Before the Pyramids: Cracking Archaeology's Greatest Mystery

by Christopher Knight

  2. Correct for latitude by sighting onto Polaris, past the top of a vertical sight-rail to calculate the Earth’s equatorial circumference.

  Setting up each crosshead ‘pair’ requires an approximately 30-m-long trench, lying east–west, full of standing water, with the crossheads a measured distance above the water (see figure 26). Identical multiple eyepiece crossheads at different heights would enable several sets of readings from one sunrise. With this equipment, and the vertical sight-rail (described in figure 27 and figure 28) to correct for latitude, only five experimental measurements are needed:

  Dimensions A, B, (about 1.5 m to water level) and C (about 30 metres) to be exactly the same both crosshead sets. Two pairs required 20–40 miles apart.

  Figure 26. Horizontal method apparatus: one set of two shown

  1. The distance between crosshead pair A and crosshead pair B

  2. The number of pendulum swings (pendulum length to be constant throughout) between sunrise or star rise at crosshead pair A and cross-head pair B

  3. The number of pendulum swings between sunrise or star rise at crosshead pair A and crosshead pair A the next day (24 hours)

  4. The inclined distance from a viewpoint to the intersection of a sightline onto Polaris and a vertical sight-rail set by plumb line (see figure 28).

  5. The horizontal distance from the viewpoint to the vertical sight-rail (see figure 28).

  To achieve accurate timings between the crosshead events 30 miles apart, the time delay in sightings could have been measured by masking signal fires, timing a signal between the two crossheads and back, then halving the time to compensate for the signal delay.

  The horizontal method is open to theoretical verification using Chris’ star program (which gives the location of any named star in the past or the future, given a date and time). Jim chose 21 March 2009, and two towns on the same line of latitude, 54.883° north, Carlisle and Stranraer, to test the method.

  Chris’ result from the program:

  1. Sunrise at Carlisle was predicted to be at 06h 18m 47s

  2. Sunrise at Stranraer was predicted to be at 06h 26m 47s

  3. Sunrise at Carlisle the next day was predicted to be 06h 18m 46s.

  Calculation

  Time lapse sunrise Carlisle to sunrise Stranraer = 8 minutes

  Scaling off a map, Carlisle and Stranraer are 79.8 miles apart

  Therefore sunrise travels 79.8 miles in 8 minutes

  Time lapse sunrise Carlisle 21 March to sunrise Carlisle 22

  March = 23h 59m 59s

  In 23h 59m 59s hours (1,439 minutes), until sunrise the next

  day, it would travel:

  79.8miles × 1,439min / 8min = 14,364 miles

  (the circumference of the Earth along the 54.883° north line

  of latitude).

  The ratio of the circumference at 54.883° north to the equatorial circumference can be obtained by observing Polaris against the top of a vertical object from a viewpoint (see figure 28).

  Then, by:

  1. Making a horizontal measurement H from the viewpoint (figure 28) to the vertical object, and

  2. Measuring the inclined length I from the viewpoint to the point of intersection of the line of sight of Polaris and vertical line,

  3. Dividing measurement H by measurement I (modern mathematicians would recognize this as the cosine of the latitude angle).

  The 54.883° circumference divided by cosine 54.883° then gives an equatorial circumference of:

  14364 / 0.575 = 24,980 miles

  (Any error comes from the inaccuracy of scaling a map).

  This simulation using modern technology confirms that the method is viable and that, weather permitting, on carefully chosen sites, using only materials available to megalithic man, it could have been used by the ancients to approximate the Earth’s circumference.

  METHOD TWO ‘THE VERTICAL METHOD’

  Instead of method one, using sunrise, we could use either the Sun due south at midday, or a star due south at night. The ancients were familiar with the concept of a sundial. Basically this method uses the principle of two very accurate sundials by day, or ‘stardials’ by night.

  If we have two points east–west of each other and we know the time between midday occurrences, and the total length of the day, and the distances between the points, we can calculate the Earth circumference at this latitude. Small sight-rail errors produce large errors in results. The Sun’s heat significantly distorted my metal sight-rail during the day. More accurate results were obtained from the stars at night.

  To prove the concept I have constructed two small-scale 10-m-high vertical sight-rails. One uses an old timber electricity pole fixed in my garden and mounted on foundation piles for rigidity. The mobile sight-rail pole is a 10-m long 168-mm in diameter hollow metal tube with the plumb line down the centre to shelter the suspension cord from the wind. It is mounted on adjustable screw feet to plumb the rail using only the plumb line for guidance. Both poles have adjustable sight-rails fixed to the side of the pole facing east. With good technique in experiments I found that an error of less than 0.1mm (4/1,000 of an inch) in these ‘proof of concept’ vertical 10 m sight-rails can be achieved. A much longer plumb line or a series of plumb lines above each other could plumb a much taller, and hence more accurate, straightedge. Neolithic man would have had trees up to 50 m tall to modify into vertical sight-rails. The sight rail does not have to be continuous down the pole, but must be accurate where the point of contact with the lines of sight occurs.

  Four timber trestles, 1.5 m high by 1.5 m wide, were made, one placed to the south of each vertical rail and one to the north (see figure 28). To set a true north–south line using only Polaris, I looked north from each southern trestle to sight Polaris as it disappeared behind the vertical sight-rail near the top, when my eye was moved from east to west. A mark (figure 28, C) was placed on the horizontal trestle at the point where Polaris disappeared. Twelve hours later another sighting was taken and marked (figure 27, D). True south lies halfway between these marks. This point is now referred to as the south eyepiece; I replaced the mark with a slice of wood with a 2-mm in diameter hole. The most accurate results are achieved when Polaris is at the 3 o’clock and 9 o’clock positions. By placing a pinhole source of light at the southern eyepiece, and viewing from the northern trestle, past the vertical sight-rail, I was able to establish a northern eyepiece. From the northern eyepiece the edge of the sight-rail was a true north–south plane running through the centre of the Earth. The Sun or a star could be timed as it passed behind each sight-rail.

  Sighting Polaris twice in the first part of the vertical method is for perfectionists; good results can still be obtained using one sighting to Polaris at both sight-rails, provided they are taken at the same time.

  The time delay between the sightings at the two locations can be used as in the previous example.

  Earth circumference at apparatus latitude

  = distance between sight rails × time for one earth revolution

  _________________________________________________

  Time between sightings

  Latitude correction is done as in the previous example.

  To confirm the accuracy of the continuous sight-rail, at night I sighted south as the constellation Orion passed behind the rail, and timed the passing of each star. The times between each star disappearance and published star charts confirmed accuracy; demonstrating that a simple vertical sight-rail could have been used to create very accurate star charts in Neolithic times.

  Setting east–west lines can be done by setting a right angle from the north–south lines.

  I cheated and used GPS, but distance measurement between two selected points, however far apart, would only require a unit of measurement and counting the number of times the unit is placed end to end. Prior to establishing a standard ‘Megalithic Yard’, any unit could have been used, the longest stick capable of being carried, perhaps by several men, would do. The fi
nal value of a ‘Megalithic Yard’ would be expressed as a fraction of the original stick-length. It is inconceivable that people capable of hauling 20-tonne stones for 20 miles and placing them 20 feet up on top of other stones could not have accurately measured 40 miles.

  The apparatus I have constructed as proof of concept is relatively small scale; in Neolithic times the apparatus could have been many times larger and hence more accurate. In the experiment there is a trade-off between measurement of time and measurement of distance. The longer the distance and the higher the vertical rail, the more accuracy can be obtained from time measurements. For example, at 50 degrees north, if 10-m high sight-rails are 45 miles apart and the time error is one second, then the circumference error is (0.416%) or 104.6 miles.

  Mount 10-metre pole (3) on adjustable base (1), plumb pole with three no-screw feet (2) and internal plumbline (5). Straighten sight-rail (4) to a temporary builder’s line (BL) by adjusting 13 no bolts (6) fixed to side of sight-rail. From south tressle (8s), sight Pole Star (P) in line with top of east side of sight-rail (4), mark point (C). 12 hours later (or 6 months later at the same time) resight Pole Star (P), mark point (D). Drill 2 mm diameter hole midway C-D 9 ‘south eyepiece’ (true south of the east side of the sight-rail). Place light in south eyepiece (9), view from, and adjust north eyepiece (10) in line with east side of sight-rail. Sight line from north eyepiece (10), (2 mm diameter) past east side of sight-rail (4) will be in true north/south plane. Time target star (T) between two sets of sight-rails 20–40 miles apart, calculate earth circumference at latitude.

  Figure 27. Vertical apparatus. Two required for experiment, located 20 to 40 miles apart, due east/west of each other on any line of latitude.

  1 Mark of lowest sighting of Polaris.

  2 Mark of highest sighting of Polaris (up to 6 months between sightings).

  6 Angle same as location latitude.

  Measure H, measure I. Use H and I in latitude correction.

  Figure 28. Apparatus to establish latitude

  Neolithic peoples would have had to put up with much less light pollution than occurs today. Apart from direct effects of stray light on the natural adjustments of the eyes, light from towns many miles away over the horizon can illuminate the base of clouds, and turn a poor observing night into an impossible night. Stars we have difficulty observing with the naked eye would have been much clearer 4,000 years ago. Observation of reflections of starlight on the surface of water, too dim to use today, may have enabled reflected light to be used to create longer light paths and hence produce more accuracy.

  On 21 March 2009, as proof of concept I took the ‘away’ mobile vertical sight-rail 30 miles from home on a lorry, set up in 30 minutes, took the readings in 3 minutes and brought the sight-rail back to the yard the same evening. The result of this short experiment was a value for Earth circumference of 25,802 miles. The error in this result was due to the effect of the wind on the unprotected plumb line on the wooden pole. Perfect weather (good visibility and no wind whatsoever) is critical to the experiments. With minor equipment modifications, I am confident this small-scale vertical apparatus will consistently produce circumference values ±200 miles. Larger vertical equipment or the horizontal method would better ±50 miles. Considering that six months ago no one had even proposed a Neolithic method of determining Earth circumference, this experiment must be considered a remarkable success.

  My equipment is ‘proof of concept’ and small scale. There are ways to improve the accuracy even on this scale. I consider I have demonstrated that Neolithic astronomers could have experimentally determined the diameter of the Earth, and could have produced more accurate results, using full-scale equipment, than I have. For either method there is no need for a henge or any megaliths. A long east–west fairly flat strip of land or foreshore (easy to measure) and a set of signal fires would have been all that was required. A Neolithic vertical sight-rail would have been made of timber and would have rotted away in a few years, the only evidence of the use of either method would be the results.

  Appendix 7

  •

  THE MEGALITHIC SYSTEM EXPLAINED

  In a solar year the Sun rises 365 times but, during the same time, a star will have risen 366 times. It sounds odd but it’s true. Each day according to the rising of a star (a sidereal day), is 23 hours 56 minutes 4 seconds in length, whereas a mean solar day is 24 hours in length. That leaves a discrepancy of 236 seconds, which over a year amounts to another 24 hours. It is part of the clockwork mechanism of our solar system that there are different sorts of years, dependent on what one is observing. Our megalithic and pre-megalithic ancestors in Britain focused on the number of times a star rose in a year, and the result was 366 times.

  Having made this realization what they did next is the most surprising aspect of our studies. They created an integrated measuring system based upon a year of 366 days. Just as surely as they recognized that the circle of the year was naturally split into 366 units, they then split the horizon into 366 units, which we would know as degrees of arc. They then split the units again, first into minutes of arc – they considered that there were 60 minutes of arc to 1 degree of arc.

  But this was not enough for them so they split the units again. Each minute of arc was split into 6 smaller units, which we would know as seconds of arc. (Note the difference between this form of geometry and the one we use now. In 360° geometry there are 60 seconds of arc to 1 minute of arc but in the megalithic system there are only 6.)

  Somehow they worked out that if they split the degree, minute and second of arc in this way, they would arrive at a stunning result because each Megalithic Second of arc of the polar Earth measured exactly 366 Megalithic Yards on the ground.

  The actual size of the Megalithic Yard could be judged by the careful use of a pendulum of exactly half this length (see Appendix 4). At first this was used in conjunction with the Sun but later a more sophisticated method was established using the planet Venus during certain parts of its orbit.

  What is absolutely incredible about the Megalithic Yard as a unit of length is not just that it is geodetic (fits into the polar circumference of the Earth in a logical and obviously intended way), but it does the same job on the Moon and the Sun. One Megalithic Second of arc on the Moon measures exactly 100 Megalithic Yards. On the Sun the same Megalithic Second of arc is 40,000 Megalithic Yards.

  Getting the sheer genius of this system across to our readers has been the hardest part of our quest because it really is incredible but it can seem complicated. Once the penny drops, the whole system is virtually miraculous, making our modern approach to measurement systems look primitive – logic is reversed. In this system a second of arc of the sky can be seen as the same thing as a second of time of the Earth turning on its axis. In other words 1 Megalithic Second of the Earth turning on its axis also represents a physical segment of the sky, albeit an extremely small one because it is 1/366th of 1/360th of the sky. The same second is also a finite measurement of part of the Earth’s circumference. Time and geometry and distance all merge into the same symmetrical whole, and astronomical calculations become much easier.

  Meanwhile, with the system we use today we have degrees, minutes and seconds of arc of the sky and of the circumference of our planet. We also have minutes and seconds of time but these don’t match the turning sky at all. This fact must have cost thousands of human lives as the first mariners to engage in transatlantic voyages tried desperately to reconcile minutes and seconds of time with minutes and seconds of geometrical arc and came up with the wrong answer. We eventually discovered that, in addition to measuring time and linear distance, the megalithic system had also been based on the mass of the Earth. How could this possibly be? It’s absurd, and yet it is self-evidently true. The unit of mass in question is virtually the same as the unit presently known as the imperial pound. The mass of the Earth is 5.9742 × 1024 kg. In pounds this figure is 1.31708565 × 1025 lb. With just a very slight change in the definiti
on of the pound this figure becomes 1.317600 × 1025 lb and then something amazing happens. Imagine we segment the earth like an orange. A segment 1 Msec of arc across would have a mass of exactly 1 × 1020 lb. That’s 100,000,000,000,000,000,000 pounds!

  This means that the imperial pound and the pound that was a part of the megalithic system are virtually identical. The Megalithic Pound had a value of 99.96% of the modern pound! The difference is 0.4 of a gram. That this level of accuracy has been maintained across such a vast period of time is little short of incredible.

  In order to turn the Megalithic Yard into a system for measuring volume and mass we need to resort to the Megalithic Inch. Alexander Thom found this unit when he carefully studied carvings that had been scratched into a number of standing stones. He established that there had been 40 Megalithic Inches to 1 Megalithic Yard. A cube with sides of 1/10th of a Megalithic Yard (4 Megalithic Inches) holds the same as a modern pint of water. If the water is poured out and the same cube is filled with any cereal grain, such as wheat, barley or even un-hulled rice, the weight of the cereal grain will be 1 imperial pound.

  So what do we have?

  The megalithic system is a system of geometry and measurement that is based upon a 366-day year, together with the physical size and mass of the Earth. It measures time, distance, mass and volume using the same figures throughout, and aspects of it are as relevant to the Moon and Sun as they are here on Earth. Without wishing to detract from our stunning scientific accomplishments as a species, anyone would surely have to admit that the megalithic system is better in a number of ways than any method of measurement used today. This is because it is ‘integrated’ and because a common terminology is used throughout. The metric system in use today may be extremely accurate, and it too was originally based on the circumference of the Earth, but it certainly does not take Earth mass into account and neither is it used for the measurement of time. Unbelievable as it may seem, thanks to our friend and colleague Edmund Sixsmith, we now believe that the Megalithic system also dealt with the measurement of temperature. If we create a temperature scale in which the freezing point of water is 0° Megalithic and the boiling point of water is 366° Megalithic something quite magical happens. Absolute zero, the lowest temperature achievable (usually considered to be –273.15 °C) becomes an absolutely round and quite accurate – 1,000° Megalithic.