IT has already been proved that the astronomers of the Copernican school merely assumed the rotundity of the earth as a doctrine which enabled them to explain certain well-known phenomena. "What other explanation can be imagined except the sphericity of the earth?" is the language of Professor de Morgan, and it expresses the state of mind of all who hold that the earth is a globe. There is on their part an almost amusing innocence of the fact, than in seeking to explain phenomena by the assumption of rotundity, another assumption is necessarily involved, viz., that nothing else will explain the phenomena in question but the foregone and gratuitous conclusion to which they have committed themselves. To argue, for instance, that because the lower part of an outward-bound vessel disappears before the mast-head, the water must be round, is to assume that a round surface only can produce such an effect. But if it can be shown that a simple law of perspective in connection with a plane surface necessarily produces this appearance, the assumption of rotundity is not required, and all the misleading fallacies and confusion involved in or mixed up with it may be avoided.
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 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.
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