Where and How could the Wallace Experiment Easily Be Repeated?

[cloudspotter]

Q. Anyone know the depth of the canal?

I'm thinking poles mounted in concrete blocks sitting on the bed.

How about floating markers able to slide up and down a fixed pole attached to a bridge?

 

[Rory]

How about floating markers able to slide up and down a fixed pole attached to a bridge?

Attached to the target bridge and the railway bridge?

How about if the targets had flashing lights on them, differently coloured for each distance?

 

[cloudspotter]

Attached to the target bridge and the railway bridge?

How about if the targets had flashing lights on them, differently coloured for each distance?

Yeah fixed poles with poles attached that can move up and down with water level. Float at the bottom and marks at the top. I wonder if flashing lights might make measurement more difficult with the glare though

 

[Rory]

Yeah fixed poles with poles attached that can move up and down with water level. Float at the bottom and marks at the top.

That's a nice idea. Do you think the railway bridge in the right place for that? What about the suggestion that a minimum of three targets would be best?

 

[Mick West]

What about the suggestion that a minimum of three targets would be best?

I wouldn't let that stop you. In part this is a historical recreation. There's already vastly better version of the experiment out there, fixed in place, with scores of markers, like the Ponchartrain causeway. Various views of which (and other similar structures) can be seen here:

Source: https://www.youtube.com/watch?v=AtODdWv6PVk


With a prime example here. Look at the tops of the dark grey regions:

That's essentially the Wallace experiment with an extra "near" marker.

Personally I'd like to see the experiment repeated as closely to the original as possible.

 

[DavidB66]

I have read somewhere - possibly in Christine Garwood's book - that Wallace originally planned to have five or six markers, at 1-mile intervals, and not just three. He set up the markers on the night before the experiment but the next day found that for some reason they were in disarray. (Blown over by wind? Knocked over by cattle? Or local hooligans on the way home from the pub? ) He therefore simplified the experiment to the version recorded in his autobiography. I don't think he mentions the original plan there. It is worth noting the lesson that the more complicated the set-up the more chances there are for it to go wrong.

 

[cloudspotter]

That's a nice idea. Do you think the railway bridge in the right place for that? What about the suggestion that a minimum of three targets would be best?

Don't know. I was just pondering the problem of mounting the poles and keeping them vertical and the markers a fixed distance above the water

 

[Z.W. Wolf]

(edby: You seem to be already thinking in this direction; just wanted to add some encouragement.)


Activity like this is bound to catch the attention of whatever government agency. Instead of fighting them you might as well take advantage of the historical significance of this and get some cooperation. A permanent set-up, a plaque, photo taking opportunities (holiday snaps), school outings, tourist dollars, eh pounds... That sort of thing. Possibly get some modest government funding.

The https://www.gov.uk/government/organisations/environment-agency/about is mentioned in the article you linked to in Post #123

Not forgetting the Bedford Borough Council: https://www.bedford.gov.uk/

They advertise a River Festival in July, and a "Rivercare Cleanup." They seem to be interested in tourism.

FE is catching the eye of the media. A story on the recreated Wallace experiment might be something of interest.


But it might be best to start off with a private organization. They are shown doing restoration work here, so they must have connections with the powers that be.:

The East Anglian Waterways Association http://www.eawa.co.uk/work.html

AWA arranges work-parties for waterway restoration, improvement and maintenance and offers advice, support and funding to local organisations with similar aims.

It's clear the canal has silted up, the banks have grown and the waterway is narrower, has grown choked with "cott weed," etc. These are impediments to your project, but may be an opportunity to fold your project into a larger restoration project.



A national group.
Inland Waterways Association: https://www.waterways.org.uk/

 

[Rory]

Personally I'd like to see the [Wallace] experiment repeated as closely to the original as possible.

So how about the original, with the addition of posts/targets at 1.5 and 4.5 miles?

That's basically the same thing, with a little extra nugget of sweetness.

Activity like this is bound to catch the attention of whatever government agency.

I could see it being a problem if that section of the river is currently used for navigation - i.e., canal boats are travelling it.

The IWA site describes the Old Bedford River as "open." I've read that boaters themselves, however, haven't been able to navigate it because of silt.

There is mention here of desilting between/at Salters Lode and the Old Bedford Sluice, but that doesn't appear to be on the straight stretches of the river either side of Welney Bridge.

I did a report for the Canals & Rivers Trust earlier this year; judging by that, and what I've read online, I'd be very surprised if any barges or powered boats are able to navigate the Old Bedford around Welney.

FYI a YouTube video using a P900, both directions from Welney Bridge.

Source: https://www.youtube.com/watch?v=J2dXoxu_Ua0

Watching this makes me somewhat doubtful that a P900 would be powerful enough to pick up on one-metre targets 6 miles away.

 

[Mick West]

Watching this makes me somewhat doubtful that a P900 would be powerful enough to pick up on one-metre targets 6 miles away.

It's perfect capable of doing that, that's only half the size of a one meter target 3 miles away. See my 3 miles gas station photos. You can see things that are much smaller like the lettering on the signs

The limit is not the camera, it's the atmospheric conditions. The video has significant haze and turbulence. Early morning would probably be best.

 

[Z.W. Wolf]

Right; your test is in dry California air.

The P900 at max optical zoom is 40 power. A 3 foot target at 3 miles is like looking at a 3 foot target 1 1/3 football fields away (sans endzones) with the naked eye. Easy.

At six miles, it's like seeing the same target at 264 yards. I've shot at a smaller target at 300 yards with open sights (no telescopic sight). Experts can hit at 800 yards.

But six miles of damp and/or turbulent air is a challenge.

 

[Rory]

The limit is not the camera, it's the atmospheric conditions. The video has significant haze and turbulence. Early morning would probably be best.

Yes, I did originally add something about the English gloom and haze - but didn't want to cast aspersions on our fair isle, nor tempt fate, nor reflect unfairly, when there are also a good number of sunny clear days (some years).

If you think the P900 is good enough for the 6-mile test - seeing as you use one - then that's good enough for me.

I was just searching Google Images for 'Old Bedford Bridge', in the hope of identifying the 'target' bridge in the Wallace experiment. It is not entirely clear from Wallace's own account where his observations were made. He says that they were between Welney Bridge and Old Bedford Bridge, six miles distant. There is only one bridge at Welney, but I have not yet been able to identify Old Bedford Bridge.

However, Wallace does refer to the town of Downham Market, which is just over six miles to the north-east of Welney, which perhaps makes it more likely that the view was from Welney to the north-east, the target bridge (OBB) being at the hamlet of Salters Lode, just outside Downham Market.

Photographs of the bridge at Salters Lode, e.g. here http://www.geograph.org.uk/photo/685667 seem a fair match for Wallace's illustration of the target bridge.

While that bridge resembles the illustration, I don't think it necessarily means it's the bridge in question. Number one, as already pointed out, it's on a different waterway. And, number two, the bridge known as 'Old Bedford Sluice' - on the right waterway - looks much more modern than 1870.

My guess therefore is that 'Old Bedford Sluice' replaced an earlier bridge, which looked similar to the bridge still at Salters Lode, and it was this bridge Wallace was using, referring to it as 'Old Bedford Bridge'.

Figuring that out, though - after we'd all been assuming he was using Welches Dam to Welney - is actually really valuable, and I'm currently thinking this stretch would be the best one. Though it's not the stretch Rowbotham used, it has the advantage of no railway bridge, and is somewhat straighter than the SW portion, which also has a large kink in it, about 3.4 miles NE of Welches Dam:

(To quickly test the straightness of the river, here's a link with a line drawn down the middle: the NE section is pretty much arrow straight; the SW part wavers around quite a bit.)

The only drawback there is that the southwest stretch has a footpath along its length.

Schedule 40 is the type of PVC tubing used for household pressure water lines in garden irrigation. It's stiff, you can cut it to size, and it has couplings that let you just push pieces together to make longer pieces, or structures like bases. It comes in different diameters, but 1" diameter should work.

Wickes looks like a good place to buy PVC pipe. There's a 40mm x 3m pipe for £4.39.

I'm doubtful about its ability to stand up straight, though. But maybe filling them with a cement mix might be a way to ensure rigidity, as well as constructing a tripod at the base for stability and verticalness.

 

[Mick West]

Wickes looks like a good place to buy PVC pipe. There's a 40mm x 3m pipe for £4.39.

I'm doubtful about its ability to stand up straight, though. But maybe filling them with a cement mix might be a way to ensure rigidity, as well as constructing a tripod at the base for stability and verticalness.

There's a variety of sizes and wall thicknesses. I picked 1" SCH40 as something that will stand up without bending (at least for an 8 foot length, and probably for two of them fitted together).

There's other portable options at slightly higher cost.

The base really depends on what that ground is like at the middle locations

 

[Rory]

I wonder if Sch40 is different in the UK? Or an import item?

This page mentions it as being a North American product:

What is different about Schedule 40 pipe and fittings?

Schedule 40 (sometimes abbreviated to Sch40) is a North American pipe standard similar to the European classification system. In the European system, however, the pipe is grouped into "classes" of the same pressure rating. The ASTM Schedule system works in a different way in that it relates to the wall thickness and bore of the pipe and has inherited its measurements from steel pipe systems. The result is that unlike the Classification of European pipe, in which everything in class C has an operating pressure of 9 bar, the pressure rating of Schedule 40 pipe changes for each size, although the minimum working pressure is still 9 bar - for example 1" pipe has a pressure rating of 31bar, 1 1/4" pipe a rating of 25.5bar, with working pressures only reaching 9 bar at sizes of 12" and over.

In North America (as well as some other parts of the world) the colour of standard PVC pressure pipe is white. Hence, when this range of pipe and fittings are imported to the UK, they come in as white pipe and fittings rather than grey.

https://www.plasticpipeshop.co.uk/White-Inch-Sch40-PVC-Fittings-and-Valves_c_2489.html

Their 1" Sch40 pipe sells at £24.44 for 10 feet - though they also advertise white, "display grade" Sch40 at £9.29 for 10 feet (i.e., for furniture, etc).

Perhaps drainage pipe may work well. It has a much larger diameter, for about the same cost.

Here's a 110mm (4.3") diameter 3-metre pipe for a smidge under eight quid:

https://www.drainagepipe.co.uk/prod...ainage-pipe-3m-unique/110mm-drainage-pipe-3m/

 

[DavidB66]

Another point I've belatedly noticed: most of the land in the relevant area is very low-lying. If Google Earth is to be believed (and in this case I don't see any reason to doubt it) much of it is actually below sea level. The river banks are in fact levees, a meter or more above the surrounding land. This could be an advantage, since any flag or measuring stick planted on a river bank should be not be obstructed by higher ground. There could also be drawbacks, but in any case it should be taken into account.

 

[Rory]

Another point I've belatedly noticed: most of the land in the relevant area is very low-lying. If Google Earth is to be believed (and in this case I don't see any reason to doubt it) much of it is actually below sea level.

When I check on the mapometer link I posted above - same data as google - it's showing that 12-mile stretch of the Old Bedford as being 2-3 metres above sea level.

 

[Rory]

So I just had a go at a rough scale model of a Bedford Levels experiment using an 18-foot long board and three plastic beakers (and even a couple of breeze blocks for good measure).

It's not as pretty as Mick's "pawns on the car roof" demonstration - but it does include what happens when the camera is both tilted and adjusted in height.

Really, it boils down to two things:

1. On a flat surface, the three targets can be shown to be level with one another, and the middle target can never appear higher than both the other two (at the same time).

2. On a curved surface, the targets can never be shown to be level, and the middle target can appear higher than both the other two.

It doesn't matter how you tilt or adjust the camera, those two statements always hold true.

All tilting does is alter the position in the frame of the group of targets as a whole, but not their relationship to one another.

Changing the height of the camera does alter the relationship between the targets - but always in ways that are entirely expected and predictable, and never in ways that can confuse the outcome.

Using three targets clears everything up: really, this is the key improvement to Wallace's original experiment. The thing is, as was pointed out at the time, when there are only two targets, the two statements above don't work.

A few more targets would be nice, and demonstrate the outcome even more dramatically, but not essential.

Anyway, here's the vid:



(E&OE)

 

[edby]

I have corresponded with some locals, with Christine Garwood who wrote an account in her book, and finally located Carpenter's book Earth Not Convex in the British Library.

1. It is unquestionable that what the 1870 experimenters called Old Bedford Bridge is the modern Old Bedford Sluice, probably built in 1920s. A local told me that the brickwork of the old building, I think 1846, is still visible, and in any case the 1886 OS map shows a construction. Moreover the whole fens would have flooded if there wasn't a sluice there! Carpenter says the Old Bedford Bridge is 'about two-and-a half miles from Downham Market, and being at the Norfolk end of the Old Bedford Canal'. Walsh (editor of The Field) mentions Welches Dam, but that can be shown to be a confusion based on an earlier letter from Hampden. Walsh actually returned to London on Wed 2 March, and never saw the final experiment, which was on Sat 5 March. There was an earlier failed experiment using barges.

2. While the first experiment used barges, the final experiment used a wooden stake as the mid point, driven into the bank of the river. This was made possible by a slight curve in the river. Helpfully, this would be a few metres beyond where the pylons cross, on the NW bank. As the original markers were 6 foot, they had to build the new one the morning of Sat 5th. See the picture below.

3. A local enthusiast tells me he has already obtained an image of Old Bedford Sluice from Welney Bridge. According to the locals in 1870, this was visible on a clear day to the naked eye. Not sure about that!

4. The experiment would have to be performed in the winter with no vegetation and no heat haze. Sat March 6th 2020, one day after the anniversary, would be perfect. And as someone says above, local organisations, government agencies, schools etc could be involved.

5. It would be great to agree with the Flat Earth community what the experiment would prove. Wallace's mistake was not to agree this clearly in advance with Carpenter. Carpenter & co, as Mick points out above, thought their case was proved by the mid marker being exactly in between the cross hair and the end point. I can see why they would think that, but it's terribly wrong. Carpenter also argues that while the points would have lined up by the naked eye, the eye is not inside the telescope, as though that made a difference.

6. We do know, from discussions at the 'other forum', that Flat Earthers agree (1) that the water is flat (to be confirmed or not), (2) that the Bedford stretch is horizontally straight i.e. from the left-right point of view. It's curious that no one denies the line of sight method in the horizontal case – if you can see six miles down river, then the river must be in a straight line, right, but have problems with up-down straightness; (3) that if the three points are exactly the same height, then they must 'line up'. I suggest using precise instrumentation to establish the three heights, followed by a separate test with the viewpoint a foot higher, also swivelling the angle of the scope/camera. Rory has an excellent video of this above.

'The telescope inverts the picture presented to the eye, so that, in each case, the sky is at th bottom of the picture. But there are the three points in a regular series, so nearly equidistant that the sharpest vision could not detect a fault, one slightly above the other in each case ... To see these views is to see a never-to-be-forgotten sight, and if Mr. WALLACE is not convinced now, he never will be!'

That's it.

Location of the original midpoint marker.

 

[Clouds Givemethewillies]

Location of the original midpoint marker.

This is where inverted thinking can get one into trouble with the 'lectric pixies.

Moving on from electrodiscombobulation, one could consider cranes, booms, cherry pickers, etc.

 

[edby]

I am now going to tackle the arguments of Straight Riverists, who claim that rivers are not bendy, as the Thames is claimed to be by scientists, but dead straight. So I have devised an experiment to determine the answer.


The map below shows the distance from Westminster boat house on the East bank, to the north pillars of Hammersmith bridge on the other side. You notice how the 'straight line' touches the East bank at Craven Cottage (home of Fulham football club). The Straight Riverists argue that the map is a fiction of the UK government, who are financing Google etc. How would we prove them wrong?


So I took a picture from the boat house to Hammersmith Bridge, and behold, the western wall of Craven Cottage lines to the pillar of the bridge. Doesn't that show the river is in fact curved? Otherwise I would be able to see the whole of Hammersmith Bridge, as well as the buildings to the East of it. But in fact the Harrods repository obscures the bridge, and Craven cottage obscures the buildings.


But they argue, as follows.


(1) The three vertical lines, i.e. the yellow crosshair, the line through the bridge and the line through Craven Cottage are 'so nearly equidistant that the sharpest vision could not detect a fault, one slightly to the left of the other in each case. To see this view is to see a never-to-be-forgotten sight, and if the Curvists are not convinced now, they never will be!

(2) The observer's eye is outside the camera, and he is bound to have the three points depicted in the camera's view. If he used his own eyes, Hammersmith Bridge would appear in full view.

(3) The camera lens refracts or collimates the light arriving from the distant scene. Otherwise Hammersmith Bridge would appear as it is.

(4) Surveying is not a precise art, and at such large distances, accuracy is paramount. If the camera had been placed a few centimetres to the right, Hammersmith Bridge would appear in its full glory.

(5) The angle of the camera is also paramount. We cannot see the Bridge because it is pointing slightly to the right.

 

[Mick West]

I am now going to tackle the arguments of Straight Riverists, who claim that rivers are not bendy, as the Thames is claimed to be by scientists, but dead straight. So I have devised an experiment to determine the answer.

You seem to be attempting to satirically turn Carpenter's objection on it's side, but I think you are probably just adding more confusion.

 

[edby]

You seem to be attempting to satirically turn Carpenter's objection on it's side, but I think you are probably just adding more confusion.

Do you think so? It seems to me that these really are just the same objections, except to the horizontal case, rather than the vertical one. And it's psychologically interesting. The vertical case does genuinely seem more difficult than the horizontal one.

Also, only the first one is Carpenter's. The rest are genuine objections I have from other Flatearthers.

 

[Mick West]

The rest are genuine objections I have from other Flatearthers.

Perhaps you should address them directly, or at least quote the objections.

A root issue here is the natural human tendency to treat vertical differently to horizontal. There's a bunch of perfectly natural evolutionary reasons for this. To get people to think about how this applies to the Wallace experiment then you need to be a bit more overt about the relationship.

Most people have a hard time with picturing 3D stuff in their heads. It's a tricky communication challenge. The above would probably work better with a slightly curving lake shore, where only one side is visible

 

[edby]

Yup that was precisely my thought, apologies for expressing it badly. I had originally thought of rotating the pictures.

There is something fundamental here. The Flat earth assumption involves (1) that the water is flat, i.e. that it lies in a plane and (2) that the Bedford river is a straight line through that plane. But how do we know the second one is true, given we don't trust maps or surveyors? Well, it looks straight. Right, but the reason it looks straight is that the points on the bank 'line up'. E converso, not looking straight is not lining up.

Yet that is precisely the logic that Wallace used to persuade the others, but in the case of a line lying at the same height over the river. And they were not persuaded, but why?

[edit] As matter of interest, what are these evolutionary reasons?

 

[Mick West]

[edit] As matter of interest, what are these evolutionary reasons?

Things our gene's survival depends on (food, threats, mates, shelter) generally occur on the ground, which is usually fairly flat, and gravity is vertical. Our field of view is wider than it is tall, our eyes and ears are side by side, not one above the other. So our bodies (and to a degree our minds) handle up/down vastly differently to left/right and in/out or near/far.

 

[deirdre]

i thought this thread was about where and how the Wallace experiment could be replicated.

 

[Mick West]

i thought this thread was about where and how the Wallace experiment could be replicated.

Indeed, but you also need to communicate the results. Still, perhaps another thread.

 

[edby]

Right. Science is about choosing between different models of reality (flat water, convex water) by comparing observations which are predicted by the models, but which conflict. Once you have the observation, you can decide.


Agreeing the observations is crucial, of course. That's why pictures from space are no good, for they may have been faked. But equally important is agreeing what the models predict.


Wallace succeeded in the first. He got Carpenter and Hampden to agree on what was seen. But he failed to explain adequately what the different models would predict, which led to a terrible 15 year legal battle.


Oldham performed the same experiment in 1901, with the same results, but did not get the opposing side to agree what the observations were. Both prediction and observation are crucial to the whole experiment.

 

[edby]

Welney Gate Sluice aka 'guillotine gate'. Looks as though the guillotine would obscure the view. There seems to be a view along the NW bank from where the couple are standing, but that looks too low, except to demonstrate the effects of refraction.

[edit] On the point that the brain did not evolve well to cope with up-down rather than left-right. I am wondering whether to duck on passing the guillotine, and I am thinking not to duck. The verbal logic is quite complex. By contrast, my instantaneous judgment is rapid.

I remember from days when I went riding, ducking situations and avoiding low branches were quite common. I think the brain has evolved reasonably well.

 

[edby]

Looking towards Welney. The pylons mark the 3 mile mid-point, so somewhere on the right the pole would have to be placed.

 

[DavidB66]

I wonder does anyone have a view on the minimum distance needed for a viable Wallace-type experiment? I have been looking at Google Earth trying to identify an alternative to the Old Bedford River in case for any reason that is not practical. I take it that such an alternative would require a straight uninterrupted line of sight between three markers of equal height, measured up from the surface of a continuous waterway to act as a natural 'level'. I don't think it is essential that the line of sight itself should pass continuously above the waterway, provided the three markers are all close enough to the water for the measurement to be convincing. Unfortunately I have not been able to find a stretch as long as 6 miles meeting these conditions. Whenever I think I have found one, on closer examination the line of sight is interrupted by a building, a clump of trees, or some other obstacle. Even in the notoriously flat and featureless Fens, it is difficult to find a 6-mile unobstructed line of sight at the sort of height required (i.e. standing height on a bridge or bank a few meters above the water level.)
However, I think I have found a suitable stretch of about 4.4 miles, on the drainage channel to the south of Tydd St Giles, with public road bridges at each end, and another one at about half-way. So would 4.4 miles be long enough? On a rough estimate I think the midway marker would be about 3 feet above a straight line of sight between the end markers, but I may have misunderstood this. If it is correct, would 3 feet be enough?

 

[edby]

4.4 miles would do, but not an expert on what we would expect to see. Can't locate the stretch you are talking about, however.

I just discovered that Downham mkt is 1 1/2 hours by train from Kings X, and I am thinking of buying a telescope similar to the one used by Wallace, and checking it out for myself.

 

[Rory]

Not sure why there would be a problem with the Old Bedford.

As for the issue with the Welney Sluice, it looks okay - with a tall enough tripod, that is.

Though the easiest solution might be to have the camera at the Salters Lode end.

 

[DavidB66]

4.4 miles would do, but not an expert on what we would expect to see. Can't locate the stretch you are talking about, however.

I just discovered that Downham mkt is 1 1/2 hours by train from Kings X, and I am thinking of buying a telescope similar to the one used by Wallace, and checking it out for myself.

Search on Google Earth for Tydd St Giles. There should be only one result. If you zoom in you should see a drainage channel to the east of the village. The main east-west street leads to a bridge over the channel. One end of my suggested line of sight starts on the north-west end of the bridge, just where the approach road narrows to pass over it. About 4.4 miles to the south-west is another bridge, just by the longitude line for 0 degrees 03 minutes east. The north-west end of this bridge is the other end of the suggested line. The mid-way marker would be on a bridge about 2.71 miles to the SW of Tydd St Giles. This is not exactly half-way, but it is convenient, and if the observation is taken from the SW end of the line it might even be an advantage, as it would increase the height difference between the mid-way and distant markers. I think there is a clear line of sight between these three bridges, but it is very sensitive to the exact placement of the end points: for example, at the NE end of the line it needs to be far enough down the approach road to be clear of a large bush on the bankside. Most of the line of sight passes above the banks of the channel, or nearby land, rather than over the water itself. I am assuming that vegetation, buildings, etc, remain as they appear on Google Earth. It would only take one big bush, or a farm vehicle, etc, to block the view.
Of course, it is better to use the Old Bedford River itself, if that is practical, not only for historical reasons but because it is a longer stretch of dead straight waterway. But there could still be practical problems such as getting access to put up markers, or with vegetation obstructing the line of sight. For example, at the northern end of the river there seem to be a couple of trees or large bushes right on the water's edge. Since there is no mid-way bridge over the river, the options for positioning markers are rather limited.

 

[Rory]

As you say, the vast majority of the line between those two bridges is over land. Also, it bypasses the two bridges in between:

Here's a link at mapometer with the line drawn in.

The advantages of using the Old Bedford river northeast of Welney are:

• Original site
• 5.85 miles of uninterrupted straight river
• Accessible
• Bridges at either end
• More than likely no boats
• Not too deep (hopefully)

The disadvantages are:

• Possible unfavourable weather

So to find a better place in the British isles, it would really have to have better weather than The Fens. Or be longer.

 

[Mick West]

I wonder does anyone have a view on the minimum distance needed for a viable Wallace-type experiment?

The height difference is between the center marker and the line between the end markers. So it's the same as the "bulge" distance in a curve calculator. 'Bulge' b = r-sqrt(4*r*r - d*d)/2

How low can you go?

Standard Wallace with a bridge at 6 miles looks like this:

With a closer bridge, the image will get larger and clearer, and distance between the flag and top marker will diminish.

So if we were to go down to 3 miles, it's 1.29 feet. That would look like:

The distance of note being between the center of the flag and the center of the top marker (assuming both are the same height above the water as the camera/telescope.

4 miles would be significantly better with a foot more at 2.29

 

[Rory]

We talk a lot of Rowbotham's measurement when he had the telescope about 8 inches above the water as his definitive experiment - easily dismissed because of refraction - yet there were others he did at the Old Bedford Levels, such as:

This seems a much better experiment, and if we can assume his honesty, it is slightly more difficult to explain.

Are we saying that the effects of refraction at 5 feet above the water also correspond exactly to the curve of the Earth?

In any case, targets 10-13 feet above the surface of the river should suffice.

(In his Experiment 1, by the way, Rowbotham states that he was at Welches Dam and looking northeast to Welney Bridge; for Experiment 2 he says he was "in the same canal" and "up to this time all [my] observations had been made in the direction of Welney". He says he lived for 9 months in a wooden shack within 100 yards of the canal.

In Experiment 3, however, he says he measured along the stretch between Welney Bridge and "the Old Bedford Bridge"; and in 1870, for Experiment 5, he began his measurements near Downham Market, at "the Old Bedford Sluice Bridge" - showing that Rowbotham also used the same section northeast of Welney that Wallace used in his test.)

 

[Mick West]

This seems a much better experiment, and if we can assume his honesty, it is slightly more difficult to explain.

His description only really covers the end flags, and does not explicitly state that the intermediate flags were all lined up. All he says about what he SAW is "the line of sight fell on the lower part of the larger flag at B" I suspect what happened was more like:

And he dismissed the middle flags as perspective, or something.

It would be an interesting thing to replicate - however remember there's several fixed in place versions of this with bridges and causeways, as documented by Soundly. https://www.youtube.com/channel/UCDXr2cbK7WlfeYEtJxC9i3w

 

[Rory]

His description only really covers the end flags, and does not explicitly state that the intermediate flags were all lined up. All he says about what he SAW is "the line of sight fell on the lower part of the larger flag at B."

Good point. He was a classic fudger, by all accounts.

 

[Z.W. Wolf]

I've never seen independent evidence that any of his experiments actually happened.