The Theory and Practice of Perspective Part 10

HOW TO MEASURE LONG DISTANCES SUCH AS A MILE OR UPWARDS

The wonderful effect of distance in Turner's pictures is not to be achieved by mere measurement, and indeed can only be properly done by studying Nature and drawing her perspective as she presents it to us. At the same time it is useful to be able to test and to set out distances in arranging a composition. This latter, if neglected, often leads to great difficulties and sometimes to repainting.

To show the method of measuring very long distances we have to work with a very small scale to the foot, and in Fig. 94 I have divided the base _AB_ into eleven parts, each part representing 10 feet. First draw _AS_ and _BS_ to point of sight. From _A_ draw _AD_ to distance, and we obtain at 440 on line _BS_ four times the length of _AB_, or 110 feet 4 = 440 feet. Again, taking the whole base and drawing a line from _S_ to 8th distance we obtain eight times 110 feet or 880 feet. If now we use the 16th distance we get sixteen times 110 feet, or 1,760 feet, one-third of a mile; by repeating this process, but by using the base at 1,760, which is the same length in perspective as _AB_, we obtain 3,520 feet, and then again using the base at 3,520 and proceeding in the same way we obtain 5,280 feet, or one mile to the archway. The flags show their heights at their respective distances from the base. By the scale at the side of the picture, _BO_, we can measure any height above or any depth below the perspective plane.

[Ill.u.s.tration: Fig. 94.]

_Note_.--This figure (here much reduced) should be drawn large by the student, so that the numbering, &c., may be made more distinct. Indeed, many of the other figures should be copied large, and worked out with care, as lessons in perspective.

x.x.xIX

FURTHER ILl.u.s.tRATION OF LONG DISTANCES AND EXTENDED VIEWS

An extended view is generally taken from an elevated position, so that the princ.i.p.al part of the landscape lies beneath the perspective plane, as already noted, and we shall presently treat of objects and figures on uneven ground. In the previous figure is shown how we can measure heights and depths to any extent. But when we turn to a drawing by Turner, such as the 'View from Richmond Hill', we feel that the only way to accomplish such perspective as this, is to go and draw it from nature, and even then to use our judgement, as he did, as to how much we may emphasize or even exaggerate certain features.

[Ill.u.s.tration: Fig. 95. Turner's View from Richmond Hill.]

Note in this view the foreground on which the princ.i.p.al figures stand is on a level with the perspective plane, while the river and surrounding park and woods are hundreds of feet below us and stretch away for miles into the distance. The contrasts obtained by this arrangement increase the illusion of s.p.a.ce, and the figures in the foreground give as it were a standard of measurement, and by their contrast to the size of the trees show us how far away those trees are.

XL

HOW TO ASCERTAIN THE RELATIVE HEIGHTS OF FIGURES ON AN INCLINED PLANE

[Ill.u.s.tration: Fig. 96.]

The three figures to the right marked _f_, _g_, _b_ (Fig. 96) are on level ground, and we measure them by the vanis.h.i.+ng scale _aS_, _bS_.

Those to the left, which are repet.i.tions of them, are on an inclined plane, the vanis.h.i.+ng point of which is _S_; by the side of this plane we have placed another vanis.h.i.+ng scale _aS_, _bS_, by which we measure the figures on that incline in the same way as on the level plane. It will be seen that if a horizontal line is drawn from the foot of one of these figures, say _G_, to point _O_ on the edge of the incline, then dropped vertically to _o_, then again carried on to _o_ where the other figure _g_ is, we find it is the same height and also that the other vanis.h.i.+ng scale is the same width at that distance, so that we can work from either one or the other. In the event of the rising ground being uneven we can make use of the scale on the level plane.

XLI

HOW TO FIND THE DISTANCE OF A GIVEN FIGURE OR POINT FROM THE BASE LINE

[Ill.u.s.tration: Fig. 97.]

Let _P_ be the given figure. Form scale _ACS_, _S_ being the point of sight and _D_ the distance. Draw horizontal _do_ through _P_. From _A_ draw diagonal _AD_ to distance point, cutting _do_ in _o_, through _o_ draw _SB_ to base, and we now have a square _AdoB_ on the perspective plane; and as figure _P_ is standing on the far side of that square it must be the distance _AB_, which is one side of it, from the base line--or picture plane. For figures very far away it might be necessary to make use of half-distance.

XLII

HOW TO MEASURE THE HEIGHT OF FIGURES ON UNEVEN GROUND

In previous problems we have drawn figures on level planes, which is easy enough. We have now to represent some above and some below the perspective plane.

[Ill.u.s.tration: Fig. 98.]

Form scale _bS_, _cS_; mark off distances 20 feet, 40 feet, &c. Suppose figure _K_ to be 60 feet off. From point at his feet draw horizontal to meet vertical _On_, which is 60 feet distant. At the point _m_ where this line meets the vertical, measure height _mn_ equal to width of scale at that distance, transfer this to _K_, and you have the required height of the figure in black.

For the figures under the cliff 20 feet below the perspective plane, form scale _FS_, _GS_, making it the same width as the other, namely 5 feet, and proceed in the usual way to find the height of the figures on the sands, which are here supposed to be nearly on a level with the sea, of course making allowance for different heights and various other things.

XLIII

FURTHER ILl.u.s.tRATION OF THE SIZE OF FIGURES AT DIFFERENT DISTANCES AND ON UNEVEN GROUND

[Ill.u.s.tration: Fig. 99.]

Let _ab_ be the height of a figure, say 6 feet. First form scale _aS_, _bS_, the lower line of which, _aS_, is on a level with the base or on the perspective plane. The figure marked _C_ is close to base, the group of three is farther off (24 feet), and 6 feet higher up, so we measure the height on the vanis.h.i.+ng scale and also above it. The two girls carrying fish are still farther off, and about 12 feet below. To tell how far a figure is away, refer its measurements to the vanis.h.i.+ng scale (see Fig. 96).

XLIV

FIGURES ON A DESCENDING PLANE

In this case (Fig. 100) the same rule applies as in the previous problem, but as the road on the left is going down hill, the vanis.h.i.+ng point of the inclined plane is below the horizon at point _S_; _AS_, _BS_ is the vanis.h.i.+ng scale on the level plane; and _AS_, _BS_, that on the incline.

Fig. 101. This is an outline of above figure to show the working more plainly.

Note the wall to the left marked _W_ and the manner in which it appears to drop at certain intervals, its base corresponding with the inclined plane, but the upper lines of each division being made level are drawn to the point of sight, or to their vanis.h.i.+ng point on the horizon; it is important to observe this, as it aids greatly in drawing a road going down hill.

[Ill.u.s.tration: Fig. 100.]

[Ill.u.s.tration: Fig. 101.]

[Ill.u.s.tration: Fig. 102.]