During my research into the legend of Bessler’s wheel I quickly became aware of the many variations between apparently similarly-named weights and measures, across Germany and elsewhere. Eventually I sorted out the correct ones, and I came to the conclusion that all these weights and measure definitions must have originated from some identifiable source and one that provided a means of verifying a particular measurement. It seems to me that resource which was once identifiable has been largely lost.
The lost resources were replaced by traditions that can seem amusing. For example in the 16th century the lawful ‘rod’ was decreed to be the combined length of the left feet of 16 men as they left church on a Sunday morning. I assume that they would be dressed in their best, including good shoes which might have been larger than their normal work wear shoes, to aid accurate measurement. The rod in question (or pole, or perch) is a surveyor’s tool, 5 and a half yards, which is equal to 16 and a half feet and that probably explains the use of 16 men’s feet as a rough guide. Another apocryphal tale records that Henry I decreed the lawful yard to be the distance between the tip of his nose and the end of his thumb.
Traces of those lost resources are still evident in some of our commonly used measurements. Degrees for instance; why are there 360 degrees in a circle?
This question puzzled me as a schoolboy and the answers I have found over the years have been few and unsatisfactory in my opinion.
The usual suggestion is that it has come down to us from the Babylonians and before them the Sumerians, who, we are told, used a 60 base system of numbering. They thrived some 6000 years ago and obviously had good reasons for using such a system.
It has been suggested that 60 was used for a base because it has so many divisors. 60 is the smallest number for which 2, 3, 4, 5, and 6 are divisors – plus 10, 12, 15, 20 and 30. That makes it much better to work with than a 10 base, so yes that is one reason but is that really the only reason. Bear in mind that they also used a 10 based system alongside the 60 base.
The Babylonians and their predecessors were familiar with the seasons and knew the earth’s rotation was about 365 days. They used the 360 day and added the additional 5 later. As we saw above 360 subdivides in so many ways. Seasons included summer and winter, spring and autumn, 90 days each. They divided the 90 days into three lots of 30, making twelve months of 30 days each - all based on 60.
Each day was divided into two lots of 12 hours because that was the average of the summer and winter day lengths. Each hour was subdivided into 60 minutes and each minute into 60 seconds. Each day is equal to 1 degree of the earth’s annual orbit around the sun so 360 degrees for a full circle made perfect sense. At midday in midsummer the sun was overhead so they could mark the middle of the day as noon, and call after noon, well, afternoon! That gave them 6 hours on either side.
With all these divisions and sub division, they could measure how far the earth rotated in, say, 1 hour or even 1 minute or a second. 1 day = 360 degree rotation and that is also 24 hours, so the shift per hour is 360/24 = 15 degrees /hour and 1 degree = 4 minutes. Today we know that each degree of latitude at the equator equals nearly 69 miles; each minute of latitude equals just over 1 mile; and each second of latitude equals a fraction over 100 feet.
You can see that the 360 degrees that the earth moves can also be used to measure the angle of arc but the Sumerians also knew that the perimeter of a hexagon is exactly equal to six times the radius of a circumscribed circle, in fact that was probably another reason why they chose to divide the circle into 360 degrees.
I mentioned the ‘rod’ in connection with 16 left feet – why the left feet? Perhaps it was common knowledge that, contrary to popular belief, the left foot is 80% of the time, the larger foot and 80% of the population is right hand dominant. Anyway, getting back to the rod, the rod is useful as a unit of length because whole number multiples of it equal one acre of square measure. The 'perfect acre’ is a rectangular area of 43,560 square feet, bounded by sides 660 feet by 66 feet long – clearly another pointer to the base 60 system.
The Sumerians gave us base 60 and thus the analogue clock. Time is measured in hours, minutes and seconds, all base 60.
Minutes of arc (and its subunit, seconds of arc) are also used in cartography and navigation. At sea level one minute of arc along the equator or a meridian equals approximately one Nautical mile (1.151 miles). A second of arc, one sixtieth of this amount, is about 30 meters or roughly 100 feet. The exact distance varies along meridian arcs because the figure of the Earth is slightly oblate.
Positions are traditionally given using degrees, minutes, and seconds of arcs for latitude, the arc north or south of the equator, and for longitude, the arc east or west of the Prime Meridian.
There is so much more to say about these ancient measuring systems, but there are some who have suggested that the rotation of the earth was only 360 days in ancient times, and was forced into a larger orbit by the close bypass of large asteroid. This would explain the Sumerians choice of the 60 base even better and there are other related factors. Perhaps the alterations in orbit might have led to a re-jigging of the distances I mentioned above to a more precise and accurate total. So each minute of latitude might equal exactly one mile, and each second of latitude equal exactly 30 yards. This knowledge would provide a constant source of verification of various measures.
One more thing; before the UK went decimal we were used to some old coinage. 12 pence to one shilling, 240 pence to one pound, four crowns to one pound - a distant echo of the 60 base numbering system?
So the old resource which allowed the precise determination of, say 1 foot, or 1 yard, by anyone, then they must have measured the earth, which begs the question if in fact the above is true, how did they know the earth’s size – exactly?
JC
