The Theory and Practice of Perspective Part 26

First draw the ground-plan _G_ at the required angle, using vanis.h.i.+ng and measuring points. Find the height _hH_, and width at top _HH_, and draw the sides _HA_ and _HE_. Note that _AE_ is wider than _HH_, and also that the back legs are not at the same angle as the front ones, and that they overlap them. From _E_ raise vertical _EF_, and divide into as many parts as you require rounds to the ladder. From these divisions draw lines 1 1, 2 2, &c., towards the other vanis.h.i.+ng point (not in the picture), but having obtained their direction from the ground-plan in perspective at line _Ee_, you may set up a second vertical _ef_ at any point on _Ee_ and divide it into the same number of parts, which will be in proportion to those on _EF_, and you will obtain the same result by drawing lines from the divisions on _EF_ to those on _ef_ as in drawing them to the vanis.h.i.+ng point.

CXLI

SQUARE STEPS PLACED OVER EACH OTHER

[Ill.u.s.tration: Fig. 253.]

This figure shows the other method of drawing steps, which is simple enough if we have sufficient room for our vanis.h.i.+ng points.

The manner of working it is shown at Fig. 124.

CXLII

STEPS AND A DOUBLE CROSS DRAWN BY MEANS OF DIAGONALS AND ONE VANIs.h.i.+NG POINT

Although in this figure we have taken a longer distance-point than in the previous one, we are able to draw it all within the page.

[Ill.u.s.tration: Fig. 254.]

Begin by setting out the square base at the angle required. Find point _G_ by means of diagonals, and produce _AB_ to _V_, &c. Mark height of step _Ao_, and proceed to draw the steps as already shown. Then by the diagonals and measurements on base draw the second step and the square inside it on which to stand the foot of the cross. To draw the cross, raise verticals from the four corners of its base, and a line _K_ from its centre. Through any point on this central line, if we draw a diagonal from point _G_ we cut the two opposite verticals of the shaft at _mn_ (see Fig. 255), and by means of the vanis.h.i.+ng point _V_ we cut the other two verticals at the opposite corners and thus obtain the four points through which to draw the other sides of the square, which go to the distant or inaccessible vanis.h.i.+ng point. It will be seen by carefully examining the figure that by this means we are enabled to draw the double cross standing on its steps.

[Ill.u.s.tration: Fig. 255.]

[Ill.u.s.tration: Fig. 256.]

CXLIII

A STAIRCASE LEADING TO A GALLERY

In this figure we have made use of the devices already set forth in the foregoing figures of steps, &c., such as the side scale on the left of the figure to ascertain the height of the steps, the double lines drawn to the high vanis.h.i.+ng point of the inclined plane, and so on; but the princ.i.p.al use of this diagram is to show on the perspective plane, which as it were runs under the stairs, the trace or projection of the flights of steps, the landings and positions of other objects, which will be found very useful in placing figures in a composition of this kind.

It will be seen that these underneath measurements, so to speak, are obtained by the half-distance.

CXLIV

WINDING STAIRS IN A SQUARE SHAFT

Draw square _ABCD_ in parallel perspective. Divide each side into four, and raise verticals from each division. These verticals will mark the positions of the steps on each wall, four in number. From centre _O_ raise vertical _OP_, around which the steps are to wind. Let _AF_ be the height of each step. Form scale _AB_, which will give the height of each step according to its position. Thus at _mn_ we find the height at the centre of the square, so if we transfer this measurement to the central line _OP_ and repeat it upwards, say to fourteen, then we have the height of each step on the line where they all meet. Starting then with the first on the right, draw the rectangle _gD1f_, the height of _AF_, then draw to the central line _go_, f1, and 1 1, and thus complete the first step. On _DE_, measure heights equal to _D 1_. Draw 2 2 towards central line, and 2n towards point of sight till it meets the second vertical _nK_. Then draw n2 to centre, and so complete the second step. From 3 draw 3a to third vertical, from 4 to fourth, and so on, thus obtaining the height of each ascending step on the wall to the right, completing them in the same way as numbers 1 and 2, when we come to the sixth step, the other end of which is against the wall opposite to us. Steps 6, 7, 8, 9 are all on this wall, and are therefore equal in height all along, as they are equally distant. Step 10 is turned towards us, and abuts on the wall to our left; its measurement is taken on the scale _AB_ just underneath it, and on the same line to which it is drawn. Step 11 is just over the centre of base _mo_, and is therefore parallel to it, and its height is _mn_. The widths of steps 12 and 13 seem gradually to increase as they come towards us, and as they rise above the horizon we begin to see underneath them. Steps 13, 14, 15, 16 are against the wall on this side of the picture, which we may suppose has been removed to show the working of the drawing, or they might be an open flight as we sometimes see in shops and galleries, although in that case they are generally enclosed in a cylindrical shaft.

[Ill.u.s.tration: Fig. 257.]

[Ill.u.s.tration: Fig. 258.]

CXLV

WINDING STAIRS IN A CYLINDRICAL SHAFT

First draw the circular base _CD_. Divide the circ.u.mference into equal parts, according to the number of steps in a complete round, say twelve.

Form scale _ASF_ and the larger scale _ASB_, on which is shown the perspective measurements of the steps according to their positions; raise verticals such as _ef_, _Gh_, &c. From divisions on circ.u.mference measure out the central line _OP_, as in the other figure, and find the heights of the steps 1, 2, 3, 4, &c., by the corresponding numbers in the large scale to the left; then proceed in much the same way as in the previous figure. Note the central column _OP_ cuts off a small portion of the steps at that end.

In ordinary cases only a small portion of a winding staircase is actually seen, as in this sketch.

[Ill.u.s.tration: Fig. 259. Sketch of Courtyard in Toledo.]

CXLVI

OF THE CYLINDRICAL PICTURE OR DIORAMA

[Ill.u.s.tration: Fig. 260.]

Although illusion is by no means the highest form of art, there is no picture painted on a flat surface that gives such a wonderful appearance of truth as that painted on a cylindrical canvas, such as those panoramas of 'Paris during the Siege', exhibited some years ago; 'The Battle of Trafalgar', only lately shown at Earl's Court; and many others. In these pictures the spectator is in the centre of a cylinder, and although he turns round to look at the scene the point of sight is always in front of him, or nearly so. I believe on the canvas these points are from 12 to 16 feet apart.

The reason of this look of truth may be explained thus. If we place three globes of equal size in a straight line, and trace their apparent widths on to a straight transparent plane, those at the sides, as _a_ and _b_, will appear much wider than the centre one at _c_. Whereas, if we trace them on a semicircular gla.s.s they will appear very nearly equal and, of the three, the central one _c_ will be rather the largest, as may be seen by this figure.

We must remember that, in the first case, when we are looking at a globe or a circle, the visual rays form a cone, with a globe at its base. If these three cones are intersected by a straight gla.s.s _GG_, and looked at from point _S_, the intersection of _C_ will be a circle, as the cone is cut straight across. The other two being intersected at an angle, will each be an ellipse. At the same time, if we look at them from the station point, with one eye only, then the three globes (or tracings of them) will appear equal and perfectly round.

Of course the cylindrical canvas is necessary for panoramas; but we have, as a rule, to paint our pictures and wall-decorations on flat surfaces, and therefore must adapt our work to these conditions.

In all cases the artist must exercise his own judgement both in the arrangement of his design and the execution of the work, for there is perspective even in the touch--a painting to be looked at from a distance requires a bold and broad handling; in small cabinet pictures that we live with in our own rooms we look for the exquisite workmans.h.i.+p of the best masters.

BOOK FOURTH