[edby]

I have an idea to celebrate the 150th anniversary of Wallace’s test by repeating it, in the same place, around February 2020 (less than 2 years’ time).
https://en.wikipedia.org/wiki/Bedford_Level_experiment

I would welcome participation from the FE Society. The rules would conform to Wallace’s, namely (i) both sides (RE/FE) would agree to the methodology, (ii) both would agree as to what observation would prove, or disprove either theory (iii) both sides would confirm the observations at first hand.

I would be prepared to fund a decent prize. We could get sponsorship from instrument makers, surveying firms, tourist boards etc. Could make a short documentary about it or post on YouTube.

It has little scientific merit, given the science has been well understood for centuries, but might help to convince the unconvinced in a world of fake news and explosion of conspiracy theories on the internet.

And we could have a beer. I appreciate 2020 some way off, but indications of interest would be appreciated.

I will be heading off to Norfolk later this year to see if the terrain still suitable for the test.

[Bobby Shafto]

That's a cool idea. I've seen (or at least heard) where others have tried to recreate the test, but with varying levels of success (mostly due to weather conditions and changes over the years to the environment).

But it would be interesting to try.

(I'd like to recreate the "Bishop Experiment" sometime. I don't have a telescope of the power Tom claims to have used, but I have one with a 127mm aperture,and 1000mm focal length, which gives me about half the magnification Tom's says he had in his observations. One of these days, maybe during my next trip to San Luis Obispo, I'm going to bring my telescope along and, if the weather conditions are similar to Tom's, try to document what he reported to have observed.)

[edby]

That's a cool idea. I've seen (or at least heard) where others have tried to recreate the test, but with varying levels of success (mostly due to weather conditions and changes over the years to the environment).

But it would be interesting to try.

Indeed. I found an old survey instrument similar to what Wallace used, although I am advised a Nikon P900 would be more modern. Could use both. The altercation between Carpenter and Wallace is amusing.

The fallacies in the remainder of Mr Carpenter's letter have been so ably refuted (by anticipation) by your correspondent Mr J. Tanner, that I need say no more about them. I would ask Mr Carpenter, however, to state, for the information of your readers, whether the universally-accepted and only known method of deciding whether three distant points are in a straight line is true or false. http://people.wku.edu/charles.smith/wallace/S162-163.htm 

[Tom Bishop]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

[inquisitive]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

Modern instruments with higher accuracy should be used.

[edby]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

Modern instruments with higher accuracy should be used.

That too, but accuracy is not the issue in the Wallace experiment, which is conclusive with a huge margin. The question is simply whether one marker is higher than another.

[edby]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

What do you understand the problem is, according to Rowbotham?

[Tom Bishop]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

What do you understand the problem is, according to Rowbotham?

I decline to rewrite something that is clearly detailed in the link provided.

[edby]

It is better to attempt to repeat Rowbotham's original experiments to the letter rather than trying to create a derived version which may be flawed. Alfred Wallace and Co. chose to create their own version; but was flawed because they had not read Earth Not a Globe closely enough on the documented issues with theodolites.

Rowbotham explains the problem with the experiment in the Wallace wager here: http://www.sacred-texts.com/earth/za/za45.htm

What do you understand the problem is, according to Rowbotham?

I decline to rewrite something that is clearly detailed in the link provided.

I thought so.

[Tom Bishop]

I thought so.

If you are not going to make a basic effort to read the material provided to you, then I see little reason for why we should engage with you on any topic. No one is going to rewrite a chapter in a book for you. It is right there to read in black and white.

[douglips]

It sounds like the Rowbotham claim is that the middle optical Target was mounted 3.75 inches too high.

So, Tom, could we not design an experiment where the targets are mounted satisfactorily to you?

[Tom Bishop]

It sounds like the Rowbotham claim is that the middle optical Target was mounted 3.75 inches too high.

So, Tom, could we not design an experiment where the targets are mounted satisfactorily to you?

The problem in the experiment is collimation of light traveling through a lens when attempting to line up bodies with the crosshairs of a theodolite.

The experiments Rowbotham performs in Earth Not a Globe are specifically designed to avoid that issue. While telescopes and theodolites are used in Earth Not a Globe, they are merely being used as magnification instruments that are observing whether bodies line up with each other in the distance, or whether they disappear to curvature.

It is best to just recreate Rowbotham's original experiments.

[edby]

The problem in the experiment is collimation of light traveling through a lens when attempting to line up bodies with the crosshairs of a theodolite.

This is not the problem. This is why I wanted to see if you understood what the flaw was supposed to be. As Wallace explained, the force of his experiment is independent of issues like 'crosshairs'.

If you are not going to make a basic effort to read the material provided to you ..

I have read that material, such as it is.

[Tom Bishop]

http://www.sacred-texts.com/earth/za/za45.htm

TANGENTIAL HORIZON.

IF a theodolite is placed on the sea shore, "levelled," and directed towards the sea, the line of the horizon will be a given amount below the cross-hair, and a certain "dip" or inclination from the level position will have to be made to bring the cross-hair and the sea-horizon together. If the theodolite is similarly fixed, but at a greater altitude, the space between the cross-hair and the sea horizon, and the dip of the instrument to bring them together, is also greater. From the above, which is perfectly true, it has been concluded that the surface of the earth is convex, and the line of sight over the sea tangential. As a proof that such is not the case, the following experiment may be tried:--

Place a theodolite on an eminence near the sea. "Level," and direct it over the water, when the horizon will be seen a little below the cross-hair or centre of the telescope, as shown in the diagram, fig. 30, page 41, and from the cause there assigned, viz., collimation, or refraction. Now let the instrument be inclined downwards until the cross-hair touches the horizon, as shown in fig. 31, page 41, and in the following diagram, fig. 92. If the theodolite had a simple tube without lenses, instead of a telescope, which causes the appearance shown in , the

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FIG. 92.

horizon would be seen in a line with the cross-hair, or axis of the eye, as at A, fig. 92, and the amount of "dip" required to bring the cross-hair and the horizon in contact with each other will be represented by the angle A, T, S, to which must be added the collimation. In every instance where the experiment has been specially tried, the dip without the collimation only amounted to the angle A, T, S; thus proving that the' surface of the sea, S, B, is horizontal, because parallel to the line A, T. If the water is convex, the line of sight, A, T, would be a tangent, and the dip to the horizon would be T, H, represented by the angle A, T, H. This angle, A, T, H, is never observed, but always A, T, S, plus collimation or divergence produced by the lenses in the telescope of the theodolite. Hence the surface of the waters is everywhere horizontal.

The words "collimation," "divergence," "refraction," &c., have many times been used in connection with this part of the subject, and the following very simple experiment will both exhibit what is meant, and show its influence in practice.

Take a "magnifying glass," or a convex lens, and hold it over a straight line drawn across a sheet of paper. If the line is drawn longer than the diameter of the lens, that part of it which is outside the lens will have a different position to that seen through it, as shown in the following diagram, fig. 93.

p. 267


FIG. 93.

Instead of the line going uninterruptedly through the lens in the direction A, B, it will diverge, and appear at 1, 2; or it will appear above the line A, B, as at 3, 4, if the lens is held to the slightest amount above or below the actual centre.

A lens is a magnifying glass because it dilates, or spreads out from its centre, the objects seen through it. The infinitesimal or mathematical point actually in the centre is, of course, not visibly influenced, being in the very centre or on the true axis of the eye, but any part in the minutest degree out of that abstract centre is dilated, or diverged, or thrown further away from it than it would be to the naked eye; hence its apparent enlargement or expansion. Whatever, therefore, is magnified, is really so because thrown more or less out of the centre, and the more or less magnifying power of the lens is really the more or less divergence of the pencils of light on passing through the substance of which it is composed. In the telescope of a theodolite, or spirit-level, the spider's web of which the cross hair is made is placed in the actual centre; hence, in an observation, the point absolutely

p. 268

opposite to it is not seen, but only some other point minutely distant from it, but the distance of which is increased by the divergence caused by the lenses; and this divergence is what is called the "magnifying power." This is the source of those peculiarities which have been so very illogically considered to be proofs of the earth's rotundity. It is from this peculiarity that several gentlemen prematurely concluded that the water in the Bedford Canal was convex.

On the 5th of March, 1870, a party, consisting of Messrs. John Hampden, of Swindon, Wilts; Alfred Wallace, of London, William Carpenter, of Lewisham, M. W. B. Coulcher, of Downham Market, and J. H. Walsh, Editor of "The Field" newspaper, assembled on the northern bank of the "Old Bedford Canal," to repeat experiments similar to those described in figs. 2, 3, 4, and 5, on pages 11 to 14 of this work. But, from causes which need not be referred to here, they abandoned their original intentions, and substituted the following. On the western face of the Old Bedford Bridge, at Salter's Lode, a signal was placed at an elevation of 13 feet 4 inches above the water in the canal; at the distance of three miles a signal-post, with a disc 12 inches in diameter on the top, was so fixed that "the centre of the disc was 13 feet 4 inches above the water-line;" and at the distance of another three miles (or six miles altogether), on the eastern side of the Welney Bridge, another signal was placed, "3 inches above the top rail of the bridge, and 13 feet 4 inches above the water-line." 1 This arrangement is represented in the following diagram, fig. 94:--

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FIG. 94.

A, the signal on the Old Bedford Bridge; B, the telescope on Welney Bridge; and C, the central signal-post, three miles from each end. The object-glass of the telescope was 4½ inches diameter; hence the centre, or true eye-line, was 2¼ inches higher than the top of the signal B, and 3¾ inches below the top of the signal-disc at C. On directing the telescope, "with a power of 50," towards the signal A, the centre of which was 2¼ inches below the centre of the telescope, it was seen to be below it; but the disc on the centre pole, the top of which was, to begin with, 3¾ inches above the centre, or line of sight, from the telescope, was seen to stand considerably higher than the signal A. From which, three of the gentlemen immediately, but most unwarrantably, concluded that the elevation of the disc in the field of view of the telescope was owing to a rise in the water of the canal, showing convexity! whereas it was nothing more than simply the upward divergence (of that which was already 3¾ inches above the line of sight) produced by the magnifying power of the telescope, as shown in the experiment with the lens, on page 267, fig. 92.

Why did they omit to consider the fact that 3¾ inches excess of altitude would be made by a magnifying power of 50, to appear to stand considerably above the eye-line, and that a mere hair's-breadth of dip--an amount which could not be detected--towards the distant signal would by magnifying,

p. 270

diverging, or dilating all above it, make it appear to be lifted up for several feet? Why did they not take care that the top of the centre disc was in a line with the telescope and the distant signal, A? Why, also, was the centre of the object glass fixed 2¼ inches higher than the centre of the object of observation at the other end? There was no difficulty in placing the centre of the telescope, the top of the middle disc, and the centre of the farthest signal mark, at the same altitude, and therefore in a straight line. For their own sakes as gentlemen, as well as for the sake of the cause they had undertaken to champion, it is unfortunate that they acted so unwisely; that they so foolishly laid themselves open to charges of unfairness in fixing the signals. Had they already seen enough to prove that the surface of the water was horizontal, and therefore instinctively felt a desire to do their best to delay as long as they could the day of general denunciation of their cherished doctrine of the earth's rotundity? Such questions are perfectly fair in relation to conduct so unjust and one-sided. It is evident that their anxiety to defend a doctrine which had been challenged by others overcame their desire for "truth without fear of consequences;" and they eagerly seized upon the veriest shadow of evidence to support themselves. In the whole history of invention, a more hasty, ill-conceived, illogical conclusion was never drawn; and it is well for civilisation that such procedure is almost universally denounced. It is scarcely possible to draw a favourable conclusion as to their motives in departing from their first intentions. Why did they not confine themselves to the repetition of

p. 271

the experiments, an account of which I had long previously published to the world, and to test which the expedition was first arranged? That of sending out a boat for a distance of six miles, and watching its progress from a fixed point with a good telescope, would have completely satisfied them as to the true form of the surface of the water; and as no irregularity in altitudes of signals, nor peculiarities of instruments, could have influenced the result, all engaged must at once have submitted to the simple truth as developed by the simplest possible experiment.

TL;DR: Wallace's version of the experiment is in error and brings up complications and one should perform the original simple experiments in Earth Not a Globe.

[edby]

(1) Rowbotham's understand of lens refraction ('collimation') is completely wrong, as far as I can see, and in any case (2) Wallace's experiment does not rely on any assumptions about lens, crosshairs and so forth.

Rowbotham's original experiment, conducted at a level close to the water, was vulnerable to problems of refraction, which is why Wallace designed his experiment in the way he did. The Wallace experiment requires minimal prior assumptions.

[Tom Bishop]

"He's wrong"

"Not so"

Good one. Your rebuttals are so convincing, well thought out, and articulate. Why not just state that the earth is round with an expletive and move on to another website? That is what most of you high thinkers do.

[edby]

And this diagram beautifully explains Rowbotham’s mistake,

C is the endmark, B is the middle pole, and A is the crosshair. Rowbotham (like Carpenter) completely misunderstands that it is enough that B and C are not lined up. Forget the crosshair. If A is my eye, B the midpoint, and C the endpoint, then by geometry the three points will form a straight line only if B and C coincide. Otherwise not.

I would ask Mr Carpenter, however, to state, for the information of your readers, whether the universally-accepted and only known method of deciding whether three distant points are in a straight line is true or false. That method is to place the eye (whether aided by a telescope or not) at or behind one of the extreme points, and see whether the other two or all three coincide, the nearer hiding or covering the more distant. If so, they are in a straight line. Every carpenter who looks along the edge of a floor board, every surveyor who runs his base lines across the country, every builder who sets out a long wall, uses this method. Does Mr Carpenter say they are all wrong, and that every line thus set out is a crooked or curved line? If so, let him prove this elementary point by experiment and diagrams, and thus found a totally new and hitherto unimagined geometry. http://people.wku.edu/charles.smith/wallace/S162-163.htm

[edby]

"He's wrong"

"Not so"

Good one. Your rebuttals are so convincing, well thought out, and articulate. Why not just state that the earth is round with an expletive and move on to another website? That is what most of you high thinkers do.

Not at all. Logic, geometry and evidence, rather than bare assertions.

[Tom Bishop]

And this diagram beautifully explains Rowbotham’s mistake,

http://www.logicmuseum.com/w/images/6/6a/Rowbotham_crosshair.jpg

C is the endmark, B is the middle pole, and A is the crosshair. Rowbotham (like Carpenter) completely misunderstands that it is enough that B and C are not lined up. Forget the crosshair. If A is my eye, B the midpoint, and C the endpoint, then by geometry the three points will form a straight line only if B and C coincide. Otherwise not.

I would ask Mr Carpenter, however, to state, for the information of your readers, whether the universally-accepted and only known method of deciding whether three distant points are in a straight line is true or false. That method is to place the eye (whether aided by a telescope or not) at or behind one of the extreme points, and see whether the other two or all three coincide, the nearer hiding or covering the more distant. If so, they are in a straight line. Every carpenter who looks along the edge of a floor board, every surveyor who runs his base lines across the country, every builder who sets out a long wall, uses this method. Does Mr Carpenter say they are all wrong, and that every line thus set out is a crooked or curved line? If so, let him prove this elementary point by experiment and diagrams, and thus found a totally new and hitherto unimagined geometry. http://people.wku.edu/charles.smith/wallace/S162-163.htm

Recall that all of this is taking place under high magnification, with the phenomenon of collimation/divergence from the crosshair. A is the cross hair, and B and C are the targets that should be lined up. If the targets are not perfectly lined up, and there is even a hair's breadth of separation, the divergence of the lens will magnify the difference.

The illustration you provided is addressed in Earth Not a Globe in that same chapter:

http://www.sacred-texts.com/earth/za/za45.htm

These same gentlemen tried another experiment, from which they, quite as prematurely and illogically as before, drew the conclusion that the water was convex, and not horizontal.

"A 16-inch Troughton level, accurately adjusted, was placed in the same position and height above the water as the large achromatic telescope employed in the last experiment," when the signal-pole, three miles, and the signal-flag on the bridge, six miles, away, were seen as shown in the following diagram, fig. 95. A is the cross-hair, B the signal-disc, and C the signal-flag on the Old Bedford Bridge. The telescope, D, D, D, carrying the cross-hair A, is on the bridge at Welney, three miles obverse from B and six from C.

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FIG. 95.

From the above observations, two of the experimenters at once concluded that the cross-hair in the line of sight was a tangent, and the water convex--the appearance of B, and C, resulting from the declination of the surface of the canal. It has been shown already that the best constructed levelling instruments necessarily produce, from the nature and arrangement of the lenses, a refraction or divergence of 1-1000th of a foot in a distance of 10 chains or 660 feet, so that the well-known and admitted refraction inseparable from the instruments employed, is fully sufficient to explain the position of the disc at B, and the flag at C, without demanding that the theory of the earth's rotundity is thereby corroborated. It is the duty of surveyors, and all who have an interest in this subject, to carefully study these peculiarities of levelling instruments, and not only to make themselves thoroughly acquainted with them, but to acknowledge their influence in every one of their operations. Should anyone have the slightest doubt of the effect of lenses in causing divergence of the line of sight, let him simply provide two

p. 273

instruments of precisely the same construction, except that one shall have the lenses taken out. It will then be seen that the instrument with lenses will not read, upon a graduated staff, the same point as that without them. The latter will give the true reading; and the difference between this and the reading of the instrument with lenses, is the amount for which allowance must be made, otherwise the results, however extensive and important, must be fallacious.

[edby]

Actually Tom, let me give you a very simple example of why Rowbotham's reasoning is faulty. Suppose I have a gun with sights that are so bad that when I aim at one thing, the shot goes off in a quite different direction, perhaps accidentally killing stray members of the public.

Then suppose there are two objects B in the middle ground, C in the distance. I then get both B and C in the sight. Now because of the fault, any shot will go nowhere near B or C. We agree that.

However, Wallace's point is that if B and C are superimposed, then I, B and C lie in a straight line. The faulty sight is irrelevant.

Now do you see?