Yes Tom, the referee was a mutually agreed independent party. Hampden's referee was not an independent party, he was another one from the Parallax crowd:
Hampden's referee, William Carpenter, was an FE'er and Wallace's referee was an RE'er. Each side got to choose their own referee.
When the two referees disagreed a third man named John Henry Walsh was asked to make the final decision. After checking the evidence himself and seeing an optician on Hampden's insistence, he decided in favor of Wallace.
John Henry was an RE'er and an associate of Wallace.
Please link to a source that shows that John Henry Walsh was an associate of Wallace. The point about him being a RE'er is moot since the general scientific consensus at the time was that the Earth was round. If he doesn't count as a fair referee who possibly could? Does this mean that we cant prove anything to each other because everyone is biased? Of course there is bias, so we have to settle on the balance of probabilities as always. Even courts have to deal with this. Only mathematicians can taste complete certainty.
Her test is completely different than Wallace's. If you hang a roughly plain sheet and obscure the bottom half, how can you know if you are seeing the whole sheet?
In the text I've provided the observer states that they were able to see the entirety of the blanket, including its reflection on the water below. Please read what I've provided.
The upper portions of the sheet would still have a reflection on the water, so there is still no way to know you are seeing the bottom of the sheet unless it is marked.
This experiment makes no measurements
Actually, it does.
Your right, one measurement is made, that the telescope was 2ft above the water. However his assumption that "sheet should be more than 20 feet below his line of sight" is totally inaccurate. I show this with my later math.
so I cant see it as being at all relevant to seriously proving the Earth is flat. Maybe if there was a bright yellow mark on the bottom of the sheet and this was still visible in the photograph it might mean something
If you had actually read what I provided you would have seen the following quote:
"His photograph showed not only the entire sheet but its reflection in the water below."
This experiment is fails math at the outset. The author is using a quadratic approximation to determine the 'drop' behind the horizon, and hence estimates that the boat will be 7ft below the horizon. In fact, the 'bulge' of water over 6mi or about 9.6km is:
h=R(1-cos(S/R))
R=Radius
S=half the arclength between points
h=heigh of bulge
Run the math and you get about 1.4m.
Well firstly, you didn't provide any math at all for your figure.
Here's a chart for earth drop:
http://www.sacred-texts.com/earth/za/za05.htm
Over six miles the earth drops 24 feet. You can find the calculations at the bottom.
The diagram you provided makes two assumptions that greatly affect the outcome of the predictions, and make the predictions in this test totally backwards.
Assumption 1: The viewers sight line is perfectly parallel with the horizontal (which it is not unless they used a level on their telescope, such as with a theodolite)
Assumption 2: The viewers sight line is tangent to the horizontal (aka the telescope or the viewers eyes are on the water)
I did provide the math. I gave you the equation for the bulge on a circle due to a secant line. I even labeled the variables nicely
Now here is a diagram to accompany:
The equation in this diagram would instead be b=R(1-cos(s/R))
The math used in this article and pointed to by your link is referring to the situation on the left, where the observer is restricted to a horizontal sight line. The case in the article is closer to the right side, where both telescope and observed object are above the water. Of course, both are not at the same height as implied in the diagram, but the 'bulge' calculated is still accurate. I will post a more general equation involving arbitrary heights of both observers, but it will take me a bit of time to simplify it.