The Theory and Practice of Perspective Part 8

XXVI

THE VANISHING SCALE CAN BE DRAWN TO ANY POINT ON THE HORIZON

From _AB_ (Fig. 77) draw _AO_, _BO_, thus forming the scale, raise vertical _C_. Now form a second scale from _AB_ by drawing _AO BO_, and therein raise vertical _D_ at an equal distance from the base.

First, then, vertical _C_ equals _AB_, and secondly vertical _D_ equals _AB_, therefore _C_ equals _D_, so that either of these scales will measure a given height at a given distance.

[Ill.u.s.tration: Fig. 77.]

(See axioms of geometry.)

[Ill.u.s.tration: Fig. 79. Schoolgirls.]

[Ill.u.s.tration: Fig. 80. Cavaliers.]

XXVII

APPLICATION OF VANISHING SCALES TO DRAWING FIGURES

In this figure we have marked off on a level plain three or four points _a_, _b_, _c_, _d_, to indicate the places where we wish to stand our figures. _AB_ represents their average height, so we have made our scale _AO_, _BO_, accordingly. From each point marked we draw a line parallel to the base till it reaches the scale. From the point where it touches the line _AO_, raise perpendicular as _a_, which gives the height required at that distance, and must be referred back to the figure itself.

[Ill.u.s.tration: Fig. 78.]

XXVIII

HOW TO DETERMINE THE HEIGHTS OF FIGURES ON A LEVEL PLANE

_First Case._

This is but a repet.i.tion of the previous figure, excepting that we have subst.i.tuted these schoolgirls for the vertical lines. If we wish to make some taller than the others, and some shorter, we can easily do so, as must be evident (see Fig. 79).

Note that in this first case the scale is below the horizon, so that we see over the heads of the figures, those nearest to us being the lowest down. That is to say, we are looking on this scene from a slightly raised platform.

_Second Case._

To draw figures at different distances when their heads are above the horizon, or as they would appear to a person sitting on a low seat. The height of the heads varies according to the distance of the figures (Fig. 80).

_Third Case._

How to draw figures when their heads are about the height of the horizon, or as they appear to a person standing on the same level or walking among them.

In this case the heads or the eyes are on a level with the horizon, and we have little necessity for a scale at the side unless it is for the purpose of ascertaining or marking their distances from the base line, and their respective heights, which of course vary; so in all cases allowance must be made for some being taller and some shorter than the scale measurement.

[Ill.u.s.tration: Fig. 81.]

XXIX

THE HORIZON ABOVE THE FIGURES

In this example from De Hoogh the doorway to the left is higher up than the figure of the lady, and the effect seems to me more pleasing and natural for this kind of domestic subject. This delightful painter was not only a master of colour, of sunlight effect, and perfect composition, but also of perspective, and thoroughly understood the charm it gives to a picture, when cunningly introduced, for he makes the spectator feel that he can walk along his pa.s.sages and courtyards. Note that he frequently puts the point of sight quite at the side of his canvas, as at _S_, which gives almost the effect of angular perspective whilst it preserves the flatness and simplicity of parallel or horizontal perspective.

[Ill.u.s.tration: Fig. 82. Courtyard by De Hoogh.]

x.x.x

LANDSCAPE PERSPECTIVE

In an extended view or landscape seen from a height, we have to consider the perspective plane as in a great measure lying above it, reaching from the base of the picture to the horizon; but of course pierced here and there by trees, mountains, buildings, &c. As a rule in such cases, we copy our perspective from nature, and do not trouble ourselves much about mathematical rules. It is as well, however, to know them, so that we may feel sure we are right, as this gives certainty to our touch and enables us to work with freedom. Nor must we, when painting from nature, forget to take into account the effects of atmosphere and the various tones of the different planes of distance, for this makes much of the difference between a good picture and a bad one; being a more subtle quality, it requires a keener artistic sense to discover and depict it.

(See Figs. 95 and 103.)

If the landscape painter wishes to test his knowledge of perspective, let him dissect and work out one of Turner's pictures, or better still, put his own sketch from nature to the same test.

x.x.xI

FIGURES OF DIFFERENT HEIGHTS

THE CHESSBOARD

In this figure the same principle is applied as in the previous one, but the chessmen being of different heights we have to arrange the scale accordingly. First ascertain the exact height of each piece, as _Q_, _K_, _B_, which represent the queen, king, bishop, &c. Refer these dimensions to the scale, as shown at _QKB_, which will give us the perspective measurement of each piece according to the square on which it is placed.

[Ill.u.s.tration: Fig. 83. Chessboard and Men.]

This is shown in the above drawing (Fig. 83) in the case of the white queen and the black queen, &c. The castle, the knight, and the p.a.w.n being about the same height are measured from the fourth line of the scale marked _C_.

[Ill.u.s.tration: Fig. 84.]