and work out one of Turner's pictures, or better still,
put his own sketch from nature to the same test.

XXXI

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.

[Illustration: 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 pawn
being about the same height are measured from the fourth line of the
scale marked _C_.

[Illustration: Fig. 84.]

XXXII

APPLICATION OF THE VANISHING SCALE TO DRAWING FIGURES AT AN ANGLE
WHEN THEIR VANISHING POINTS ARE INACCESSIBLE OR OUTSIDE THE PICTURE

This is exemplified in the drawing of a fence (Fig. 84). Form scale
_aS_, _bS_, in accordance with the height of the fence or wall to be
depicted. Let _ao_ represent the direction or angle at which it is
placed, draw _od_ to meet the scale at _d_, at _d_ raise vertical _dc_,
which gives the height of the fence at _oo'_. Draw lines _bo'_, _eo_,
_ao_, &c., and it will be found that all these lines if produced will
meet at the same point on the horizon. To divide the fence into spaces,
divide base line _af_ as required and proceed as already shown.

XXXIII

THE REDUCED DISTANCE. HOW TO PROCEED WHEN THE POINT OF DISTANCE
IS INACCESSIBLE

It has already been shown that too near a point of distance is
objectionable on account of the distortion and disproportion resulting
from it. At the same time, the long distance-point must be some way out
of the picture and therefore inconvenient. The object of the reduced
distance is to bring that point within the picture.

[Illustration: Fig. 85.]

In Fig. 85 we have made the distance nearly twice the length of the base
of the picture, and consequently a long way out of it. Draw _Sa_, _Sb_,
and from _a_ draw _aD_ to point of distance, which cuts _Sb_ at _o_, and
determines the depth of the square _acob_. But we can find that same
point if we take half the base and draw a line from 1/2 base to 1/2
distance. But even this 1/2 dist