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A common claim in support of "Flat Earth" models is that a cannonball fired precisely vertically drops back upon the cannon, even back down the muzzle. One such claim appears here http://www.atlanteanconspiracy.com/

These claims clearly echo the 19th century one reproduced here in Samuel Rowbotham's "Zetetic Astronomy":

http://www.sacred-texts.com/earth/za/za21.htm#page_67

Although it's clearly claimed that the experiment was performed, the stated consistency of the shots (maximum sideways variation of 2 feet in a 28 second flight) seems implausible, at least given the popular understanding of smooth-bore cannon accuracy and possible effects of wind and cannonball spin. Is there any corroborating evidence for the experiment as reported, or for subsequent enactments of it?

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    So, to be clear, you are not asking whether such an experimental result - if true - is evidence that the Earth does not move. – Oddthinking Jun 17 '16 at 3:10
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    Adding to Oddthinking's comment: Because it is not. – sashkello Jun 17 '16 at 3:39
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    (in fact simple kinematics suggests quite a low muzzle velocity for a 19th century artillery piece, so possibly he's relating an older account without giving any attribution. His suggestion that the ascent and descent times would be equal adds to the air of hearsay [unless of course he performed the experiment on the moon, in which case his observations of the Earth's shape become a lot more interesting...] – Tom Goodfellow Jun 17 '16 at 6:30
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    I truly doubt anyone conducted this experiment. Rowbotham has the physics incorrect. Ignoring air resistance, the Coriolis effect will deflect a cannonball shot perfectly straight up at the latitude of London that flies for 28 seconds by about 5.3 feet west of the cannon, not 8400 feet. Air drag will reduce this somewhat. Nobody sane would perform that experiment; there's too good a chance the cannon will not be aimed straight up, resulting in the cannonball hitting the cannon. All it takes is less than a two arc minute error in the wrong direction. – David Hammen Jun 17 '16 at 20:20
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    Coriolis deflections of vertically falling projectiles were measured in mine-shafts by the end of the early modern. It's a hard experiment to do well, and people continued to do them as cutting edge science for more than a century. – dmckee Jun 18 '16 at 0:33
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Yes, the experiment was done, but much earlier.

See Vertical Projection in a Resisting Medium: Reflections on Observations of Mersenne The American Mathematical Monthly Vol. 121, (2014), pp. 499-505

Mersenne began carrying out experiments with vertically launched projectiles in the 1630s.

http://images.fineartamerica.com/images-medium-large/behavior-of-falling-bodies-omikron.jpg

Also, Rene Descarte wrote to Mersenne in 1636:

Thank you for the account of the ball shot vertically that doesn’t drop back; it is very remarkable

and in 1638

There is also the observation [mentioned on page 29] that you told me you have made yourself, and that other writers have described, namely that cannon balls that are shot straight up don’t fall down again.

and Descarte was in 1634 the one who suggested the experiment in the first place:

Also: you told me in a previous letter that some people you knew could help to perform the experiments that I wanted done; so let me tell you about an experiment that was published not long ago in Leurechon’s Mathematical Games. It involves a large cannon placed on flat ground, pointing straight up at the sky, and fired. I would like this experiment performed by people who are interested and have the means. The author of the book says that the experiment has already been performed many times, and the cannon-ball didn’t once fall back to the ground. Many might think this quite incredible, but I don’t judge it to be impossible, and I think it’s well worth looking into.

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    Thanks for the lead (also for the belly-laugh of that woodcut). Sadly a quick look for Mersenne in the referenced "Nouvelles Conjectures sur la Pesanteur" gives no further details. Amir Aczel's "Pendulum" has two versions of the story. In the first Mersenne & Petit are baffled when the cannonball simply vanishes, in the second (attributed to Camille Flammarion) they tried three shots, with 1st disappearing, 2nd 2000' west, 3rd 2000' east, whereupon "law of averages" convinced them that the next shot would drop upon them and they ceased experimentation. So fairly wide of Rowbotham's claim. – Tom Goodfellow Dec 18 '16 at 23:42
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    But it's certainly impressive to see some stout empiricists at work, in an age before experimental reports had a section for safety precautions. Naively I'd interpret the vanishing cannonballs as being shots so far astray that their impact wasn't noted (perhaps needing dusty ground to leave an easily noticed trace?) – Tom Goodfellow Dec 18 '16 at 23:47

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