The following is a summary of Rowbotham's perspective (http://www.sacred-texts.com/earth/za/za32.htm), using only quotes and logic. This should probably go in Information Repository, but I'm guessing a few FEers will get their panties in a twist and either debate this or ignore it. Mods, feel free to move at your pleasure.
Rowbotham's Perspective
Chapter 14 of Zetetic Astronomy
"The smallest angle under which an object can be seen is upon an average, for different sights, the sixtieth part of a degree, or one minute in space; so that when an object is removed from the eye 3000 times its own diameter, it will only just be distinguishable; consequently the greatest distance at which we can behold an object like a shilling of an inch in diameter, is 3000 inches or 250 feet."
-- "Wonders of Science," by Mayhew, p. 357
The above may be called the law of perspective. It may be given in more formal language, as the following:. when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.
From the above it follows:--
1.--That the larger the object the further will it require to go from the observer before it becomes invisible.
2.--The further any two bodies, or any two parts of the same body, are asunder, the further must they recede before they appear to converge to the same point.
3.--Any distinctive part of a receding body will be-come invisible before the whole or any larger part of the same body.
if a similar disc is coloured black, except a segment of say one inch in depth at the lower edge, on moving it forward the lower segment will gradually disappear, as shown at A, B, and C, in diagram fig. 74. If the
(http://www.sacred-texts.com/earth/za/img/fig74.jpg)
Fig. 74.
disc is allowed to rest on a board D, the effect is still more striking. The disc at C will appear perfectly round--the white segment having disappeared.
From these we can formulate the following rules for perspective:
- Any object, or portion of an object, less than 1 arcminute in size will be indiscernible to the naked human eye. This will happen when its distance to size ratio is roughly 3000:1 (actual number is just shy of 3438:1)
- A portion of a smaller object will vanish before the object as a whole vanishes.
- If a portion of an object reaches this distance, but the object as a whole has not, the portion will disappear but leave the object as a whole unchanged.
(Rowbotham's list is slightly different--His first and second are similar to the point of being the same, so I have combined them (and added the metric he quoted). I moved his third into slot 2 and added a third of my own, stated by Rowbotham in his disk experiment.)
Rowbotham illustrates this with the following diagram. On the left are three objects, two of identical size with one above and one below eye-level, and a third (http://www.sacred-texts.com/earth/za/img/fig75.jpg)
larger object above the eye-line. The two identical objects both will vanish at point H, as that's where they reach a size of less than 1 arcminute, but the larger one would still be visible and not vanish until it's gone on to W.
The theory which affirms that all parallel lines converge to one and the same point on the eye-line, is an error. It is true only of lines equi-distant from the eye-line; lines more or less apart meet the eye-line at different distances, and the point at which they meet is that only where each forms the angle of one minute of a degree, or such other angular measure as may be decided upon as the vanishing point. This is the true law of perspective as shown by nature herself; any idea to the contrary is fallacious, and will deceive whoever may hold and apply it to practice.
In accordance with the above law of natural perspective, the following illustrations are important as representing actually observed phenomena. In a long row of lamps, standing on horizontal ground, the pedestals, if short, gradually diminish until at a distance of a few hundred yards they seem to disappear, and the upper and thinner parts of the lamp posts appear to touch the ground, as shown in the following diagram, fig. 77.
(http://www.sacred-texts.com/earth/za/img/fig77.jpg)
Fig. 77.
This is another way of saying the First Law of Perspective, that being that the distance at which an object will reach this is related to its size, specifically a ratio of roughly 3000:1. The diagram also agrees with the Third Law, that being that even though the lower portion of the lamp has vanished, the rest of the lamp still recedes until it's full distance is 3000 times its full length.
However, the diagram also breaks the First Law. The upper bulb of the lamp, in the diagram, is about the same height as the base pedestals. Thus, the upper bulb, having roughly the same size, should vanish at roughly the same point--that is, point H in the diagram.
Rowbotham further demonstrates these laws with a woman on a street, a train engine, a series of flags on a canal, and a lighthouse on a wall. All of these demonstrate more of the same thing, so I shall skip them and move onto the final part of the chapter: a vanishing ship.
The hull is a distinctive part of a ship.
Ergo, the hull of a receding or outward bound ship must disappear before the whole, inclusive of the mast head.
To give the argument a more practical and nautical character it may be stated as follows:
That part of any receding body which is nearest to the surface upon which it moves, contracts, and becomes in-visible before the parts which are further away from such surface--as shown in figs. 63, 64, 65, 66, 67, 68, 69, and 70.
The hull of a ship is nearer to the water--the surface on which it moves--than the mast head.
Ergo, the hull of an outward bound ship must be the first to disappear.
Those who believe that the earth is a globe have often sought to prove it to be so by quoting the fact that when the ship's hull has disappeared, if an observer ascends to a higher position the hull again becomes visible. But this, is logically premature; such a result arises simply from the fact that on raising his position the eye-line recedes further over the water before it forms the angle of one minute of a degree, and this includes and brings back the hull within the vanishing point
I feel the need to point out to Rowbotham the First Rule of Perspective: "Any object, or portion of an object, less than 1 arcminute in size will be indiscernible to the naked human eye. This will happen when its distance to size ratio is roughly 3000:1." Or, as Rowbotham himself puts it "That the larger the object the further will it require to go from the observer before it becomes invisible."
Rowbotham has suddenly switched from the vanishing point being determined by the size of the object to it being determined by the object's height above the horizon. According to this theory, a kite 6 inches across, if flown 2000 feet away at an altitude of 350 feet above the ground would remain visible even though its angular size is only .85 arcminutes--well below the vanishing size.
Hence his assumption that the size of an object is equal to its distance above eye-level is completely false, and the First Rule of Perspective, as stated by Rowbotham himself, is correct--that the vanishing point is determined by the size of the object.
And that concludes the chapter. Just to iterate, the Three Laws of Perspective, as proposed by Rowbotham, are:
- Any object, or portion of an object, less than 1 arcminute in size will be indiscernible to the naked human eye. This will happen when its distance to size ratio is roughly 3000:1 (actual number is just shy of 3438:1)
- A portion of a smaller object will vanish before the object as a whole vanishes.
- If a portion of an object reaches this distance, but the object as a whole has not, the portion will disappear but leave the object as a whole unchanged.