"The issue was the relatively straightforward one of whether the Earth was flat (as the Zetetics held) or round (the Globularists). It's tempting from the comfort of a
21st century scientific perspective to laugh at the Zetetics, but we should perhaps be inclined to a little humility. The Zetetic philosophy was essentially one of 'proceeding
by inquiry', which meant that any proof that the Earth was round would have to be the result of an experiment, not simply calculation. The world looks flat (just as the sun
seems to orbit the earth) so it should be presumed flat unless it could be demonstrated otherwise.
The first attempt at an experiment was in 1838, when one Samuel Birley
Rowbotham ('Parallax') made observations along the Old Bedford River, one of Vermuyden's finest drainage constructions and which, from Welney, runs dead straight for six
miles.
Rowbotham was a convinced flat-earthist, which may have influenced his observational technique.
But nevertheless, from Welney Bridge (below) he clearly saw (through a telescope) barges on the river some six miles distant.
In fact, because of the curvature of the earth, from ground level looking over
a flat surface, you can see no more than three miles -- his barges should have been well below the horizon. The Zetetics concluded erroneously that the earth was flat, and
everything went quiet until 1870..
There were doubtless many scientists around who could have pointed out that Rowbotham's results are comfortably explained by the refraction of light close to a warm surface,
the basis of many desert mirages.
Rowbotham is challenged, and wagers made
But no one seemed to have the stomach for more experimenting until Alfred Russel Wallace, noted for espousing the new theory of evolution and hence used to the impolite cut
and thrust involved, set up a rather more elaborate experiment. In part, this was because one John Hampden of Swindon had underwritten a wager of some £500
[£1,000?] that a new experiment would establish the flatness of the earth for all time.
Three barges were used, on each of which was erected a straight rod, all the same height. The barges were moored two miles from each other along the same stretch of water.
The tops of the rods were thus all the same distance above the surface of the earth. Using a theodolite, Wallace sighted from the top of the first rod to the top of the third. If the
earth was flat, the top of the middle rod would lie on the same line.
In fact, because the earth was curved, the third rod was lower than the second: the second marker was a clear 32 inches above the line from the first to the third (sometimes
reported to be five feet -- doubtless to emphasise the clear victory for the Globularists).

This makes the diameter of the earth 7920 miles -- pretty good for 1870, as we now believe that the earth's equatorial diameter is 7926 miles (the earth isn't a perfect sphere,
and has different diameters at different places).Unfortunately for Wallace, but fortunately for those of us who are enjoying the story, the Zetetics (also known as the 'planists',
by the way) looked at the same results and somehow managed to convince themselves that a trick of perspective was involved and that this did, after all, prove that the earth
was flat!
John Hampden refused to pay up, and the matter went to court some six years later. In a wonderful instance of jurisprudential cunning, the presiding judge declined
to rule on what might be deduced from the experiments and contented himself with adjudging that such wagers were not legally binding!
Hampden responded badly to a verdict
that had, after all, saved him £500. He became obsessed and conducted a campaign of vilification against Wallace for the rest of his life, which led to several prosecutions for
libel and accompanying prison sentences. As so often happens when people disagree, neither side ever managed to convince the other -- indeed, the Flat Earth Society continued
in being until the 1980's. It was later resurected, and in 2026 was still in existence.
What happened thereafter was that newcomers simply repeated the experiment associated with what they wanted to prove. In 1901, H. Yule Oldham repeated the Wallace
experiment pretty exactly and got the same result, which he reported to the British Association for the Advancement of Science.
In 1904, a Lady Blount repeated essentially the
Rowbotham experiment with the added value of new-fangled photography: at least her result was demonstrable, and didn't rely on hearsay. This time, she photographed a white
sheet hanging two feet above the water, six miles away -- just as Rowbotham had (and for the same reasons) she could see the theoretically hidden bottom of the sheet, and
what's more its reflection in the water!
We may laugh now, but it is hard to disbelieve the evidence of our eyes, and the Zetetics were not fools. One modern analogy might provoke some reflection. The Bedford Level
experimenters used the river because it was flat and straight. As with us, they looked around and saw jagged mountains, ocean trenches and very little flatness -- the river was a
godsend. But in fact, considering the scale, compared to a billiard ball the earth is several orders of magnitude smoother on its surface!"

cover of Rowbotham's 1870 book refers to a wager of £1,000
2015, a re-enactment (so called!)
Cambridge Archaeological Unit (CAU) were commissioned through lottery funding to re-enact Rowbotham's experiments (incorrectly calling them trials) as part of an Environment Agency (EA) "Ousefest" fun-day festival. The sign at the car-park should have pre-warned us they may not have got things quite right.

The sign seems to indicate a footpath over nice flat land for those unable to manage uneven ground rather than the way to a professional re-enactment.
The 'show' wasn't on the Old Bedford River, it was held on the Cut-Off Channel. They hadn't obtained a Victorian boat, just a glossy modern glass fibre EA motor launch, and instead of a hand-held Victorian telescope, they had a top-of-the-range digital surveying level mounted on a fancy tripod. Well, none of that really matters, does it?
Another thing CAU got wrong was the start time, it didn't happen until about an hour after the time specified.

Spectators waiting for something to happen
Anon

While we waited, in the cold, for some action long after it was due to start, a disheveled-looking man appeared in front
of us and without introduction spoke in a North American accent telling us what the "Bedford Level" trials were about.
He then walked away and we continued waiting and getting colder.
Half an hour later the launch appeared and moored up not far away. Then another long delay before they started the "trial". We then noticed that the object they were viewing through their surveyor's level wasn't a mile distant as in Rowbotham's
second experiment, this was just a 100 yards or so away, with another just beyond.
We all felt cheated.

Two target flags on wooden pallets
The three guys next to my party were science professors from Cambridge University. They were even
more scathing than we were.
Now, my apologies to Americans. The unknown speaker we later discovered was Canadian, and not a tramp but a celebrated archaeolologist, Dr. Chris Evans, head of the CAU, and he wasn't dressed in Victorian workman's costume, thats how he normally looks, as I discovered when I lunched with him a year later. But thats another story.

Dr Evans re-enacted Rowbotham using a hand-held telescope to view boats and flags several miles away, with a tripod-mounted ultra-modern digital surveyor's level looking at objects just a hundred or so yards / meters away.
the 3 photos above and the trials/trails one are screenshots from the CAU video on You Tube
The whole so-called "re-enactment" event was a very disappointing un-professional mess from start to finish; CAU managed to get every single aspect wrong - even that sign.
Fortunately, the day got better.
I did my flat-earth spiel to camera, which was applauded by those watching.

Doing my flat-earth spiel to camera
And later had a ride in a very fast EA speedboat.

I was at the rear, far side, with my face covered by a camera taking photos of my friends on the bank, one of who was Mike Petty, the Cambridgeshire historian.
photos of filming and speedboat, courtesy Mike Petty
Appendix
Update, January 2010
The (non-band) Flat Earth Society was 'resurrected' in 2004, and in October 2009 it re-opened to new members.
In November 2009 Daniel Shenton, the President of the Society wrote to Welney Parish Council requesting permission to display a plaque on the Bedford Bridge commemorating the 1838 experiment. The matter was discussed at the Council's meeting in December 2009 and it was suggested he should contact the Highways dept [of Norfolk CC] who have jurisdiction over such matters. You can read more at item 11g in the
Council's minutes.
At the same meeting a letter from Russell Duffy regarding Mr Shenton's request was discussed. See item 11i in the same minutes.
Shortly after posting this update I learned that the Parish Council should have told Mr Shenton to
contact the Bridges Department [of NorfolkCC] as it is they that deals with such matters, not Highways.
One of the Councillors, Mark Brown, wrote an article about the experiments published in the local bi-monthly parish magazine,
Welney News, issue 75, June/July 2010.
Learn more of the Flat Earth Society at their own
new website.
The Welney Website