the diagonal _AC_.

[Illustration: Fig. 238.]

Figure 238, which is practically the same as the preceding only
differently shaded, is drawn in the following manner. Draw arch _EGF_
facing us, and proceed with the rest of the corridor, but first finding
the flat ceiling above the square on the ground _ABcd_. Draw diagonals
_ac_, _bd_, and the curves pending from them. But we no longer see the
clear arch as in the other drawing, for the spaces between the curves
are filled in and arched across.

CXXXI

A CLOISTER, FROM A PHOTOGRAPH

This drawing of a cloister from a photograph shows the correctness of
our perspective, and the manner of applying it to practical work.

[Illustration: Fig. 239.]

CXXXII

THE LOW OR ELLIPTICAL ARCH

Let _AB_ be the span of the arch and _Oh_ its height. From centre _O_,
with _OA_, or half the span, for radius, describe outer semicircle. From
same centre and _oh_ for radius describe the inner semicircle. Divide
outer circle into a convenient number of parts, 1, 2, 3, &c., to which
draw radii from centre _O_. From each division drop perpendiculars.
Where the radii intersect the inner circle, as at _gkmo_, draw
horizontals _op_, _mn_, _kj_, &c., and through their intersections with
the perpendiculars _f_, _j_, _n_, _p_, draw the curve of the flattened
arch. Transfer this to the lower figure, and proceed to draw the tunnel.
Note how the vanishing scale is formed on either side by horizontals
_ba_, _fe_, &c., which enable us to make the distant arches similar to
the near ones.

[Illustration: Fig. 240.]

[Illustration: Fig. 241.]

CXXXIII

OPENING OR ARCHED WINDOW IN A VAULT

First draw the vault _AEB_. To introduce the window _K_, the upper part
of which follows the form of the vault, we first decide on its width,
which is _mn_, and its height from floor _Ba_. On line _Ba_ at the side
of the arch form scales _aa'S_, _bb'S_, &c. Raise the semicircular arch
_K_, shown by a dotted line. The scale at the side will give the lengths
_aa'_, _bb'_, &c., from different parts of this dotted arch to
corresponding points in the curved archway or window required.

[Illustration: Fig. 242.]

Note that to obtain the width of the window _K_ we have used the
diagonals on the floor and width _m n_ on base. This method of
measurement is explained at Fig. 144, and is of ready application in a
case of this kind.

CXXXIV

STAIRS, STEPS, &C.

Having