Bedford Level experiment

{{Sciencenav}}
[[File:Rowbotham–curvature.jpg|thumb|300px|right|Diagram of Rowbotham's experiment on the Bedford Level, taken from his book "Earth not a globe"]]

The '''Bedford Level experiment''' was a series of attempts, beginning in the late 19th century, to deny the curvature of the Earth's surface. First conducted by [[Flat Earth|Flat-Earther]] Samuel Birley Rowbotham, observations along a long straight stretch of drainage canal in the English county of Norfolk seemed to confirm that the Earth is flat.

The basic idea was to use a surveyor's telescope to observe marks at a uniform height above the water, spaced three miles apart.<ref>[http://blogs.scientificamerican.com/rosetta-stones/wallace-8217-s-woeful-wager-how-a-founder-of-modern-biology-got-suckered-by-flat-earthers/ Scientific American, Rosetta Stones: "Wallace’s Woeful Wager: How a Founder of Modern Biology Got Suckered by Flat-Earthers"]</ref> If the earth is curved, the marks will not line up. Mariners had been correcting their lunar sights for the {{wpl|atmospheric refraction}} of light near the horizon since the eighteenth century, but the flat-earth proponents [[Dunning-Kruger effect|failed]] to [[Willful ignorance|account for it]], and claimed the observed existing misalignment showed curvature (on still water) but much less than the crazy Round-Earth fanatics had predicted.

Years later, Rowbotham's results were taken up by one of his supporters, one John Hampden, who wagered a bet that he would prove the earth is flat. [[Alfred Russel Wallace]] took him up on this, and by accounting for optic refraction, he repeated the experiment and showed the Earth to be curved. Wallace was judged the winner by the editor of ''The Field'' (a gamblers' magazine), but Hampden claimed Wallace had cheated. Death threats, libel cases,<ref>[http://query.nytimes.com/mem/archive-free/pdf?_r=1&res=9C00EFDF113EEE34BC4852DFBE66838A669FDE&oref=slogin The Form of the Earth&mdash; A Shock of Opinions] New York Times, August, 1871</ref> and Hampden's incarceration ensued.

=== Samuel Rowbotham's Experiment (1838)===

==== The Crank ====

Samuel Birley Rowbotham, the father of modern flat earth crankery, was an elementary-school dropout, snakeoil salesman with no medical degree,<ref>which makes it even funnier when Eric Dubay [https://youtu.be/SauZfMS-lZo?feature=shared&t=3094 calls] Rowbotham a doctor.</ref> and who got several people killed with his phosphorus based cure-all "medicine". He also accidentally poisoned one of his children, who then died. At the age of 46, he married a 15 year old girl with whom he produced 15 children.

==== The Crank Experiment ====

The experiment took place at the {{wpl|Old_Bedford_River|Old Bedford River}} ([https://earth.google.com/web/search/Old+Bedford+River/@52.51899635,0.24981118,-0a,394.31282896d,35y,-137.10838296h,74.55993183t,0r/data=CiwiJgokCQSYTzQUX0hAEb3rkq5qWTlAGQZURdrbq1TAIbgEQnvyAmPAQgIIAUICCABKDQj___________8BEAA map], [https://earth.google.com/web/@52.4514426,0.16284201,6.03011227a,0d,71.14466254y,31.01795207h,80.3221621t,0r/data=CgRCAggBIhoKFlFxSjdEWlhUVkVJQmtVUGVDU1VUNWcQAkICCABKDQj___________8BEAA street view]), that is 6 miles (9.66km) long and roughly 10 m (30ft) wide.

Rowbotham estimated the drop over 6 mile distance to be 8 inches per mile. This is acceptable, as the approximation formula produces only 0.6mm of error at three mile mark.

The curve was observed at 8 inches (20.3cm) altitude. The target was a boat that had a flag on it, the tip of which was at 3 feet (91 cm) height from the water. Rowbotham claimed the boat was visible entire time, and that in the globe model, the mast should have been 11 feet (3.4m) below his line of sight.


===Alfred Russel Wallace's Reproduction (1870)===

[[File:Welney bridge observation point.png|thumb|right|The Old Welney Bridge that was used as the observation point.]]
[[File:Old bedford bridge.png|thumb|right|Old Bedford Bridge 6.00 miles from the Welney Bridge. Wallace attached a giant white cotton cloth with a large black stripe the bottom of which was at the same height as the iron parapet of the Welney bridge: 13ft 3in = 403.86cm.]]

In 1870, {{wpl|Alfred_Russel_Wallace|Alfred Russel Wallace}}, a naturalist, explorer, geographer, anthropologist, biologist, an illustrator, and a qualified {{wpl|Surveying|surveyor|,}} took one John Hampden's 500 pound wager (63,500 USD, inflation adjusted to Dec '24), to replicate [[Flat_Earth#Samuel_Rowbotham.27s_Bedford_Level_Experiment|Rowbotham's Bedford Level experiment]].

Wallace removed errors from Rowbotham's experiment. He didn't go hang about in the canal, or use flimsy boats. He strived for replicability of his experiment.

'''The observation point (Point A)''' was the Old Welney Bridge ([https://earth.google.com/web/search/52%c2%b031%2710%22N+0%c2%b015%2703%22E/@52.5194444,0.2508333,3.24398591a,490.17852011d,35y,0h,0t,0r/data=Cl4aMBIqGZALcyd9QkpAIT_bDx2nDdA_KhY1MsKwMzEnMTAiTiAwwrAxNScwMyJFGAIgASImCiQJ0PHovJlCSkAR9IHEzGdCSkAZoF22g0Ma0D8hiGD2WXcD0D9CAggBQgIIAEoNCP___________wEQAA 52°31'10"N 0°15'03"E]). Wallace wanted to minimize the effect of refraction, so from the observation point, he set a sight line at the altitude of Welney bridge's railing. The distance from the top of the iron parapet of the bridge, to the surface of the water below it, was 13ft 3in = 403.86cm. 

'''The sight line's target (Point C)''' would be at the Old Bedford Bridge ([https://earth.google.com/web/search/52%c2%b027%2705%22N+0%c2%b009%2746%22E/@52.45138891,0.16277782,3.57998465a,491.00524105d,35y,0h,0t,0r/data=Cl4aMBIqGYKjiRzHOUpAIenlwSfn1cQ_KhY1MsKwMjcnMDUiTiAwwrAwOSc0NiJFGAIgASImCiQJFkLFFPU5SkARxppqJ5k5SkAZ8HHbwCBxxT8hcNpoG7U6xD9CAggBQgIIAEoNCP___________wEQAA 52°27'05"N 0°09'46"E]) that was 6.00 miles (9.66 km) North-West from the Welney bridge's observation point. Because Welney bridge was made of bricks, Wallace had to mark the sight line. This was done by attaching a 6 feet wide by 3 feet tall white cotton cloth, with a large black horizontal line, to the side of the Old Bedford Bridge. The height of the cloth was set so, that the bottom of the black line also sat 13 feet 3 inches (403.86 cm) above water.

'''A marked stick (Point B)''' was then placed in the exact middle point between the two bridges, i.e., 3 miles from both bridges. The stick had two large red discs. The middle point of the upper disc was also set at altitude of 13 feet 3 inches (403.86 cm). The second disc was 4 ft (121.92 cm) lower, i.e., its middle point was 9 feet 3 inches (281.94cm) above water.

'''The prediction''' Wallace made was this: If the Earth was flat, (Fig. 2), then, when observing the sight line with a telescope, the upper disc will be at the same altitude as the sight line. If on the other hand, Earth was round, (Fig. 1), then the middle point of water would bulge, and upper disc would be 5 ft 8 in (172.72 cm) higher, and since the lower disc was only 4 feet below the upper one, even that one would be above the sight line. Wallace estimated atmospheric refraction to cause roughly 8 inches (20 cm) inches of deviation.

{{collapse|The mathematical equations|width=500}}
Let 

* '''R''' be the {{wpl|Earth_radius|radius of Earth|,}} '''6,371,008.8 m''',
* '''L''' be the distance between the bridges, '''6.00 miles = 9,656.064 m''',


'''The sagitta'''

The {{wpl|Sagitta_(geometry)|sagitta|,}} (the height of the bulge on a spherical Earth) would be

'''s = R − √( R² − (L² / 4) )'''

'''s = 6,371,008.8 − √(6,371,008.8² − (9,656.064² / 4))'''

'''s ≈ 1.829375 m'''

'''s ≈ 6.001886 ft'''



'''The error in Wallace's sagitta'''

Wallace stated that the known size of the Earth would predict a '''5 ft 8 in''' sagitta, when in reality it's '''6.001886 ft''' or '''6 ft 0.02 in''', which is '''5.9%''' off.

The reason for this disparity is unknown, but it's possible he (or his source) ran the calculations in SI-units, and either misremembered or misrecorded the radius of Earth to be '''6,731 km''' as opposed to '''6,371 km'''. This mistake yields sagitta '''s''' of 

'''s = R − √( R² − (L² / 4) )'''

'''s = 6,731,000 − √(6,731,000² − (9,656.064² / 4))'''

'''s ≈ 1.731778 m'''

'''s ≈ 5.67907 ft'''

'''s ≈ 5 ft 8.15 in'''



'''Refraction'''

Wallace predicted the refraction to lead to apparent '''5 ft''' sagitta.

According to <ref>Schadewald, Bob (ca. 2000). [https://www.cantab.net/users/michael.behrend/ebooks/PlaneTruth/pages/Chapter_02.html "The Plane Truth"]</ref>, it was a "fine day and the sun [was] warm on their faces".

The refraction index on a sunny day is '''k ≈ 0.10–0.15'''.


For a 5 feet apparent sagitta, the '''k''' for the correct size Earth ('''r = 6,371 km'''), would be 

'''k = 1- 5.00 / 6.0019 = 0.167'''


For a 5 feet apparent sagitta, the '''k''' for the misremembered size Earth ('''r = 6,731 km'''), would be 

'''k = 1- 5.00 / 5.6791 = 0.119'''


Both are within the ballpark of a sunny day. Also, the refraction is reducing the real bulge, so it's trying to make the Earth look flatter than it is, as opposed to making a flat Earth look spherical.



Also, as per <ref>Young , Andrew T. (2020). [https://aty.sdsu.edu/explain/atmos_refr/dip.html "Dip of the Horizon"]. Via sdsu.edu.</ref>, "''Values of k around 0.13 have been used in correcting surveyors' data for a century or more''".


Using '''k = 0.13''' and the correct Earth radius ('''R = 6,371,008.8 m'''), the apparent sagitta '''s''' is 

'''s = 6.001878 × (1 − 0.13) '''

'''s = 5.221634 ft'''


Using '''k = 0.13''' and the misremembered Earth radius ('''R = 6,731 km'''),

'''s = 5.680882 × (1 − 0.13)'''

'''s = 4.942368 ft'''


Both are easy to round to the 5 ft ballpark. Thus, Wallace's prediction of 5 ft apparent sagitta during the experiment was highly accurate.
{{collapse end}}


[[File:Wallace predictions.jpg]]

'''The result''' that both Wallace and Hampden observed and signed, showed obvious curve:

[[File:Wallace result.jpg]]

This debunked Rowbotham's hand-wavy experiments that failed to account for atmospheric refraction and proved the curve.


==== The bitching and whining ====

According to {{wpl|Bedford_Level_experiment|wikipedia|,}} Hampden who lost the bet, refused to accept the result. He wrote pamphlets that called Wallace a cheater, and like a good charlatan, sued Wallace to get his money back. He was also imprisoned for libel and for threatening to kill Wallace.

Today, flerfs like [https://youtu.be/SauZfMS-lZo?feature=shared&t=3072 Eric Dubay] lie by omission by telling the story of all Rowbotham's experiments, but they do not even mention Wallace's experiment that revealed flerfs' party trick.

==Further reading==
*Rob Hernlund - Flat Earth Confusion: Rowbotham Missed the Boat (2023) ASIN: B0BTKHP3MW

==See also==
*[[The Final Experiment]]

*[[Lake_Minnewanka_curve_experiment|Lake Minnewanka Curve Experiment]]

*[[Zetetic]]

==External links==
*{{wpa|Bedford Level experiment}}

==References==
{{reflist}}

{{stub|Science}}

[[Category:Science-related stubs]]
[[Category:Denialism]]

Categories: Science-related stubs, Denialism