[alex]

On the TFES Wiki I found two articles:

http://www.sacred-texts.com/earth/za/za00.htm
http://wiki.tfes.org/Lady_Blount_Trials

which puzzles me. In chapter II of the work, "EXPERIMENTS DEMONSTRATING THE TRUE FORM OF STANDING WATER, AND PROVING THE EARTH TO BE A PLANE." the statement that an earth with circumference of  25,000 English statute miles would show a declination of 8 inches in the first statute mile. This statement is bluntly incorrect!

Over a distance of 6 miles the declination really is 2.18 mm. So, if the telescope is 2 feet(!) above the water, sure you can see the distant flag to the bottom. This experiment does not prove the earth is flat!

I can show the math for this very simple derivation, if someone needs to see it...

[Pete Svarrior]

It is, indeed, a very simple derivation.

For simplicity, let's assume that the round Earth is a sphere of r=3963mi. This will introduce a very minor error to our result, but given that your argument concerns the order of magnitude of the answer, this should be negligible. Let us also assume that we're measuring 1 mile ahead of us in a straight line, along the tangent of the Earth's curve, rather than 1 mile along its surface. This, again, is purely for simplicity's sake, and won't affect the result significantly.

With these assumptions, we can simplify this problem to a right-angle triangle:



With the starting location being P and x=1mi, we are now searching for the value of a. The difference between a and 3963mi will be the perceived drop.

Employing the Pythagorean theorem, we know that . Substituting 1 for x we get , or . This finally gives us . Taking the square root of this (and ignoring the negative root), we get .

.

, or 8 inches rounding up.

What particularly surprises me about your question is that all this information (and more precise derivations which do not rely on simplifying the problem) are abundantly available on the Internet and are well accepted by Round Earthers. A quick Google search to the effect of "how much does the earth drop in a mile" would have been a sensible approach to finding this out.

[alex]

Hi,

I have to admit you are right. My calculations were wrong.

But did those measurements did include refraction of light due to temperature changes close to the water's surface? The same effect to seeing a mirage on a hot roads surface!

[Tom Bishop]

In Earth Not a Globe the author Samul Birley Rowbotham takes terrestrial refraction into account in his experiments. See Experiment 9, for instance:

...

The only modification which can be made in the above calculations is the allowance for refraction, which is generally considered by surveyors to amount to one-twelfth the altitude. of the object observed. If we make this allowance, it will reduce the various quotients so little that the whole will be substantially the same. Take the last case as an instance. The altitude of the light on Cape Bonavista, Newfoundland, is 150 feet, which, divided by 12, gives 13 feet as the amount to be deducted from 491 feet, making instead 478 feet, as the degree of declination.

Many have urged that refraction would account for much of the elevation of objects seen at the distance of several miles. Indeed, attempts have been made to show that the large flag at the end of six miles of the Bedford Canal (Experiment 1, fig. 2, p. 13) has been brought into the line of sight entirely by refraction. That the line of sight was not a right line, but curved over the convex surface of the water; and the well-known appearance of an object in a basin of water, has been referred to in illustration. A very little reflection, however, will show that the cases are not parallel; for instance, if the object (a shilling or other coin) is placed in a basin without water there is no refraction. Being surrounded with atmospheric air only, and the observer being in the same medium, there is no bending or refraction of the eye line. Nor would there be any refraction if the object and the observer were both surrounded with water. Refraction can only exist when the medium surrounding the observer is different to that in which the object is placed. As long as the shilling in the basin is surrounded with air, and the observer is in the same air, there is no refraction; but whilst the observer remains in the air, and the shilling is placed in water, refraction exists. This illustration does not apply to the experiments made on the Bedford Canal, because the flag and the boats were in the same medium as the observer--both were in the air. To make the cases parallel, the flag or the boat should have been in the water, and the observer in the air; as it was not so, the illustration fails. There is no doubt, however, that it is possible for the atmosphere to have different temperature and density at two stations six miles apart; and some degree of refraction would thence result; but on several occasions the following steps were taken to ascertain whether any such differences existed. Two barometers, two thermometers, and two hygrometers, were obtained, each two being of the same make, and reading exactly alike. On a given day, at twelve o'clock, all the instruments were carefully examined, and both of each kind were found to stand at the same point or figure: the two, barometers showed the same density; the two thermometers the same temperature; and the two hygrometers the same degree of moisture in the air. One of each kind was then taken to the opposite station, and at three o'clock each instrument was carefully examined, and the readings recorded, and the observation to the flag, &c., then immediately taken. In a short time afterwards the two sets of observers met each other about midway on the northern bank of the canal, when the notes were compared, and found to be precisely alike--the temperature, density, and moisture of the air did not differ at the two stations at the time the experiment with the telescope and flag-staff was made. Hence it was concluded that refraction had not played any part in the observation, and could not be allowed for, nor permitted to influence, in any way whatever, the general result.

In may, the author delivered a course of lectures in the Mechanics' Institute, and afterwards at the Rotunda, in Dublin, when great interest was manifested by large audiences; and he was challenged to a repetition of some of his experiments--to be carried out in the neighbourhood. Among others, the following was made, across the Bay of Dublin. On the pier, at Kingstown Harbour, a good theodolite was fixed, at a given altitude, and directed to a flag which, earlier in the day, had been fixed at the base of the Hill of Howth, on the northern side of the bay. An observation was made at a given hour, and arrangements had been made for thermometers, barometers, and hygrometers--two of each--which had been previously compared, to be read simultaneously, one at each station. On the persons in charge of the instruments afterwards meeting, and comparing notes, it was found that the temperature, pressure, and moisture of the air had been alike at the two points, at the time the observation was made from Kingstown Pier. It had also been found by the observers that the point observed on the Hill of Howth had precisely the same altitude as that of the theodolite on the pier, and that, therefore, there was no curvature or convexity in the water across Dublin Bay. It was, of course, inadmissible that the similarity of altitude at the two places was the result of refraction, because there was no difference in the condition of the atmosphere at the moment of observation.

[alex]

If I understand this quotation right, there is no bending of light in air. Do I understand that correct?

[Tom Bishop]

No significant bending of light, or of the earth, was observed at that distance.

[alex]

What about mirages you can see on hot days on a street or road? Isn't that the effect of light bending traveling through air with considerable temperature differences?

[Tom Bishop]

What about mirages you can see on hot days on a street or road? Isn't that the effect of light bending traveling through air with considerable temperature differences?

Experiments to test the temperature, humidity, pressure, and altitude was done at the two locations in the experiment and were found to be nearly identical.

Besides, what are the chances of a mirage projecting the image of a shoreline to the exact distance into the air, no higher or lower so that it is not sunken or floating, whereby it looks to a distant observer that the earth is flat, and this happens every time the experiment is performed, and that this effect adjusts itself accounting for the observer's distance from the shore in accordance to round earth curvature?

[alex]

Experiments to test the temperature, pressure, and altitude was done at the two locations in the experiment and were found to be identical.

What about atmospheric conditions inbetween the two points of measurement? What about mirages?

Can you specify a mathematical formula describing refraction of light in air?

[Tom Bishop]

What about atmospheric conditions inbetween the two points of measurement? What about mirages?

If the atmosphere only differed in the middle of the lake to cause light to curve upwards the photons from the opposite shoreline would cross the lake towards the observer and be curved upwards into the air and lost. All light would curve upwards in the middle of the lake and the observer would be seeing the lake's surface suspended in the air instead of the opposite shoreline that was seen in the experiment.

Can you specify a mathematical formula describing refraction of light in air?

The values for refraction are given in Experiment 9:

"The only modification which can be made in the above calculations is the allowance for refraction, which is generally considered by surveyors to amount to one-twelfth the altitude of the object observed. If we make this allowance, it will reduce the various quotients so little that the whole will be substantially the same."

Also, I have not heard a rebuttal for this comment:

Besides, what are the chances of a mirage projecting the image of a shoreline to the exact distance into the air, no higher or lower so that it is not sunken or floating, whereby it looks to a distant observer that the earth is flat, and this happens every time the experiment is performed, and that this effect adjusts itself accounting for the observer's distance from the shore in accordance to round earth curvature?

[markjo]

Besides, what are the chances of a mirage projecting the image of a shoreline to the exact distance into the air, no higher or lower so that it is not sunken or floating, whereby it looks to a distant observer that the earth is flat, and this happens every time the experiment is performed, and that this effect adjusts itself accounting for the observer's distance from the shore in accordance to round earth curvature?

Since there is no documentation available for every instance that this experiment was performed, it's impossible to say.  In fact, we have no documentation saying that the same results occurred every time this experiment was performed.

Tom, you say that there was no observable bending of light over a 6 mile distance, yet in another thread you would have us believe that there is a significant bending of light from the sun that accounts for sunrises and sunsets.  It's a real shame that there is no workable formula to describe this conveniently conditional bending of light that you like to go on about.

[Tom Bishop]

Besides, what are the chances of a mirage projecting the image of a shoreline to the exact distance into the air, no higher or lower so that it is not sunken or floating, whereby it looks to a distant observer that the earth is flat, and this happens every time the experiment is performed, and that this effect adjusts itself accounting for the observer's distance from the shore in accordance to round earth curvature?

Since there is no documentation available for every instance that this experiment was performed, it's impossible to say.  In fact, we have no documentation saying that the same results occurred every time this experiment was performed.

Samuel Birley Rowbotham performed the experiment over many years. A replication of the experiment was published by The English Mechanic. Lady Blount spent significant time peer reviewing the Earth Not a Globe Experiments in Earth Not a Globe Review. The effect is reported in Zetetic Cosmogony by Thomas Winship. Samuel Shenton and Charkes K Johnson reported the effect. Even Daniel on the .org forum reported the effect.

Tom, you say that there was no observable bending of light over a 6 mile distance, yet in another thread you would have us believe that there is a significant bending of light from the sun that accounts for sunrises and sunsets.  It's a real shame that there is no workable formula to describe this conveniently conditional bending of light that you like to go on about.

6 miles is quite a different number than 3000 miles.

[markjo]

Besides, what are the chances of a mirage projecting the image of a shoreline to the exact distance into the air, no higher or lower so that it is not sunken or floating, whereby it looks to a distant observer that the earth is flat, and this happens every time the experiment is performed, and that this effect adjusts itself accounting for the observer's distance from the shore in accordance to round earth curvature?

Since there is no documentation available for every instance that this experiment was performed, it's impossible to say.  In fact, we have no documentation saying that the same results occurred every time this experiment was performed.

Samuel Birley Rowbotham performed the experiment over many years. A replication of the experiment was published by The English Mechanic. Lady Blount spent significant time peer reviewing the Earth Not a Globe Experiments in Earth Not a Globe Review. The effect is reported in Zetetic Cosmogony by Thomas Winship. Samuel Shenton and Charkes K Johnson reported the effect. Even Daniel on the .org forum reported the effect.

I'm sorry, but do you understand the concept of documentation?

Tom, you say that there was no observable bending of light over a 6 mile distance, yet in another thread you would have us believe that there is a significant bending of light from the sun that accounts for sunrises and sunsets.  It's a real shame that there is no workable formula to describe this conveniently conditional bending of light that you like to go on about.

6 miles is quite a different number than 3000 miles.

Yes, they are very different numbers.  Do you have a formula that works with both of them?