I've been reading through Earth Not a Globe's section on perspective, and came to the conclusion that there is nothing described here by Rowbotham that is fundamentally incorrect.

Before explaining the influence of perspective in causing-the hull of a ship to disappear first when outward bound, it is necessary to remove an error in its application, which artists and teachers have generally committed, and which if persisted in will not only prevent their giving, as it has hitherto done, absolutely correct representations of natural things, but also deprive them of the power to understand the cause of the lower part of any receding object disappearing to the eye before any higher portion--even though the surface on which it moves is admittedly and provably horizontal.

"The range of the eye, or diameter of the field of vision, is

p. 203

[paragraph continues] 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." 1

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 first and second of the above propositions are self-evident.

The majority of what is written here is correct. It is true that art schools teach an imprecise version of the laws of perspective. Artists are not generally good mathematicians, and so try their best with as little math as possible. As a result, mathematical errors do occur in artwork. However, due to the freedoms of artistic expression, such errors are mostly trivial.

It should be noted that what Rowbotham is describing as the smallest angle visible is not, in fact the same thing as the vanishing point which schools teach about. The vanishing point as taught by schools, which I will refer to as the “standard” represents a direction, in which all lines parallel to that direction point to. It does not represent a finite distance. Rowbotham's vanishing point does represent a variable distance dependant on physical size of the object observed. Objects will in fact always “vanish” at Rowbotham's vanishing point before reaching the standard vanishing point. There really is no ground here to say that art schools have it wrong. The only thing they really get wrong is where the vanishing points are placed within an image. Beyond that there's nothing that Rowbotham describes that is incompatible with what art schools teach.

So to my final point, there is nothing about what Rowbotham describes here that is mathematically incorrect, and neither is there anything here that contradicts the math performed by Flat Earth Skeptics to analyze maps presented by FES. So I find it confusing that Flat Earth supporters would refer to Rowbotham when presented with numbers. If there is anything to question in an FE skeptic's argument, it's either his math or his logic. Telling them to read ENAG won't help, as there is nothing here to correct their math or logic.