Perspective

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.

"The range of the eye, or diameter of the field of vision, is 110°; consequently this is the largest angle under which an object can be seen. The range of vision is from 110° to 1°.  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."

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:

• That the larger the object the further will it require to go from the observer before it becomes invisible.
• 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.
• Any distinctive part of a receding body will become invisible before the whole or any larger part of the same body.

The first and second of the above propositions are self-evident. The third may be illustrated by the following diagram, fig. 73.

FIG. 73.

Let A represent a disc of wood or card-board, say one foot in diameter, and painted black, except one inch diameter in the centre. On taking this disc to about a hundred feet away from an observer at A, the white centre will appear considerably diminished--as shown at B--and on removing it still further the central white will become invisible, the disc will appear as at C, entirely black. Again, 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

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.

If a receding train be observed on a long, straight, and horizontal portion of railway, the bottom of the last carriage will seem to gradually get nearer to the rails, until at about the distance of two miles the line of rail and the bottom of the carriage will seem to come together, as shown in fig. 79.

Fig. 79.

Diamond Princess leaving Harbour

Diamond Princess partly over horizon

Diamond Princess well over horizon (framed for overlay)

Diamond Princess original ship overlayed on prev picture

RANGE ESTIMATION
Question CIC concerning the radar ranges to visual contacts and compare them
with your estimated range. 

HEIGHT OF EYE	RANGE TO	HORIZON
FEET	YARDS	MILES
20	10,200	5.1
40	14,400	7.2
60	17,800	8.9
80	20,600	10.3

Figure 5-5: Range – Height Table

The only readily available reference point you can use when estimating ranges is the
horizon.  Knowing your height above the waterline will help you estimate ranges because
the distance to the horizon varies with the height of the eye (Figure 5-5).

At a height of 50 feet, for example, the distance to the horizon is about 16,000 yards (8
miles); at a height of 100 feet, the distance is about 23,000 yards (11-1/2 miles).  Practice estimating ranges to other vessels in company whose distances are known or can be easily determined. 
 

Do you think those poor sailors got confused when they found that the Navy had lied to them? 

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).

You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.

Read it again, rabinoz: Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly than those farther from it. Art school perspective makes no account of this and this is the difficulty it finds itself in.

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.

FIG. 73.

Fig. 74.

Fig. 82.

Fig. 81.

Poolbeg Lighthouse, Dublin Bay

My whole point is that the apparent size of whole object is must be reduced in proportion to its distance, in exactly the way Rowbotham showed in his Fig 73 and 74:

FIG. 73.

Fig. 74.

Parts thereby separated by less than the resolution limit will not be seen as separate objects.

Those diagrams are fine, but then he somehow seems to treat eye level as something special, and shows the parts of the object below eye level as being artificially truncated. He shows:

Fig. 82.

which when seen from one end is supposed to look like:

Fig. 81.

He reduces the sea-wall down to nothing, but only reduces the lighthouse by about around 50%.

All parts of a scene at the same distance should get reduced by the same amount.

Yes, "Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly" but he can claim what he likes. I said that I went so far with his reasoning, then when he starts having things converge at different rates, I disagree.

These images shows the biggest flaw of Rowbotham's perspective that, based on my personal obesrvation, are just repeated without questioning.

1. Perspective lines converg to a point within our eye's sight of range.

Quote from: rabinoz on August 17, 2016, 05:36:14 AM

Yes, "Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly" but he can claim what he likes. I said that I went so far with his reasoning, then when he starts having things converge at different rates, I disagree.

Well, since that is the point of contention, I'd spend more time demonstrating your belief and less time laying out fundamentals on which we already agree...

• Light in the atmosphere travels in straight lines - apart from very slight refraction where there is a temperature gradient.
  
  
• The apparent size (the angle subtended at the eye or camera) of an object and its parts is simply (^{relevant dimension}/_{distance from the eye}) in radians.
  
  
• The apparent size of all parts of an object (irrespective of the closeness to the eye line) reduce at the same rate.
  
  
• The angular resolution limit of the eye (or any optical device) is the smallest apparent angular separation for which the eye (or other device) can detect that two objects are distinct. This does not mean that the eye cannot detect objects of smaller apparent size.
  This limit for healthy well-focussed eyes in good light is accepted as being about 1 arcminute. This means that the distance limit for two objects to be able to be resolved apart is about 3,000 times the separation of the objects.
  The contention with Rowbotham to this point is that he claims that this limit "the smallest angle under which an object can be seen". I am claiming that it is "The smallest angle for which objects can be separated". There is a big difference.
  
  
• Under favourable circumstances much smaller objects can be detected with the naked eye (or camera). The most obvious examples are stars. Even Betelgeuse, a very bright star and easily visible, has an angular size of only 50 mas (about 0.0008 arc minutes). The estimated distance (not measured) that candle could be seen on a clear night is about 2.7 km (if the flame is 1cm in diameter, that puts the angular size at about 0.013 arcminutes).
  Placing a limit of how small an object we can detect is actually very difficult. On a dark, given 100 photons of light, we would certainly see a flash.
  The reader can look this up as well as I, and it's probably not too relevant here.
  

Fig. 74.

Fig. 79.

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

This is the crux of Dr. Rowbotham's perspective, and as it is somewhat abstract and difficult to convey it is frequently overlooked. It took me some time and multiple readings before the idea registered fully for me, but was quite a "eureka" moment.

I think you're playing a sort of rhetorical game with "separated", "discerned", and "seen". I'm not in disagreement with you there, and I'm not convinced Dr. Rowbotham would be either.

Alpha Centauri

α Centauri and β Centauri, with Proxima circled

Quote from: Ski on August 17, 2016, 11:34:43 PM

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

  Still, why parallel lines will not converge to the point at horizon line? Ship wake is quite good demonstration for that.

Ship's Wake

Suez Canal

Looking East along the "Bight"

Quote from: zork on August 18, 2016, 01:38:15 AM

Quote from: Ski on August 17, 2016, 11:34:43 PM

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

  Still, why parallel lines will not converge to the point at horizon line? Ship wake is quite good demonstration for that.

Do you mean like this?

Ship's Wake

Suez Canal

Looking East along the "Bight"

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.
...

The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline).

This is why they have not decreased in size proportionately.

The shape is obviously not preserved and they do converge at different rates.  This is not demonstrated in art school perspective,  which is why we're having this discussion.

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).

Quote from: Ski on August 16, 2016, 07:58:13 PM

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).

The shape is obviously not preserved and they do converge at different rates.  This is not demonstrated in art school perspective,  which is why we're having this discussion.

Quote from: Ski on August 16, 2016, 07:58:13 PM

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).