Talk:Bedford Level experiment

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Problems needing fixing[edit]

I started to edit this article after I noticed a big chunk of text that seemed to be the remains of a paragraph that had not been properly removed. Looking at the history, it seems like there have been some pretty major changes to the meaning this article within the last few months (Nov. 2015 - Jan 2016). The changes appear to reverse the conclusion of the experiment, from disproving to proving the earth is flat. Many references were also removed.

There does not appear to have been any discussion to justify the changes.

I don't know what to do at this point - I do not think I am qualified to fix the article. Phil56 (talk) 01:46, 29 January 2016 (UTC)

I'm not sure this is the only problem you noticed, Phil56, but someone at IP address User: (possibly the same person as User:Jake Gibson) has repeatedly edited this page over the past several weeks, removing references and flipping the alleged result of the experiment (i.e. claiming that it proved the earth is flat). I've just hit the revert button on their changes for the second time today, and I'm considering flagging this article for moderator attention, only I don't know which of the legion of moderator boards is the right place. Elwoz (talk) 03:01, 2 February 2016 (UTC)

I am not sure how to fix this, but this article is seriously being repetitively vandalized. Seems people are trying to advance a flat earth view. Chad (talk) 04:27, 2 February 2016 (UTC)

I have attempted to raise the issue on the administrators' noticeboard for edit wars:'_noticeboard/Edit_warring#User:

I'm still not sure that was the right place to take it, but everything else seems more wrong. Elwoz (talk) 14:28, 2 February 2016 (UTC)


A possible explanation is given in the "Mirage" paragraph, yet the "Evidence" paragraph now reads "No explanation has been given of the results of these experiments". --Old Moonraker (talk) 12:48, 10 October 2009 (UTC)

Resolved by replacing with a WP:SS link to the main article. --Old Moonraker (talk) 11:13, 13 October 2009 (UTC)

Problem in First Paragraph[edit]

This statement implies Samuel Rowbotham, the performer of the Bedford Level Experiment, had a bias against the idea of the Earth being round: "It was an attempt to demonstrate that the Earth was flat." It is clear by Samuel Rowbotham's writings in Zetetic Astronomy: Earth Not a Globe (Available here: that the philosophy of Zeteticism, which he promotes within, Rowbotham's written examination of data from experimentation within this book, and the detailed explanations of experiments within the book indicates an openness to whatever conclusion may logically result from data from experimentation. There is no clear indication that he had a bias against the idea of the Earth being round, and if such a bias existed, there is no written record or obvious proof of it. I'll assume everyone understands that however he truly and privately felt within is unknowable and irrelevant to the article. I apologize if this _seems_ pedantic, but I assure you that this is a detail which should not be overlooked. I have edited the sentence and part of the following one to say the following: "It was an attempt to determine the shape of the Earth. Early results seemed to prove the Earth to be flat," The first half of the second sentence originally said: "Early results seemed to prove this contention," (talk) 04:37, 24 January 2011 (UTC)

This would be a valid point, supported by WP:NEUTRAL, but I can't see what's wrong with your fix: "attempt to determine the shape of the Earth". It doesn't seem to carry any preconception. Citations in lead paragraphs are generally avoided, unless the statement is controversial: as a summary of what follows the content relies on adequate citing of the rest of the article. I propose to remove the {{cn}} tag, subject to other editors' views (or, of course, a patient explanation why I am missing the point here). --Old Moonraker (talk) 08:20, 24 January 2011 (UTC)
One tag removed, one given a ref and removed.--Old Moonraker (talk) 07:42, 25 January 2011 (UTC)

Dodgy caption[edit]

The caption Photo of the site published by "Parallax" (1870) is under a diagram, not a photo!
--Robert EA Harvey (talk) 06:53, 26 June 2014 (UTC)

Hampden threatening to kill Wallace?[edit]

The article currently states that "Several protracted court cases ensued, with the result that Hampden was imprisoned for libel and threatening to kill Wallace" and provides two supposed references to that claim. Having investigated both references (the pamphlet and the article which I reuploaded from The Times' archive), I have found no evidence of death threats being made. I briefly tried searching for other references, but that turned out to be fruitless. With that in mind, I'm removing the mention of Hampden threatening to kill Wallace from the article. Please feel free to restore it if you can provide a reference. Apples grow on pines (talk) 01:09, 31 July 2014 (UTC)

You may be right that the Times doesn't include the threat, but it was made all right. In his autobiography Wallace recalls the following on p368:
he sent the following letter to my wife:
Mrs. Wallace,
"Madam-If your infernal thief of a husband is brought home some day on a hurdle, with every bone in his head smashed to pulp, you will know the reason. Do you tell him from me he is a lying infernal thief, and as sure as his name is Wallace he never dies in his bed.
"You must be a miserable wretch to be obliged to live with a convicted felon. Do not think or let him think I have done with him.
"John Hampden."
Seems clear to me. Chris55 (talk) 13:45, 31 July 2014 (UTC)

I suggest to add the following section into this article along with the image and chart from the links.

Earth's curvature and how to calculate it[edit]

IF the earth is a globe, and is 25,000 English statute miles in circumference, the surface of all standing water must have a certain degree of convexity--every part must be an arc of a circle. From the summit of any such arc there will exist a curvature or declination of 8 inches in the first statute mile. In the second mile the fall will be 32 inches; in the third mile, 72 inches, or 6 feet, as shown in the following diagram:

Let the distance from T to figure 1 represent 1 mile, and the fall from 1 to A, 8 inches; then the fall from 2 to B will be 32 inches, and from 3 to C, 72 inches. In every mile after the first, the curvature downwards from the point T increases as the square of the distance multiplied by 8 inches. The rule, however, requires to be modified after the first thousand miles. 1 The following table will show at a glance the amount of curvature, in round numbers, in different distances up to 100 miles.

--Steveengelhardt (talk) 09:09, 20 June 2015 (UTC)

Unfortunately, as should be obvious by just LOOKING at the diagram provided by Rowbotham, this formula doesn't give you the amount the Earth "drops" away from you as it curves, but instead gives the height an object would have to be for its top to appear level with your line of sight tangential to the Earth. These are not the same thing at all. The actual formula for calculating the amount a spheroidal Earth (with a mean radius) would "drop" away from you as it curves is given here: And would be sqrt((2*sin(360(c)/(2pi*r)/2)r)^2-(sin(360(c)/(2pi*r))*r)^2), where r is the radius of the Earth and c is the distance along the surface of the Earth. As should be evident from the following diagram: The value you want to calculate is "d", which is obviously sqrt(n^2-m^2).

n is the arc width of the central angle "C", and so is 2*sin(C/2)*r, as can be seen here:

m is simply sin(C)*r, as can be proven here:

Since the central angle "C" is just the distance "c" over the surface of the Earth divided by the circumference and multiplied by 360, or 360*c/(2*Pi*r)

Putting the other values solely in the terms of the variables we know (the distance over the surface of the Earth "c" and the radius of the Earth "r") we can express the equation to find the "drop" of the Earth away from you sqrt(n^2-m^2) into: sqrt((2*sin(360(c)/(2pi*r)/2)r)^2-(sin(360(c)/(2pi*r))*r)^2)


I'm afraid Rowbotham's geometry is just demonstrably false - and this demonstrably false formula is still being thrown around today, by many in the flat Earth community. It is fine for an approximation over short distances, where the value given will be very close to the true value, but over further distances the formula begins to break down incredibly quickly.

Whilst I think it is a matter of import to show how Rowbotham was calculating the curvature, it is also a matter of import to demonstrate where he was incorrect and how. Otherwise, people will think that this really IS the correct formula for calculating the amount the Earth "drop" away from you after a set distance.

I'm thinking of adding this in, but want to see what others think. However, I do believe there is a possibility that people will read this page and think that Rowbotham's formula is correct, and thus will get the wrong idea about geometry. Vyr Cossont (talk) 22:16, 7 July 2015 (UTC)

Seriously, guys, we need to at least make a note that the calculations used by Rowbotham are geometrically inaccurate, if we're to have them in the article at all. Otherwise, as the stand there, they appear to be an authoritative account for the geometry, which is clearly incorrect. I'd like to make such an amendment, but I'm waiting for confirmation. If I don't hear anything, I'll make a note and take the lack of protest as consent. If we're to make a note of the formula he used, we also have to make a note of the error it contained, or we are giving a false impression of the geometry involved. Vyr Cossont (talk) 12:38, 8 July 2015 (UTC)

I'm not quite sure if your point is that the word "drop" is misleading or that you think the actual calculation is wrong. Clearly Hampden either failed to understand the sight through a level (or refused to) and that's part of the problem. Also Rowbotham failed to realise that the theoretical sight distance has to take into account both the height of the target and that of the observer (ignoring any refraction issues at this point). But the '8" squared per mile" calculation is a reasonable approximation however you calculate it for distances up to, say, 100 miles. Chizzlewit's trigonometric formula was predated by the Greek's approximation: height*diameter of circle=tangential distance^2. But the two give very close results over this range. (I haven't checked it but I did a similar trigonometrical calculation.)
If you want to add more, that's fine, but you need to use a reliable source. Chris55 (talk) 20:05, 8 July 2015 (UTC)

I don't have any concern with the term "drop", just that the thing Rowbotham is actually claiming to calculate is not what he is really calculating - though, as you say, it is OK over short distances. The major concern was that the section appeared to suggest that this is the formula to calculate the amount the Earth "drops" away from you, when in actual fact it gives you an approximate value for the exsecant, which is actually the height an object has to be in order to lie at the point of zero declination with your eyesight, if you were lying flat with the surface of the Earth. The 2 are not the same thing. Although, as you say this formula gives close approximations for the "drop" over short distances. I just think it is important to point this out, in order to make sure the readers don't get the geometry wrong, as people may use this formula for larger distances, or think they can extrapolate it to other similar geometric problems. My main concern is that the section does very much seem to try to suggest that this is HOW to calculate the value in question, rather than stating that this is an approximation as used by Rowbotham, which I think would be more correct to state.

The article I've given is the only place where I can find the formula being given (and full disclosure, I wrote it up, because there was nowhere actually dealing with the geometry involved in the question, which I find interesting purely from a geometric stand point), but you can happily check through the geometry and see that it is correct for calculating the "drop" of the Earth's curvature, rather than just the height an object has to be in order to have a declination of zero with your line of sight. The article doesn't need to be linked, nor the formula given - I just feel that it is important to highlight the fact that Rowbotham's formula is an approximation that works over short distances, rather than giving people the false idea that this is THE formula to give you an accurate result for all distances.

If you think I should link the article, fine - or if you think it's best to just highlight the fact that it is an approximation, that's fine as well. I don't want to do anything - certainly not beyond the latter - without confirmation that you think it is appropriate for the article. Vyr Cossont (talk) 21:46, 8 July 2015 (UTC)

Vyr, I agree with you that what it measures is "the height an object has to be in order to lie at the point of zero declination with your eyesight, if you were lying flat with the surface of the Earth". It might well be that that was why Rowbotham got his eye-level right down to the water: he may have been trying to mimic that diagram. You have to remember that he was not well educated and this was in the early days in which your "average man" received any education at all. I think it would be well worth adding this to that section, but it doesn't necessarily need the full geometrical treatment. There's a good example in his book about seeing the Isle of Man from the Welsh cliffs which illustrates these misconceptions. (His conjuring with the Eddystone Lighthouse shows however that he was a master at obfuscation!)
But the problem with the Bedford Level experiment was that there was apparently no curvature, not that it was underestimated. This wasn't due to his miscalculation but that he got his eye right down there next to the water - presumably, as you have pointed out, because his diagram starts from there - and so experienced something similar (but opposite) to a mirage.
As a point of information, blogs do not normally qualify as WP:Reliable sources so shouldn't be referenced. The Wiki article Horizon#Objects above the horizon does contain most of the formulae, although of course cross-references to wiki articles in an article are also not encouraged! Chris55 (talk) 22:40, 8 July 2015 (UTC)

Cool. I wasn't sure if it would need the geometric treatment for clarification, or if just noting that it was an approximation that was close enough over short distances, but which was ultimately based on a misunderstanding of the geometry, would be enough. Personally, like you, I think that latter is fine. Just to highlight the problem with the formula he was using, look at what happens when you get to a point of a quarter circumference over the surface of the Earth (which would describe an arc length of a 90 degree angle), looking at the geometric proof he uses to demonstrate his formula - the geometric proof falls down as the 2 lines (that of your eye line, and that of the height of the object) become parallel. The fact he didn't spot this kind of says a lot about him, and highlights the meaninglessness of the formula as anything other than an approximation for short distances. Still, I'll work on a good wording for a short note to the effect that the formula is approximate and based on a misconception and add it shortly. If people think the wording needs to be edited afterwards, then I shall be happy to leave it to them. I'll also leave a reference blank for the time being, and if people think it needs something, or they have something reliable in mind, they can add it. Thanks again. (talk) 23:26, 8 July 2015 (UTC)

You can very rarely see long distances at sea: there's too much haze. I remember sailing round the heel of Italy at dawn and my surprise at seeing mountains (Albania) ahead of me. Within half an hour they'd disappeared and I didn't see them the rest of the day as I sailed towards Corfu. In this case Mount Çika at 2,044m was 120km away and the 3.57*sqrt(2044) formula gives 161km (and is incidentally only 0.0078% wrong). But refraction could have played some part in making them seem taller. It's easy even for the sailor to make mistakes in these situations.
As you say the squared formula is only of use for smallish distances because the geometrical formula is actually height*(height+diameter) and one ignores the second term. Chris55 (talk) 13:37, 9 July 2015 (UTC)
I see looking back that the Isle of Man example I quoted only occurs in the 1865 version p14 which may be found here. But it's a good example of his methods, combining exaggeration and debating skills to baffle win over his audience. The diagram is quite acceptable and shows the realistic situation in which Great Orme near Llandudno (height 682ft) and South Barrule on the Isle of Man (1,584ft) are within sight of each other. But he then throws in a doubtful fact: that the Great Orme can been seen from 100' above Douglas and proceeds to use it to produce some enormous numbers: this makes the horizon only 13 miles from Douglas leaving 47 to the Great Orme, which leaves a height of 1,472ft which is 872' more than the height of that mountain.
In fact, by my calculation you'd have to be about 570' up at Douglas to see the Great Orme so the distance to the horizon is then 29 miles leaving only 31 instead of 47. And he's cut down the height of that hill from 682' to 600'. But his horizon lines are shown not from the middle where they should be but the ends which produce the effects that you described earlier. (And in fact most people probably viewed the Isle of Man from the Great Orme rather than the other way round so seeing a much higher hill and you can see that from 100'.)
So you can see how a skilful debater will be able to delude his audience. You have to sit down and do the sums to demonstrate the falsity. The curious thing in these examples is that they don't dispute the curvature of the earth - only the amount of the curvature - but they then use this to 'prove' that the curvature doesn't exist. Presumably these discrepancies were pointed out at the time so he left them out of the 1881 version. Chris55 (talk) 13:01, 11 July 2015 (UTC)

The table that keeps getting put in and taken out[edit]

It's true that there is a table in the original document that's being quoted, as User:Theophil789 observes. (And the quotation refers to the table, so not having the table is confusing.) It's also true that the table we had is not the table in the original document, as User:GraemeLeggett observes.

But I think really what we want is a different quotation; the table is long, boring, and distracts from the point, which is to demonstrate why Rowbotham considered the Bedford Level an appropriate location for his experiment. I propose the following instead:

IF the earth is a globe, and is 25,000 English statute miles in circumference, the surface of all standing water must have a certain degree of convexity--every part must be an arc of a circle. From the summit of any such arc there will exist a curvature or declination of 8 inches in the first statute mile. In the second mile the fall will be 32 inches; in the third mile, 72 inches, or 6 feet, as shown in the following diagram:
(existing diagram here)
...[A]fter the first few miles the curvature would be so great that no difficulty could exist in detecting either its actual existence or its proportion...In the county of Cambridge there is an artificial river or canal, called the "Old Bedford." It is upwards of twenty miles in length, and []passes in a straight line through that part of the Fens called the "Bedford Level." The water is nearly stationary--often completely so, and throughout its entire length has no interruption from locks or water-gates of any kind; so that it is, in every respect, well adapted for ascertaining whether any or what amount of convexity really exists.

That avoids the issue of what table, if any, to have altogether.

--Elwoz (talk) 17:02, 7 September 2016 (UTC)

That sounds a reasonable approach to take. GraemeLeggett (talk) 11:13, 8 September 2016 (UTC)
Agreed. I did check the height arising from the distance for Great Orme Head to Isle of Man some time ago but if I remember right his calculation wasn't accurate enough to be worth quoting. I think most people will get the idea without it being spelled out. Of course the haze is usually enough to prevent any of these observations. Chris55 (talk) 11:19, 8 September 2016 (UTC)

IP user edits[edit]

I invite to discuss their attempted edits here. 331dot (talk) 21:02, 5 October 2016 (UTC)

Who the F*ck is Alfred Russel Wallace[edit]

",but after adjusting the method to avoid the effects of atmospheric refraction, Alfred Russel Wallace found a curvature consistent with a spherical Earth." - The quoted text in the second sentence keeps being added and removed. I see it as unnecessary and poorly written. What is with this need to have it stated BUT HE WAS WRONG! in the second sentence of the article. If it needs to be stated at all, it would make more sense later in the article. Steveengelhardt (talk) 04:14, 6 October 2016 (UTC)

In the context of this article, Alfred Russel Wallace is the fellow who debunked Rowbotham's claim of proving the Earth to be flat. The debunking and protracted litigation around the experiment are very much part of the story. Stripping the mention of that context from the lead paragraph goes against MOS:LEAD, which says "The lead serves as an introduction to the article and a summary of its most important contents." Just plain Bill (talk) 14:33, 6 October 2016 (UTC)