The drawing of most buildings occurring in ordinary practice will
resolve itself into applications of this problem. In general, any
house, or block of houses, presents itself under the main conditions
assumed here in Fig. 54. There will be an angle or corner somewhere
near the spectator, as _AB_; and the level of the eye will usually be
above the base of the building, of which, therefore, the horizontal
upper lines will slope down to the vanishing-points, and the base
lines rise to them. The following practical directions will, however,
meet nearly all cases:—
[Illustration: Fig. 54.]
Let _AB_, Fig. 54., be any important vertical line in the block of
buildings; if it is the side of a street, you may fix upon such a line
at the division between two houses. If its real height, distance,
etc., are given, you will proceed with the accurate construction of
the problem; but usually you will neither know, nor care, exactly how
high the building is, or how far off. In such case draw the line _AB_,
as nearly as you can guess, about the part of the picture it ought to
occupy, and on such a scale as you choose. Divide it into any
convenient number of equal parts, according to the height you presume
it to be. If you suppose it to be twenty feet high, you may divide it
into twenty parts, and let each part stand for a foot; if thirty feet
high, you may divide it into ten parts, and let each part stand for
three feet; if seventy feet high, into fourteen parts, and let each
part stand for five feet; and so on, avoiding thus very minute
divisions till you come to details. Then observe how high your eye
reaches upon this vertical line; suppose, for instance, that it is
thirty feet high and divided into ten parts, and you are standing so
as to raise your head to about six feet above its base, then the
sight-line may be drawn, as in the figure, through the second division
from the ground. If you are standing above the house, draw the
sight-line above _B_; if below the house, below _A_; at such height or
depth as you suppose may be accurate (a yard or two more or less
matters little at ordinary distances, while at great distances
perspective rules become nearly useless, the eye serving you better
than the necessarily imperfect calculation). Then fix your sight-point
and station-point, the latter with proper reference to the scale of
the line _AB_. As you cannot, in all probability, ascertain the exact
direction of the line _AV_ or _BV_, draw the slope _BV_ as it appears
to you, cutting the sight-line in _V_. Thus having fixed one
vanishing-point, the other, and the dividing-points, must be
accurately found by rule; for, as before stated, whether your entire
group of points (vanishing and dividing) falls a little more or less
to the right or left of _S_ does not signify, but the relation of the
points to each other _does_ signify. Then draw the measuring-line
_BG_, either through _A_ or _B_, choosing always the steeper slope of
the two; divide the measuring-line into parts of the same length as
those used on _AB_, and let them stand for the same magnitudes. Thus,
suppose there are two rows of windows in the house front, each window
six feet high by three wide, and separated by intervals of three feet,
both between window and window and between tier and tier; each of the
divisions here standing for three feet, the lines drawn from _BG_ to
the dividing-point _D_ fix the lateral dimensions, and the divisions
on _AB_ the vertical ones. For other magnitudes it would be necessary
to subdivide the parts on the measuring-line, or on _AB_, as required.
The lines which regulate the inner sides or returns of the windows
(_a_, _b_, _c_, etc.) of course are drawn to the vanishing-point of
_BF_ (the other side of the house), if _FBV_ represents a right angle;
if not, their own vanishing-point must be found separately for these
returns. But see Practice on Problem XI.
[Illustration: Fig. 55.]
Interior angles, such as _EBC_, Fig. 55. (suppose the corner of a
room), are to be treated in the same way, each side of the room having
its measurements separately carried to it from the measuring-line. It
may sometimes happen in such cases that we have to carry the
measurement _up_ from the corner _B_, and that the sight-magnitudes
are given us from the length of the line _AB_. For instance, suppose
the room is eighteen feet high, and therefore _AB_ is eighteen feet;
and we have to lay off lengths of six feet on the top of the room
wall, _BC_. Find _D_, the dividing-point of _BC_. Draw a
measuring-line, _BF_, from _B_; and another, _gC_, anywhere above. On
_BF_ lay off _BG_ equal to one third of _AB_, or six feet; and draw
from _D_, through _G_ and _B_, the lines _Gg_, _Bb_, to the upper
measuring-line. Then _gb_ is six feet on that measuring-line. Make
_bc_, _ch_, etc., equal to _bg_; and draw _ce_, _hf_, etc., to _D_,
cutting _BC_ in _e_ and _f_, which mark the required lengths of six
feet each at the top of the wall.