sun") measurements.
- Some way to make permanent marks on the driveway. A marking pen? (Later, when the project is over, you can wash off the ink using alcohol.)
- Sunny days
- A camera to take the final pictures of your marks on the driveway.
- (Optional) A magnetic compass to set down by the driveway markings when you take your photograph. If you do use a magnetic compass, you will also want to know the magnetic deviation from north at your location. This information can be obtained from various on-line sources (Happy web-surfing!).
How to do it:
- In the center of your flat, level portion of the driveway, set your stick down, and carefully mark the edges of the supporting block on the concrete. You always want to put this block down the same way each time in exactly this same place. To assist you in this, write a star on one edge of the supporting block and a star on the concrete next to that block's star. You will always make sure that the stars are together!
- Sunny Day Number One: with your stick in place on the driveway, start taking "readings" as early in the morning as possible on a sunny day (of course!).
- Here is how you make a "reading:" you will see where the shadow of the tip-top of the stick is projected onto the driveway. Place a small "X" on that spot.
- An hour later, mark your second reading on the concrete. You will see that the shadow has moved. (It is not necessary to write down the time you made each reading.)
- Every hour or so you take further readings. As the day progresses, you will likely see that your "X's" are making a gentle curve. (Oh, oh! What do you do if the day started out sunny and then gets cloudy? Easy, if the next day or two is clear and sunny, add those readings to the ones your already have. But if you have 4 or 5 days of cloudiness, you must start a new day-long set of readings.
- On March 20 and/or September 22 or a day before and after get as many readings as you can over the whole day. (If it is to be cloudy, the readings can be made either a day one side or the other of those dates. What is so special about March 20 and September 22?)
- Wait a week or so and take some more readings. You should see that your markings are making a gentle curve in the opposite direction from your first curve.
- Place your magnetic compass near your March 20 or September 22 line of marks and take a piece of dark string and stretch it out under the compass to indicate the correction for the deviation from true north.
- Climb onto a chair with your camera. Don't fall off when you are taking your pictures. You want only black marks on the concrete and no red puddles, if you know what I mean! Make sure that your own shadow is not in the picture. If you see your shadow, move your chair to another location.
- Aim the camera as straight down as you can, focus, and snap the picture.
- Next have someone take a side-views of the set-up and of you as you make a mark where the tip's shadow is cast. A few distant and a few close-ups would be good.
- Develop the film (or print out the digital pictures) to make sure your photography shows all the good stuff. If your camera work was not very good, you can always do it again!
- So what? What do your readings tell you with regard to compass directions?
- Once you have good pictures, get some alcohol from your drugstore, supermarket or paint store and scrub off the markings from your driveway. (Unless, you want to keep them for a souvenir!)
- You are now ready to write your report; make a poster; and even submit your work to some journal of archeology - because this :"simple, low-tech" method has never yet been reported as a method for determining compass directions that could have been used by the ancient Egyptians. (The method has long been known, but the connection to the pyramids' orientations has never been officially reported!)
(These should be incorporated into your report's introduction or discussion at the end.)
- What is so special about March 20 and September 22?
- What are the geological names given to those two dates? (The vernal ["spring"] equinox and the autumnal equinox.)
- What is special about June 21 and December 21? What are their geological names?
- If March 21 is when the sun passes directly overhead IF you are standing on the equator, how could the Egyptians or the Druids in England determine that March 21 was "the" special date?
- Since the Druids and the Egyptians lived north of the equator, do you think this method would work for Australians? What would their driveway markings look like?
- Could the space travellers to Mars use this method to determine directions on Mars. Remember that some planets don't have magnetic fields and, hence, compasses won't work there.
- What does your experiment say as whether the earth is flat or "round"?
- Did the ancient people determine that the earth was round? (Yes! But how? And how big was the earth? Remember to think "simple and low-tech"!)
- Can you make a demonstration of your experiment using a globe of the world, a small stick and a flashlight "sun" in a darkened room?
Doesn't This Tell Me More?
It shouldn't surprise you to know that once you have marked your driveway on the equinox, you should be staring at even more information than just compass directions. But what is it?
Here are a few other tools you will need for this next revelation:
- a carpenter's square (looks like a large capital letter "L")
- a protractor, or other device for measuring angles (a trigonometry table or quite possibly your electronic pocket calcular has this capability)
- a tape measure
What to do:
- Draw the best "straight" line through the points on your driveway.
- Using the carpenter's square, find and permanently mark the point on the line that makes a right angle with the place where you had set up your pole. (The little red "r" means a right, or 90° angle.) This point marks what is called your own "local solar noon." (People living east and west of you have different local solar noons. Prior to the adoption of time zones, every town set their clocks to their own solar noons. What a mess for reading train schedules! Yes, the railroads were the ones to first adopt "time zones.") Would the direction of this shadow, disregarding the length, change throughout the year? What does this tell you about sun dials? (The picture to the right shows a shovel handle as the pole, and the peg in the grass is at solar noon.)
- Measuring the shadow's angles, "a" and "b", in the diagram. (The picture to the right may be enlarged by clicking on it, and then upon the picture draw the hypotenuse and appropriately label the angles.)
- Using a protractor (the larger the better)
- Tack a string to the top of your pole and, with the pole vertically in place, pull the string taut to the "local solar noon" point.
- A this point, it would be best to take a side photograph - exactly at right angles off to the side. Place a parent in the picture to personalize it. (Do not put yourself in the photo, because if you can use this for a report in another class several years from now, you don't want to look like a kid!) You can draw lines on the photograph as you proceed to the next step.
- Get a friend to using the protractor to measure both of the angles, "a" and "b"
- The sum of the angles should be 90°.
- Using trigonometry (actually more precise)
- Measure the noon shadow, "S" (the distance between "local solar noon" and point where the pole stood on the driveway), and measure the height of the pole, "H".
- Calculate both S/H (= tangent of ∠a) and H/S (= tangent of ∠b)
- Using an angle/tangent table or your calculator find what angles those correspond to.
- By this time, BRILLIANT students will be saying "Ah, ha!"
But this author had to have a hint!
- Hint: What is your latitude and longitude? (Where would you find such information?)
- Sorry, no more hints! You have enough information now to write your own BRILLIANT report.
- Don't forget to include in your report where inaccuracies were introduced into your procedure. Teachers relish marking off for improper decimal places of significance! How could you have improved your precision? What's the difference between precision and accuracy?
- Oh, don't forget to find out what an Eratosthenes is, and how it fits in with what you have done - especially if you had another friend do all the above somewhere far to the north or south of you.
As mentioned in the opening paragraphs when we were discussing how they made the bedrock level and ready to receive the first layer of stones, the Egyptians soon needed to make sure that upper levels of stones were also level. Of course, the ancients didn't have bubble-levels like masons use today, so what might they have improvised?
A first thought might be that they set up a flat table atop the layer of stones and then leveled the table by sighting the horizon across the table-surface in all directions. As this author is a novice navigator with a sextant (about a "1-minuter" - accurate to about 1 minute or 60 miles - very novice!), he knows there are two pitfalls to this method. The first is that the horizon on land is not like that at sea. At sea it is by definition "level" and very regular, while the terrestrial horizon might be tilted and quite irregular with distant mountains or hills. The second reason is that one is always looking downward at the horizon and not looking straight out. And the higher one is, the more downward one is looking. Marine navigators using sextants measure the distance their eye is above the waterline, and make a correction for that. (You see, from a higher vantage point you can see further over the horizon than from a lower vantage point - all courtesy of the curvature of the earth.) Thus we must seek a better way - next.
The ancients were perfectly capable of drawing straight lines and making right angles. Right angles can be derived by making a square, which has, of course, diagonals that are exactly equal.
The next thing they would need to be able to produce was a perfectly flat (planar) table - no warpings or undulations on the surface. This table would serve as a reference plane. What is needed is a planar surface of some sort of abbrasive material. You might imagine making a large puddle of fluid concrete and allowing it to harden, but Egyptians probably hadn't invented concrete as far back as 2000 BC, so they may have used something like plaster instead. A moderately flattened square of wood could then be rubbed around on this hardened plaster surface to grind it flat. (By the way, the Romans had not only invented concrete, but also a type of concrete that hardened under seawater - all the better to make shipping wharves and breakwaters.)
By carefully affixing right-angled supports to the sides of the planar table, and seeing how weighted plumb lines hung, the table could be leveled. Then either by sighting directly across the surface, or using some type of mobile sighting guide that slid around on this table top, distant level-measurements could be made over to where rod-men stood. (We do know that the ancients used plumb lines and there are ancient pictures of tabletops on tripods.)
"Simple and low-tech" was mentioned over and over here for good reason. People today like thinking in "high tech" terms, and are often befuddled at how primitive and ancient people could accomplish rather precise tasks. "Elegant" thinking (simple, clever, low-tech) is almost a lost art.
For any teachers reading this, you will note the number of potential intersections with other subjects in this project: astronomy, geology, simple physics, history, art work and so on and on. One of the recognitions by scientists is that the "arts" are first to go in school systems with tight budgets. Thus this is an attempt to teach a little art, and social studies along with science. Why are scientists concerned about the loss of arts and humanities? We have kids in school, too!