You may have seen from some other posts that I am reading, with a lot of interest, Earth Not a Globe by Stanley Birley Rowbotham and I have come to a part of the work that has confused me. Would you please give me some guidance on the section of perspective that appears on pages 32 and 33 of Earth Not a Globe.
In the text on page 32 the author states "
that the smallest angle under which an object can be seen is upon an average for different sights the 60th part of a degree, or one minute in space; so that when an object is removed from the eye 3000 times it?s own diameter, it will only just be distinguishable." He then explains that "
the greatest distance at which we can behold an object, like a shilling, of an inch in diameter is 3000 inches or 250 feet." This I can understand, it is a very elegant and simple explanation especially as coins of that size are still readily available to test the theory.
However he then goes on to explain how a ship reaches the vanishing point. I'll quote:
It may, therefore, be very easily understood that a line passing over the hull of a ship, and continuing parallel to the surface of the water, must converge to the vanishing point at the distance of about 3000 times it's own elevation; in other words, if the surface of the hull be 10 feet above the water it will vanish at 3000 times 10 feet; or nearly 6 statute miles; but if the mast-head be 30 feet above the water, it will be visible for 90,000 feet or over 17 miles so that it could be seen upon the horizon for a distance of eleven miles after the hull had entered the vanishing point!
Now Mr Bishop, please help me. Using the mathemetics of Mr Rowbotham's own example of the shilling being visible up to a distance of 250 feet, let's assume that the width of the disappearing ship is 30 feet or 360 inches, not unreasonable I'm sure you'll agree. Using Mr Rowbotham's own calculations, 3000 x 360 inches = 1,080,000 inches. (I hope you agree!). There are 12 inches in a foot so the hull of the ship should still be visible at a distance of 1080000"/12" = 90,000 feet, which as every schoolboy knows is 30,000 yards which is just over 17 miles.
Can we now take the example of the mast-head mentioned by Mr Rowbotham. It would be a strange ship indeed that had a mast-head of the same width as the hull of the ship so I'll be generous and use a crows-nest in my example (Mr Rowbotham lived in the age of sail so I think that's fair) and let's suppose that the crows-nest is 3 feet across, i.e. 36 inches. Using Mr Rowbotham's own mathematics, 3000 x 36 inches = 108000 inches (I hope you agree!) and 108000 inches = 9000 feet which is equivalent to 1.7 miles or so. My experiences of perspective are that the hull of the ship would appear to get narrower as it recedes, and so would the mast-head/crows nest in my example. In fact, using Mr Rowbotham's mathematics, the crows nest should disappear from my view nearly 15 miles before the hull of the ship. This is where I am confused. How can Mr Rowbotham state so unequivocally that the mast-head would still be visible some 11 miles after the hull had vanished when using his own methods it shows the mast-head would not be able to be seen considerably earlier regardless of it's height above the level of the sea? Leap forward to today and there is even less chance of seeing a mast-head at distance. Mr Rowbotham may have mistakenly used the word 'mast-head' when he was actually referring to the sails (I find it hard that such an eminent scientist such as Mr Rowbotham would make such an error so maybe it is a typo). A modern cargo ship for example without sails . . .
Can I give you another example? From my house, when the atmospheric conditions are good (usually in the winter) I can see a mountain that is about 70 miles away; it's called Babadağ. Like all mountains it is wider at the bottom than it is at the top (I actually can't see the bottom as other hills obscure it but I can see its basic shape easily). Now according to Mr Rowbotham the top of the mountain which is narrower should disappear from my view before the bottom (I can only see a shilling up to a distance of about 250 feet but I can see something 1 metre across up to a distance of about 1.7 miles; see above). The top of the mountain, being narrower should not be visible at 70 miles surely? How can this be?
Also, in the Sunrise/Sunset thread (
http://theflatearthsociety.org/forum/index.php?topic=29819.40)
you Mr Bishop, state quite categorically that "A man has a Vanishing Point about 30 miles away." Now I can see the top of the mountain from my house which is elevated and I can also see it from sea level; if you were to visit me in the Winter you would surely be able to do the same! Even Mr Rowbotham states in earth Not a Globe that Great Orm's Head can be seen from Douglas Harbour, a distance of 60 miles! How am I to reconcile your statement that "A man has a Vanishing Point about 30 miles away" with these observations and with the science in Earth Not a Globe? Is '
about' a technical term that stretches to 70 miles?
It would appear that I am obviously missing something and I really need clarification on these points Mr Bishop. I simply cannot get my head around it. Please help me. I hope I don't come across too many more parts of Earth Not a Globe that I can't grasp!