Water is not convex

Rowbotham's experiments have been conducted many times in the 150 year history of the Flat Earth Society. Just check out the link in my signature. A woman named Lady Bount was among the first to provided photographic evidence for a Flat Earth -

"The Old Bedford Level was the scene of further experiments over the years, until in 1904, photography was used to prove that the earth is flat. Lady Blount, a staunch believer in the zetetic method hired a photographer, Mr Cifton of Dallmeyer's who arrived at the Bedford Level with the firm's latest Photo-Telescopic camera. The apparatus was set up at one end of the clear six-mile length, while at the other end Lady Blount and some scientific gentlemen hung a large, white calico sheet over the Bedford bridge so that the bottom of it was near the water. Mr Clifton, lying down near Welney bridge with his camera lens two feet above the water level, observed by telescope the hanging of the sheet, and found that he could see the whole of it down to the bottom. This surprised him, for he was an orthodox globularist and round-earth theory said that over a distance of six miles the bottom of the sheet should bemore than 20 feet below his line of sight. His photograph showed not only the entire sheet but its reflection in the water below. That was certified in his report to Lady Blount, which concluded: "I should not like to abandon the globular theory off-hand, but, as far as this particular test is concerned, I am prepared to maintain that (unless rays of light will travel in a curved path) these six miles of water present a level surface."

The description clearly shows refraction is happening. How can one see a reflection in the water when one is only 2 ft above the surface? This is very similar to a mirage that one sees in hot weather where there are upside down images of objects on the horizon.

From "100 Proofs the earth is not a globe" by William Carpenter we read -

36. If we take a journey down the Chesapeake Bay, by night, we shall see the "light" exhibited at Sharpe's Island for an hour before the steamer gets to it. We may take up a position on the deck so that the rail of the vessel's side will be in a line with the "light" and in the line of sight; and we shall find that in the whole journey the light will won't vary in the slightest degree in its apparent elevation. But, say that a distance of thirteen miles has been traversed, the astronomers' theory of "curvature" demands a difference (one way or the other!) in the apparent elevation of the light, of 112 feet 8 inches! Since, however, there is not a difference of 100 hair's breadths, we have a plain proof that the water of the Chesapeake Bay is not curved, which is a proof that the Earth is not a globe.

Where is the eyewitness account and data to back up this assertion?

If the earth were a globe then lighthouses should be seen, at a certain distance, to be below the horizon

From "100 Proofs the earth is not a globe" by William Carpenter we read -

5. The lights which are exhibited in lighthouses are seen by navigators at distances at which, according to the scale of the supposed "curvature" given by astronomers, they ought to be many hundreds of feet, in some cases, down below the line of sight! For instance: the light at Cape Hatteras is seen at such a distance (40 miles) that, according. to theory, it ought to be nine-hundred feet higher above the level of the sea than it absolutely is, in order to be visible! This is a conclusive proof that there is no "curvature," on the surface of the sea - "the level of the sea,"- ridiculous though it is to be under the necessity of proving it at all: but it is, nevertheless, a conclusive proof that the Earth is not a globe.

How do ships know how far away they are from a lighthouse?

The North Star can be seen beyond the equator

The North Star can actually be seen at over 20 degrees beyond the equator before disappearing to perspective, an impossibility on a Round Earth. This is a proof for a Flat Earth. Samuel Birley Rowbotham reports observing the North Star at 23.5 degrees beyond the equator. William Carpenter includes this well known discrepancy as proof number 71 in a book entitled "A hundred proofs the earth is not a globe." -

71. The astronomers' theory of a globular Earth necessitates the conclusion that, if we travel south of the equator, to see the North Star is an impossibility. Yet it is well known this star has been seen by navigators when they have been more than 20 degrees south of the equator. This fact, like hundreds of other facts, puts the theory to shame, and gives us a proof that the Earth is not a globe.

That is absolute bullshit. Where are the first-hand accounts to verify this claim?

A half sunken ship can be restored through the aid of a telescope

This is an impossibility on the Round Earth model. If the ship's hull were really behind a hill of water and not just lost due to perspective merging the water and hull in the distance then it would be impossible to restore the ship's hull with the aid of a telescope.

Thomas Winship writes about it in his book Zetetic Cosmogony:

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There are also accounts of restored hulls in the book Cellular Cosmogony by Cyrus Teed:

http://www.sacred-texts.com/earth/cc/cc21.htm

The fact that half sunken ships can be restored with the aid of a telescope due to perspective proves that the ship was not behind a "hill of water" and that the earth is not really convex.

I see a tiny ship on the horizon with eyes. How exactly can I tell how much of it appears sunken? It's too small to tell, and it can be very subjective. Those FE pioneers were biased and convinced themselves ships appeared sunken when they really were not. Also, consider that none of the evidence posted on this forum has ever supported that sunken ships can be restored.

Distances between latitudes should are farther apart in the South

From "100 Proofs the earth is not a globe" by William Carpenter:

16. If the, Earth were a globe, the distance round its surface at, say, 45 "degrees" south latitude, could not possibly be any greater than it is at the same latitude north; but, since it is found by navigators to be twice the distance -- to say the least of it -- or, double the distance it ought to be according to the globular theory, it is a proof that the Earth is not a globe

If the earth were a globe the horizon line would not be at eye level

Where is the data to back up this assertion?

If the earth were a globe the horizon line would not be at eye level

From "100 Proofs the earth is not a globe" by William Carpenter we read -

30. If the Earth were a globe, an observer who should ascend above its surface would have to took downwards at the horizon (if it be possible to conceive of a horizon at all under such circumstances) even as astronomical diagrams indicate that angles - varying from ten to nearly fifty degrees below the "horizontal" line of sight! (It is just as absurd as it would be to be taught that when we look at a man full in the face we are looking down at his feet!) But, as no observer in the clouds, or upon any eminence on the earth, has ever had to do so, it follows that the diagrams spoken of are imaginary and false; that the theory which requires such things to prop it up is equally airy and untrue; and that we have a substantial proof that Earth is not a globe.

Where is the math to back this up? By my calculation, the angle the horizon is below eye level is cos

^{-1}(r/(r+h)) on a RE. Even at a height of 1 km, the angle is only about 1 degree, which is hardly perceptible.

If the earth was a globe surveyors would make allowance for the earth's curvature

From "100 Proofs the earth is not a globe" by William Carpenter we read -

3. Surveyors' operations in the construction of railroads, tunnels, or canals are conducted without the slightest "allowance" being made for "curvature," although it is taught that this so-called allowance is absolutely necessary! This is a cutting proof that Earth is not a globe.

According to Lynn Nelson, who once worked as a surveyor,

"Well, a surveyor can operate using standard geometry for nine miles. Beyond that distance, the curvature of the Earth becomes a factor, and the surveyor has to switch his calculations of lines to spherical geometry and his computation of angles to spherical trigonometry."

http://www.kancoll.org/articles/nelson/surveyor.htm