IV. The Station-Point.—
On this line, mark the distance S T at your pleasure, for the distance at which you wish your picture to be seen, and call the point T
the “Station-Point.”
Fig. 2.
In practice, it is generally advisable to make the distance S T about as great as the diameter of your intended picture; and it should, for the most part, be more rather than less; but, as I have just stated, this is quite arbitrary. However, in this figure, as an approximation to a generally advisable distance, I make the distance S T equal to the diameter of the circle N O P Q. Now, having fixed this distance, S T, all the dimensions of the objects in our picture are fixed likewise, and for this reason:—
Let the upright line A B, [Fig. 2.], represent a pane of glass placed where our picture is to be placed; but seen at the side [p7] ]of it, edgeways; let S be the Sight-point; S T the Station-line, which, in this figure, observe, is in its true position, drawn out from the paper, not down upon it; and T the Station-point.
Suppose the Station-line S T to be continued, or in mathematical language “produced,” through S, far beyond the pane of glass, and let P Q be a tower or other upright object situated on or above this line.
Now the apparent height of the tower P Q is measured by the angle Q T P, between the rays of light which come from the top and bottom of it to the eye of the observer. But the actual height of the image of the tower on the pane of glass A B, between us and it, is the distance P′ Q′ between the points where the rays traverse the glass.
Evidently, the farther from the point T we place the glass, making S T longer, the larger will be the image; and the nearer we place it to T, the smaller the image, and that in a fixed ratio. Let the distance D T be the direct distance from the Station-point to the foot of the object. Then, if we place the glass A B at one-third of that whole distance, P′ Q′ will be one-third of the real height of the object; if we place the glass at two-thirds of the distance, as at E F, P″ Q″ (the height of the image at that point) will be two-thirds the height[Footnote 5] ] of the object, and so on. Therefore the mathematical law is that P′ Q′ will be to P Q as S T to D T. I put this ratio clearly by itself that you may remember it: