The Theory and Practice of Perspective Part 25

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 _aaS_, _bbS_, &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.

[Ill.u.s.tration: 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.

Cx.x.xIV

STAIRS, STEPS, &C.

Having decided upon the incline or angle, such as _CBA_, at which the steps are to be placed, and the height _Bm_ of each step, draw _mn_ to _CB_, which will give the width. Then measure along base _AB_ this width equal to _DB_, which will give that for all the other steps. Obtain length _BF_ of steps, and draw _EF_ parallel to _CB_. These lines will aid in securing the exactness of the figure.

[Ill.u.s.tration: Fig. 243.]

[Ill.u.s.tration: Fig. 244.]

Cx.x.xV

STEPS, FRONT VIEW

In this figure the height of each step is measured on the vertical line _AB_ (this line is sometimes called the line of heights), and their depth is found by diagonals drawn to the point of distance _D_. The rest of the figure explains itself.

[Ill.u.s.tration: Fig. 245.]

Cx.x.xVI

SQUARE STEPS

Draw first step _ABEF_ and its two diagonals. Raise vertical _AH_, and measure thereon the required height of each step, and thus form scale.

Let the second step _CD_ be less all round than the first by _Ao_ or _Bo_. Draw _oC_ till it cuts the diagonal, and proceed to draw the second step, guided by the diagonals and taking its height from the scale as shown. Draw the third step in the same way.

[Ill.u.s.tration: Fig. 246.]

Cx.x.xVII

TO DIVIDE AN INCLINED PLANE INTO EQUAL PARTS--SUCH AS A LADDER PLACED AGAINST A WALL

[Ill.u.s.tration: Fig. 247.]

Divide the vertical _EC_ into the required number of parts, and draw lines from point of sight _S_ through these divisions 1, 2, 3, &c., cutting the line _AC_ at 1, 2, 3, &c. Draw parallels to _AB_, such as _mn_, from _AC_ to _BD_, which will represent the steps of the ladder.

Cx.x.xVIII

STEPS AND THE INCLINED PLANE

[Ill.u.s.tration: Fig. 248.]

In Fig. 248 we treat a flight of steps as if it were an inclined plane.

Draw the first and second steps as in Fig. 245. Then through 1, 2, draw 1V, _AV_ to _V_, the vanis.h.i.+ng point on the vertical line _SV_. These two lines and the corresponding ones at _BV_ will form a kind of vanis.h.i.+ng scale, giving the height of each step as we ascend. It is especially useful when we pa.s.s the horizontal line and we no longer see the upper surface of the step, the scale on the right showing us how to proceed in that case.

In Fig. 249 we have an example of steps ascending and descending. First set out the ground-plan, and find its vanis.h.i.+ng point _S_ (point of sight). Through _S_ draw vertical _BA_, and make _SA_ equal to _SB_. Set out the first step _CD_. Draw _EA_, _CA_, _DA_, and _GA_, for the ascending guiding lines. Complete the steps facing us, at central line _OO_. Then draw guiding line _FB_ for the descending steps (see Rule 8).

[Ill.u.s.tration: Fig. 249.]

Cx.x.xIX

STEPS IN ANGULAR PERSPECTIVE

First draw the base _ABCD_ (Fig. 251) at the required angle by the new method (Fig. 250). Produce _BC_ to the horizon, and thus find vanis.h.i.+ng point _V_. At this point raise vertical _VV_. Construct first step _AB_, refer its height at _B_ to line of heights hI on left, and thus obtain height of step at _A_. Draw lines from _A_ and _F_ to _V_. From _n_ draw diagonal through _O_ to _G_. Raise vertical at _O_ to represent the height of the next step, its height being determined by the scale of heights at the side. From _A_ and _F_ draw lines to _V_, and also similar lines from _B_, which will serve as guiding lines to determine the height of the steps at either end as we raise them to the required number.

[Ill.u.s.tration: Fig. 250.]

[Ill.u.s.tration: Fig. 251.]

CXL

A STEP LADDER AT AN ANGLE

[Ill.u.s.tration: Fig. 252.]