"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:--
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.
The very essence of Rowbotham's argument is here: the human eye has a resolution of 0.016 degrees, which seems about right. Rowbotham goes on to say that what you cannot see is now apparently below the observed horizon (the apparent border between sky and floor, so that discussion does not start again).
That part can be conceded, for argument's sake. But then comes the catastrophe for this argument: telescopes have easily 10 to 200 times that resolution. Any ship that would appear to be sinking if seen with the naked eye would again be seen in its entirety if seen with a telescope.
Lets say we see a boat has 5 meters from the water line to the top deck. According to Rowbotham the top deck would disappear when at a distance of:
distance = 5 meters / tan(0.0166) = 17 kilometers. or some 11 miles.
But then, that same boat would be seen almost completely above the water line if seen with a telescope. Lets assume the telescope has 100 times enlarging power:
Distance obscured = 17 kilometers * tan(0.000166) = 0.05 meters, or some 2 inches.
What you can see in several photographs in this forum and elsewhere is that the "sinking ship" illusion is seen with and without telescopes. If this were the explanation, the photographs of Toronto from the other side of Lake Ontario would show the beaches of Toronto.
This mistake from an 19th century science amateur is acceptable. From 21st century high school and college graduates it is not.