ch 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.

[Illustration: Fig. 257.]

[Illustration: Fig. 258.]

CXLV

WINDING STAIRS IN A CYLINDRICAL SHAFT

First draw the circular base _CD_. Divide the circumference into equal
parts, according to the number of steps in a complete round, say twelve.
Form scale _ASF_ and the larger scale _ASB_, on which is shown the
perspective measurements of the steps according to their positions;
raise verticals such as _ef_, _Gh_, &c. From divisions on circumference
measure out the central line _OP_, as in the other figure, and find the
heights of the steps 1, 2, 3, 4, &c., by the corresponding numbers in
the large scale to the left; then proceed in much the same way as in the
previous figure. Note the central column _OP_ cuts off a small portion
of the steps at that end.

In ordinary cases only a small portion of a winding staircase is
actually seen, as in this sketch.

[Illustration: Fig. 259. Sketch of Courtyard in Tol