The Theory and Practice of Perspective Part 19

HOW TO DRAW CONCENTRIC CIRCLES

[Ill.u.s.tration: Fig. 178.]

First draw a square with its diagonals (Fig. 178), and from its centre _O_ inscribe a circle; in this circle inscribe a square, and in this again inscribe a second circle, and so on. Through their intersections with the diagonals draw lines to base, and number them 1, 2, 3, 4, &c.; transfer these measurements to the base of the perspective square (Fig.

179), and proceed to construct the circles as before, drawing lines from each point on the base to the point of sight, and drawing the curves through the inter-sections of these lines with the diagonals.

[Ill.u.s.tration: Fig. 179.]

Should it be required to make the circles at equal distances, as for steps for instance, then the geometrical plan should be made accordingly.

Or we may adopt the method shown at Fig. 180, by taking quarter base of both outer and inner square, and finding the measurement _mn_ on each side of _C_, &c.

[Ill.u.s.tration: Fig. 180.]

XCVI

THE ANGLE OF THE DIAMETER OF THE CIRCLE IN ANGULAR AND PARALLEL PERSPECTIVE

The circle, whether in angular or parallel perspective, is always an ellipse. In angular perspective the angle of the circle's diameter varies in accordance with the angle of the square in which it is placed, as in Fig. 181, _cc_ is the diameter of the circle and _ee_ the diameter of the ellipse. In parallel perspective the diameter of the circle always remains horizontal, although the long diameter of the ellipse varies in inclination according to the distance it is from the point of sight, as shown in Fig. 182, in which the third circle is much elongated and distorted, owing to its being outside the angle of vision.

[Ill.u.s.tration: Fig. 181.]

[Ill.u.s.tration: Fig. 182.]

XCVII

HOW TO CORRECT DISPROPORTION IN THE WIDTH OF COLUMNS

[Transcriber's Note: The column referred to as "1" in the text is marked "S" in both Figures.]

The disproportion in the width of columns in Fig. 183 arises from the point of distance being too near the point of sight, or, in other words, taking too wide an angle of vision. It will be seen that column 3 is much wider than column 1.

[Ill.u.s.tration: Fig. 183.]

[Ill.u.s.tration: Fig. 184.]

In our second figure (184) is shown how this defect is remedied, by doubling the distance, or by counting the same distance as half, which is easily effected by drawing the diagonal from _O_ to D, instead of from _A_, as in the other figure, _O_ being at half base. Here the squares lie much more level, and the columns are nearly the same width, showing the advantage of a long distance.

XCVIII

HOW TO DRAW A CIRCLE OVER A CIRCLE OR A CYLINDER

First construct square and circle _ABE_, then draw square _CDF_ with its diagonals. Then find the various points _O_, and from these raise perpendiculars to meet the diagonals of the upper square at points _P_, which, with the other points will be sufficient guides to draw the circle required. This can be applied to towers, columns, &c. The size of the circles can be varied so that the upper portion of a cylinder or column shall be smaller than the lower.

[Ill.u.s.tration: Fig. 185.]

XCIX

TO DRAW A CIRCLE BELOW A GIVEN CIRCLE

Construct the upper square and circle as before, then by means of the vanis.h.i.+ng scale _POV_, which should be made the depth required, drop perpendiculars from the various points marked _O_, obtained by the diagonals, making them the right depth by referring them to the vanis.h.i.+ng scale, as shown in this figure. This can be used for drawing garden fountains, basins, and various architectural objects.

[Ill.u.s.tration: Fig. 186.]

C

APPLICATION OF PREVIOUS PROBLEM

That is, to draw a circle above a circle. In Fig. 187 can be seen how by means of the vanis.h.i.+ng scale at the side we obtain the height of the verticals 1, 2, 3, 4, &c., which determine the direction of the upper circle; and in this second figure, how we resort to the same means to draw circular steps.

[Ill.u.s.tration: Fig. 187.]

[Ill.u.s.tration: Fig. 188.]

CI

DORIC COLUMNS

It is as well for the art student to study the different orders of architecture, whether architect or not, as he frequently has to introduce them into his pictures, and at least must know their proportions, and how columns diminish from base to capital, as shown in this ill.u.s.tration.

[Ill.u.s.tration: Fig. 189.]