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Editor Flaming Sword:—Please harmonize two statements made in the Cellular Cosmogony: On page 60 you say an object removed to a distance which equals 3,000 times its diameter will have reached its vanishing point. On page 70 you say you saw with the unaided eye, two targets, one 21x27, and the other 26x38 inches, at a measured distance of five miles. Would not the vanishing point of the largest target be less than two miles?—A Reader.
The statement that an object reaches its vanishing point at a distance of about 3,000 times its own diameter is a general statement, and constitutes a rule for estimating the distance at which objects may be seen by the average eye. It is generally recognized that for most persons a receding object becomes invisible when it subtends an angle of less than 1'. An object 10 inches in diameter subtends an angle of 1' at about 3,000 feet distant; and to most eyes an unillumined disc or ball one foot in diameter would be reduced to the vanishing point if removed to a distance of about 3,000 feet. But there are some eyes that are able to perceive objects which subtend a much less angle—to some the vanishing point is where the angle subtended is only a few seconds of a degree, especially if the object is illumined, or appears clear cut between the eye and the sky. Some opticians make the vanishing point of an object 5,000 times its diameter, with the corresponding angle subtended about 30". The one is applicable to the average eye in casual observations; the other more particularly to better eyes, and where the gaze is fixed intently upon the exact point where the object is known to be.
There is a great deal of difference between the distance to the vanishing points of objects of same size, subject to different degrees of illumination. The above rule applies to non-luminous objects. The distance at which objects may be seen depends upon their degree of brilliancy. In the case of the targets it will be noted that we mentioned the fact that they were white, and occupied a position in the sunlight. The two targets were placed side by side, so that the effect upon the eye would be about the same as that produced by a single target about 23x65 inches; but even if viewed singly, the illumination would be sufficient to render them visible considerably beyond the point at which unillumined targets could be seen against objects in the background of the view. There is no inharmony or contradiction between the two statements referred to; the apparent discrepancy is due to degrees of illumination, and to the difference between the average eye, and to the eye used to such observations.
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The Flaming Sword · Vol. 17, No. 17 · 13 Mar 1903 · PDF p. 12