Sine I am not a physician, and a lousy mathematician, you might as well write your formulas in greek. Makes no difference to me. Get a physician to register here who may explain. :/

I'm not a physician either, nor am I a formally trained physicist. But you know, you did ask for scientific proof:

I want proof, evidence, scientific support, of the FE theories.

Anything would be fine, just post away. As long as it is scientifically reliable.

But okay, if it's not clear to you what I meant, then I'll explain:

If two objects are very close to the surface of a round Earth, but are far apart from one another (for example, two rowboats on a long, straight river), they should be obscured by the curvature of the Earth, right? The water between them will act like a "hill". REers bring this up all the time: it's the whole "ships on the horizon" thing.

What Samuel Rowbotham did was to compute exactly how "high" this hill of water should be. Note that water is a good place to do the experiment because as long as it doesn't have any waves, it will be perfectly smooth and conform itself exactly to the curvature of the Earth, due to gravity.

Anyway, the exact values he calculated mean the following thing: imagine you put a very long, straight rod on the ground. "Long" means "many miles long". If the Earth were flat, then the rod would touch the ground the whole way. If the Earth were round, the rod would only touch the ground at a single point (such a rod is idealized mathemetically as a "tangent" line). Sure, the Round Earth curves very slowly, so you might not notice. But as you get farther away from the point of tangency (the single point where the rod touches the ground) the ground will get further and further away from the rod; it will appear to be dropping away (if you imagine yourself as an ant or something walking along the rod).

Rowbotham gives a table describing how big this drop is, given how far along the rod you've gone. I don't know how he got his values, but I got mine using simple trigonometry and the radius of the Earth given in Wikipedia, and our values were very close.

Here's how I got my formula: at the centre of the Earth, let the angle between the rod's point of tangency and your current position be, say, T. Then the distance from the centre of the Earth to you is called the "secant of T", and the distance from you to the point of tangency is called the "tangent of T" (in both cases, the units are Earth radii; i.e. the Earth has radius 1). If you are a distance X along the rod, then T = arctan(X). "arctan(X)" is the angle whose tangent is X. Therefore the distance from the centre of th Earth to you is sec T = sec arctan X. To get the distance from you to the surface, we subtract off the distance from the surface to the centre, which is 1, to get: D = sec arctan X - 1. I left the radius of the Earth in my formula, so that you can use whatever units you like (miles/feet/inches in the case of my and Rowbotham's tables). I used a calculator to compute all the values by plugging in different values of X.

For references on the trigonometry I used, I recommend Wikipedia's

article on the unit-circle definitions of the trigonometric functions. In particular, look at the picture whose caption is "

*All* of the trigonometric functions can be constructed geometrically in terms of a unit circle centred at

*O*."

Anyway, Rowbotham found that the Earth did

*not* curve enough to obscure his view of objects close to the surface when the calculations made using the RE model predicted they would be obscured.

If you're not clear on any particular points, feel free to ask and I'll try to clarify further.

On the issue of the proof being "mathematical": aside from having asked for scientific proof, how can you believe any "proof" that the Earth is round if you claim not to understanding the underlyng mathematics? Pictures from space, for example, don't show an image that you

*cannot conclude to be anything other than a round Earth*, since one thing you could conclude, for example, is that it is a faked photograph of the Earth. You could also conclude that it is simply a restricted-field-of-view photograph of the flat Earth. Basically, such things are not proof that the Earth is round; proof that the Earth is round should be in the form of a logically sound argument in the formal, rigorous language of mathematics, whose conclusion is that the Earth is round. Only then can the proof be interpreted unambiguously.