The Gravity Cubit (cont.)
By Scott Creighton
TIME AND GRAVITY
When a leaf flutters to the ground in an autumn breeze, it does so as a result of gravitational forces. Newton was the first to recognise this fundamental natural force; a force that affects every part of our existence here on Earth. Gravitational force is pretty much the same all over the planet with very negligible variations. If, for example, you were to drop a ball or some other heavy object from a tower that is, for example, 16 feet high, it will take that object almost exactly 1 second to hit the ground. Provided the object is always dropped from the same height (16 feet), then it will always take 1 second for the object to reach the ground. And, as stated, this effect is more or less consistent all over the world with very slight but negligible latitudinal variation.
We can say then that 1 second of Earth time is equal to 16 "gravity feet" (i.e. the distance an object will fall in 1 second of time). One full Earth day would then be equal to 261.81 miles i.e. 86,400 (seconds per day) x 16 gravity feet = 1,382,400 feet. It doesn't matter if we drop a ton or a kilogramme - both will fall at the same rate, reaching the ground at the same time. And what's more - this will never change. By allowing an object to fall for precisely 1 second of time, we will require to construct a "drop tower" that is 16 feet high. Thus we have a unit of measure (16 feet) that is defined by time and gravity; a unit of measure that can be consistently reproduced virtually anywhere on Earth and in any age.
Of course, calibrating a drop tower to produce a drop height of exactly 1 second duration would be problematic, if not impossible. One second of time is simply too quick for humans - especially in ancient times - to have measured. If the duration was longer - say 5 or 10 seconds - this would make calibrating the drop height much easier. However, this does not simply mean constructing a drop tower that is 5 x 16 feet. Although gravity is constant, it also causes falling objects to constantly accelerate! This means that the higher the drop becomes the quicker a falling object will be allowed to travel to reach the ground because the falling object (excluding external factors such as wind resistance) is continually building up speed as it falls (gravitational acceleration). The effect of this means that for an object to fall for a duration of 5 seconds would require a drop tower of over 400 feet! Clearly this would be quite impractical - there has to be a simpler method of using time and gravity to define a linear unit of measure.
Gravitational force acting upon a simple pendulum can produce a very similar effect but without the need to build a drop tower of over 400 feet. To achieve a 2 second pendulum swing (i.e. 1 second outward swing and 1 second return swing) requires the pendulum cord length to be a fraction over 3.25 feet (39 inches) in length - much more practical and manageable. By calibrating the swing of the pendulum by the use of a 30 second hourglass or water clock until the pendulum produces exactly 30 swings to the 30 second timer means that the ancients could not have failed to produce a pendulum cord length of a fraction over 39 inches. Gravity dictates it! A longer cord length would produce too few swings within the 30 second timer whereas a shorter cord length would produce too many swings within the same period.
And so we have defined the "Gravity Cubit". And once again this unit of measure will be almost identical all over the Earth with a negligible fluctuation in the gravitational force resulting in the tiniest fractional difference in the pendulum cord length - so small in fact as to be considered negligible. It is also worth noting here that the Gravity Cubit is almost identical in length to the modern metre which measures 39.37 inches!
The height of the Great Pyramid is 5,772 inches. This, in turn, is equal to 148 Gravity Cubits (5772 ÷ 39). But why 148 Gravity Cubits? Why not a nice rounded number like 150 Gravity Cubits? What is so significant or special about the number 148?
The answer to this problem presented itself to me in one of ancient Egypt's most enigmatic and puzzling hieroglyphs - the Akhet (Figure 1).
Figure 1 - 'Ahket Khufu' Hieroglyph
Could it be that the height of the Great Pyramid of Khufu - 148 Gravity Cubits -was determined by the setting sun i.e. the duration it takes the sun to set at Giza as depicted in the Ahket hieroglyph? If this was to remain possible then the setting sun at Giza should take 148 seconds (148 x 39" = 5,772").
Quite incredibly, on the autumn equinox at Giza it takes the sun precisely 147.757 seconds to set from when the lower rim of the solar disc of the sun first touches the horizon until the upper rim of the solar disc fully sets below it. Naturally it would make sense for the ancient designers to round up this sunset duration to 148 seconds since it is inconceivable that they would have been able to measure precisely a fraction of one second; a fraction of one swing of a pendulum.
Thus the height of the Great Pyramid of Khufu can be defined by the Gravity Cubit (39 inches) multiplied by the duration of the sunset at Giza at the autumn equinox (148 seconds). And the base of the Great Pyramid being in a ratio of 1.571 to the pyramid's height is equivalent to 232.51 Gravity Cubits (9,067 inches). But how do we then find the ancient Egyptian Royal Cubit from the Gravity Cubit?
By simply adding the height and width of the Great Pyramid together we find the value of 14,839 inches. This is an interesting figure in its own right simply by virtue of the fact that it demonstrates the key values of 148 and 39! We have found through the use of time (148 seconds) that we can define the height of the Great Pyramid. If we simply extend this idea of time and use the number of minutes in half of 1 solar day (720 minutes) we find the ancient Egyptian Royal Cubit 14839 ÷ 720 = 20.61 inches. The Royal Cubit then may well have been based upon the dimensions of the Great Pyramid divided by the number of minutes in half of one solar day. And given that the average length of a man's forearm also approximates this length, this glyph may have been used to symbolise the measure.