In this figure we have made use of the devices already set forth in the foregoing figures of steps, &c., such as the side scale on the left of the figure to ascertain the height of the steps, the double lines drawn to the high vanishing point of the inclined plane, and so on; but the principal use of this diagram is to show on the perspective plane, which as it were runs under the stairs, the trace or projection of the flights of steps, the landings and positions of other objects, which will be found very useful in placing figures in a composition of this kind. It will be seen that these underneath measurements, so to speak, are obtained by the half-distance.
Fig. 256.
[ CXLIV]
Winding Stairs in a Square Shaft
Draw square ABCD in parallel perspective. Divide each side into four, and raise verticals from each division. These verticals will mark the positions of the steps on each wall, four in number. From centre O raise vertical OP, around which the steps are to wind. Let AF be the height of each step. Form scale AB, which will give the height of each step according to its position. Thus at mn we find the height at the centre of the square, so if we transfer this measurement to the central line OP and repeat it upwards, say to fourteen, then we have the height of each step on the line where they all meet. Starting then with the first on the right, draw the rectangle gD1f, the height of AF, then draw to the central line go, f1, and 1 1, and thus complete the first step. On DE, measure heights equal to D 1. Draw 2 2 towards central line, and 2n towards point of sight till it meets the second vertical nK. Then draw n2 to centre, and so complete the second step. From 3 draw 3a to third vertical, from 4 to fourth, and so on, thus obtaining the height of each ascending step on the wall to the right, completing them in the same way as numbers 1 and 2, when we come to the sixth step, the other end of which is against the wall opposite to us. Steps 6, 7, 8, 9 are all on this wall, and are therefore equal in height all along, as they are equally distant. Step 10 is turned towards us, and abuts on the wall to our left; its measurement is taken on the scale AB just underneath it, and on the same line to which it is drawn. Step 11 is just over the centre of base mo, and is therefore parallel to it, and its height is mn. The widths of steps 12 and 13 seem gradually to increase as they come towards us, and as they rise above the horizon we begin to see underneath them. Steps 13, 14, 15, 16 are against the wall on this side of the picture, which we may suppose has been removed to show the working of the drawing, or they might be an open flight as we sometimes see in shops and galleries, although in that case they are generally enclosed in a cylindrical shaft.