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Keimpe
In: Leeuwarden, Frisia




When studying monuments like Stonehenge it becomes clear (or at least seems probable) that the ancients knew what the size of the earth was.
This becomes even more evident when reading books like these.
But how did they figure it out?
And why hasn't anyone ever seriously tried to answer that question? Or even ask it?
Did they think it was impossible or unlikely?
Well, it seems it wasn't. In fact it's quite easy. All you need is a lot of time and some manpower (or was it the other way around?).
But let's not spoil the surprise by just telling you outright. Let's see if you can find out for yourself how the earth was measured some 3000 years B.C.
So let's suppose it's 3000 B.C.
You are in England.
You have no boat.
You want to know the size of the planet you're on.
Where do you start?






Mick Harper
Site Admin
In: London




By realising that we are not on the Tropic of Cancer like what the Gyppoes are so we can't use Eratosthenes simple trick of peering down a well to know when (and where) the sun is overhead at midday at midsummer.






Keimpe
In: Leeuwarden, Frisia




Exactly. So we have to find ourselves an equivalent of a well (so to speak). Because then we have prerequisite A, which is ....






Keimpe
In: Leeuwarden, Frisia




which is (I've started, so I'll finish) ...
a fixed moment in time when you know where the sun will be.
In Eratostenes case it was (I believe) June 21st when the sun was directly overhead some well in Aswan.
Is there a fixed moment in time in Britain where one can know beforehand where the sun will be?






Chad
In: Ramsbottom




Sunrise, May 1st, Michael line...






Chad
In: Ramsbottom




...If you then take sightings, from either end of the Michael Line, to see where abouts the sun sets on the Horizon  and knowing the length of the Michael Line it should be possible to work out the dimensions of the planet.
The longer the base line, the more accurate the result.. and we know the Michael Line is the longest such line, possible in Britain. (Now we know why.)
I'm sure there's a bit more to it than that... but those with a good knowledge of three dimensional geometry should be able to figure it out.






Keimpe
In: Leeuwarden, Frisia




Chad wrote:  Sunrise, May 1st, Michael line... 
Exactly!
Here's some more information. It was this single fact that got me interested in this question.






Keimpe
In: Leeuwarden, Frisia




Chad wrote:  ...If you then take sightings, from either end of the Michael Line, to see where abouts the sun sets on the Horizon... 
Could be, could be... but would you have a clear view of the sunset from either end? I don't know. But there's a bigger problem:
Chad wrote:  and knowing the length of the Michael Line 
Right. But, how do we measure the length of the St. Michael's Line without referring to Google Earth/Maps? There's way too many hills in between to measure it by cart. Even Eratosthenes' calculations were a whopping 16% wrong! We're aiming at something a bit more accurate. Now, where might we get a better measurement?
(And besides, suppose they did have a clear view of the sunset from both ends of the St. Michael's Line, and they did know the length of the St. Michael's Line accurately, what good would it do them? What would they be able to measure?)






Mick Harper
Site Admin
In: London




This is how the Michael Line trick is worked.
1. The angle between sunset and sunrise varies proportionately with latitude.
2. On May 1st measure this angle at St Michael's Mount
3. On May 1st measure this angle at the Norfolk end.
4. The difference between the two will be the difference in latitude.
5. Measure how far north the Norfolk coast is from St Michael's Mount.
6. Multilply by coefficient x for the complete latitude of the earth
7. The complete latitude of the earth is half its circumference.






Mick Harper
Site Admin
In: London




This is essentially the same method that Eratosthenes used later on. All he had to know was how far north Alexandria was from Aswan but then used sunoverhead to synchronise measurements in the two places. The Megalithics used the Michael Line because that was, as it were, presynchronised. If this is true, it remains to be discovered whether the Michael Line was laid out for this purpose or was merely used later when its earthsurveying potentialities was recognised.






Brian Ambrose




Don't you need to measure the time difference between observing the sun rising at one end of the line, and the other? If you measure that time difference, t, knowing the length of the line d (chord) and how long a day is, you should be able to calculate earth's diameter (ie dia=24hrs/t * d). Obviously, you need some sort of clock to do this.






Mick Harper
Site Admin
In: London




No, Brian. If you had such a timepiece you'd be able to solve all longitude problems (and therefore all earthsurveying problems) as they did in the eighteenth/nineteenth centuries (AD). The whole point of the Greek and My Megalithic method is to obviate the need for timemeasurement by using displaced correlation. However time does come into Keimpe's method (insofar as I understand it) but I will leave him to develop this.
The two measurements, Cornwall and Norfolk, are not time dependent because you are measuring the same phenomenon at two vantage points on the earth's surface which have a known relationship. The fact that sunrise is a few minutes earlier in Norfolk does not affect the measurement of the angle.






Keimpe
In: Leeuwarden, Frisia




Mick Harper wrote:  1. The angle between sunset and sunrise varies proportionately with latitude.. 
Yes, that's why days are shorter/longer in different parts of the world on the same day.
But will this give you a number you can use to calculate the size of the earth? Or do we only know this since we know what the size of the earth is?
2. On May 1st measure this angle at St Michael's Mount. 
You probably won't be able to see the sun at the exact moment of sunrise from St Michael's Mount, because the sun rises from the sea at Norfolk.
3. On May 1st measure this angle at the Norfolk end. 
Ditto, the other way around.
5. Measure how far north the Norfolk coast is from St Michael's Mount. 
I have stated previously that this is in fact the biggest drawback of this technique, even if the rest of the solution would be possible/feasible.
And you can't measure how far north A is from B without knowing the length from A to B and their respective latitudes. Unless you can find a point C, which is north of A and parallel to B (so C completes a triangle). Unfortunately in this case, point C would be somewhere in the Irish Sea.
What we need is a part of England that is relatively void of hills. Any suggestions? I know of one...






Brian Ambrose




Mick Harper wrote:  No, Brian. If you had such a timepiece you'd be able to solve all longitude problems (and therefore all earthsurveying problems) as they did in the eighteenth/nineteenth centuries (AD). The whole point of the Greek and My Megalithic method is to obviate the need for timemeasurement by using displaced correlation. However time does come into Keimpe's method (insofar as I understand it) but I will leave him to develop this.
The two measurements, Cornall and Norfolk, are not time dependent because you are measuring the same phenomenon at two vantage points on the earth's surface which have a known relationship. The fact that sunrise is a few minutes earlier in Norfolk does not effect the measurement of the angle. 
Pardon my ignorance. Here's what wiki says about Eratosthenes:
Eratosthenes measured the circumference of the earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle (7°12') south of the zenith at the same time .

Without a clock, how did he know the difference of angle of elevation 'at the same time'?






Keimpe
In: Leeuwarden, Frisia




Brian Ambrose wrote:  Without a clock, how did he know the difference of angle of elevation 'at the same time'? 
I don't know the specifics, but I reckon you can use a simple sun dial to know whether it is noon or not.
And please don't rely on Eratosthenes too much, he did everysinglething wrong:
The sun is never directly overhead in Aswan.
Alexandria is not directly north of Aswan.
The distance between Aswan and Alexandria is different then the distance Eratosthenes measured.
He probably used a sun dials as described above, so 'noon' might have been slightly (but only slightly) off.
And it seems he was also slightly off with the angle he measured towards the sun.
Fortunately, my method is much more reliable ;)






