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If a person stands upon the earth’s surface, with his vision resting upon the horizon in the distance, the most distant objects appear very small in comparison to those viewed in the foreground. Why is this? The technical, and crisp answer is, because the rays of incidence from the outlines of the object, provide a more obtuse angle, than the rays from the same sized object, viewed from a closer distance, and they therefore make a shorter imprint upon the retina.
To illustrate this, let the reader take a pencil and rule, and with them follow the directions herein given. Place the paper on the table in front of you. Lay the rule down upon the paper and draw a line six inches long, extending from left to right. Across the left extremity of this line, draw a transverse one, extending one half inch above and below the first line. On the left-and-right line, one-half inch to the right of the transverse one, fix a point. Two inches farther to the right, draw another transverse line, two inches long, extending one inch above and below the left-and- right line. Two inches to the right of the last line, draw another two inch transverse line, observing the same direction as for the last one drawn.
Now place your rule at the top of the first two inch transverse line, extending it across the point on the left-and-right line, and draw your line by the rule to the first transverse line at the left extremity of the left-and-right one. Then place your rule at the bottom of your second transverse one, across the point to the first line as above.
The dot or point is at the angles of the incidence of the lines drawn from the two extremities of the first two inch transverse line. If, now, the dot or point represents the visual focus at or near the lens of the eye, and the first transverse line at the left ■ extremity of the left-and-right line, the retina; the distance between the two extremities of the lines of incidence on the first transverse line, would represent the picture of the second one, or the first two inch transverse line.
Now draw two more lines of incidence, from the extremities of the second two inch transverse line, crossing the dot or point as in the first instance. These two lines will form a more acute angle of incidence, than the first lines of incidence, and they will therefore make a shorter line on the first transverse one.
This explains to you the reason, why a distant object of a given length appears shorter than a nearer object of the same length or height.
You may extend the application, by extending the left-and-right, and transverse lines, till the lines of incidence will form so acute an angle, or run so nearly parallel as not to divide after crossing the dot or point of incidence before reaching the first transverse line, at the left extremity of the left-and-right line. In this case there could be no picture on the line representing the retina. The object would then be out of sight.
Starting out with the principle of perspective-foreshortening as above described, the reader may take the retina of the eye as the first transverse line, and the visual focus at or near the lens of the eye, as the point or dot of incidence. A telegraph pole I fifty feet high, ten rods from the point of vision, may be taken as the second transverse line, and the distant pole on the horizon which appears as a mere speck, as the last of a line of transverse lines. A straight line drawn from the nearest pole to the distant one, will appear to make a rapid descent of twenty-five feet, and the earth will appear to have ascended twenty-five feet, because the two lines of linear perspective, the one at the top of the poles, the other at the bottom, while they run parallel, seem to converge to a point at the distant pole. The smart scientists take this linear foreshortening for convex rotundity of the earth.
The Flaming Sword · Vol. 1, No. 16 · 22 Mar 1890 · PDF p. 1