Fig. I.

I. The Sight-point. - Let a b c d, Fig. I., be your sheet of paper, the larger the better, though perhaps we may cut out of it at last only a small piece for our picture, such as the dotted circle n o p q. This circle is not intended to limit either the size or shape of our picture: you may ultimately have it round or oval, horizontal or upright, small or large, as you choose. I only dot the line to give you an idea of whereabouts you will probably like to have it; and, as the operations of perspective are more conveniently performed upon paper underneath the picture than above it, I put this conjectural circle at the top of the paper, about the middle of it, leaving plenty of paper on both sides and at the bottom. Now, as an observer generally stands near the middle of a picture to look at it, we had better at first, and for simplicity's sake, fix the point of observation opposite the middle of our conjectural picture. So take the point s, the centre of the circle n o p q; - or, which will be simpler for you in your own work, take the point s at random near the top of your paper, and strike the circle n o p q round it, any size you like. Then the point s is to represent the point opposite which you wish the observer of your picture to place his eve, in looking at it. Call this point the Sight-Point.

II. The Sight-line. - Through the Sight-point, s, draw a horizontal line, G H, right across your paper from side to side, and call this line the Sight-Line.

This line is of great practical use, representing the level of the eye of the observer all through the picture. You will find hereafter that if there is a horizon to be represented in your picture, as of distant sea or plain, this line defines it.

III. The Station-Line. - From s let fall a perpendicular line, S r, to the bottom of the paper, and call this line the Station-Line.

This represents the line on which the observer stands, at a greater or less distance from the picture; and it ought to be imagined as drawn right out from the paper at the point s. Hold your paper upright in front of you, and hold your pencil horizontally, with its point against the point s, as if you wanted to run it through the paper there, and the pencil will represent the direction in which the line s R ought to be drawn. But as all the measurements which we have to set upon this line, and operations which we have to perform with it, are just the same when it is drawn on the paper itself, below s, as they would be if it were represented by a wire in the position of the levelled pencil, and as they are much more easily performed when it is drawn on the paper, it is always in practice, so drawn.

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.

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 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.

Fig. 2.

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 height1 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 or in words: