N

OF SHADE LINES.

In outline drawings, or drawings which consist simply of the lines employed to indicate the form of the object represented, the roundness, the flatness, or the obliquity of individual surfaces, is not indicated by the lines, although it may generally be inferred from the relation of different views of the same part. The direct significance of an outline drawing may, however, be considerably increased, by strengthening those lines which indicate the contours of surfaces resting in the shadow; and this distinction also improves the general appearance of the drawing. The strong lines, to produce the best effect, ought to be laid upon the sharp edges at the summits of salient angles; but bounding lines for curve surfaces should be drawn finely, and should be but slightly, if at all, strengthened on the

shade side. This distinction assists in contrasting flat and curve surfaces. To understand and apply the shade lines, however, we must know the direction in which the light is supposed to fall upon the object, and thence the locality of the shadows.

It is necessary for the explicitness of the drawing, that firstly, the light be supposed to fall upon the object in parallel lines, that all the parts may

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be shade-lined according to one uniform rule; secondly, that the light should be supposed to fall upon the object obliquely, as in this way both the horizontal and vertical lines may be relieved by shading. To distribute the shadows equally, the light is supposed to fall in directions forming an angle of 45° with both the horizontal and the vertical planes of projection. In general, the light should fall, as it were, from towards the upper lefthand corner of the sheet of paper, supposing it square, making also an angle of 45° with the surface.

To illustrate what has been stated, let a b c d and a' b'e ƒ (figs. 181 and 182) represent the elevation and plan of a solid rectangular body, N O being the ground line. Let the direction of the light in both views be represented in projection by the arrows A B; these lines form the angle 45° with the line N O, and by drawing the parallels at b, d, a', e', so as to embrace the extreme contour, we may readily perceive the way in which the light falls upon the body: it falls upon three faces, namely, the two vertical faces af, fe, and the top a'b'ef. Consequently, the intersections or lines at which these planes meet ought to be lightly drawn, namely, ab, a d; af and fe. Again, the lateral planes represented by b c, c d, b'e', and a' b', are obviously in the shade, as no light falls upon them directly; and these lines are strengthened to express the distinction.

In figs. 183 and 184, the portion of the exterior from 6 by c to d is in the shade, while the rest is light; and the inverse is the case with the inner edges. A peculiarity, however, occurs at d, for here the edges, inner and outer, are parallel to the direction of the light. It is plain that the surfaces which come up to these edges will be in a medium shade, and that the lines at d should be of medium thickness.

Figs. 185 and 186 represent a hollow cylinder in projection. In the plan, two lines, a, c, drawn parallel to the direction of the light, and touching the exterior of the cylinder, define the semicircular outline a b' c, which is thrown in the shade, and ought to be strengthened. The outlines a and care, like the edges at d (fig. 183), parallel to the light, and the contour on each side gradually recedes and advances to the light. The thickness of the line should, therefore, be rather gradually reduced at the points a, c. In the elevation, the base-line df should be shaded, and b d is often halfshaded, as it lies in a curve surface; more generally full-shaded.

If, again, the cylinder be hollow, presenting in plan the interior contour circle eh, then the semicircle e g h expresses the shady side of the interior, the light striking directly upon the oppposite semicircle.

These examples illustrate every case of shade-lining that occurs in outline drawings. The effect is enhanced by proportioning the thickness of

the lines to the depth of the surfaces to which they belong, below the original surfaces from which the shadows.

arise.

In the later French system of shading, the light is supposed, in plan, to strike towards the right hand upper corner, falling, as it were, in front of the objects; but in elevation, towards the right hand and foot of the sheet (figs. 188, 187).

A

Fig. 187.

a

B

It will be observed in the illustrations of this work, that in the tinted drawings, the shadow is thrown according to the French system; that is, the light is supposed to fall on the drawing over the left shoulder at an angle of 45°. But in outline drawings, on account of its greater simplicity, the more usual system of throwing the shade line one way, both in plan and elevation, is adopted.

Fig. 188.

PROJECTIONS OF SIMPLE BODIES.

Projections of a regular hexagonal pyramid (plate I).—It is evident that two distinct geometrical views are necessary to convey a complete idea of the form of the object: an elevation to represent the sides of the body, and to express its height; and a plan of the upper surface, to express the form horizontally.

It is to be observed that this body has an imaginary axis or centre-line, about which the same parts are equally distant; this is an essential characteristic of all symmetrical figures.

Draw a horizontal straight line L T through the centre of the sheet; this line will represent the ground line. Then draw a perpendicular Z Z' to the ground line. For the sake of preserving the symmetry of the drawing, the centres of the lower range of figures are all in the same straight line M N, drawn parallel to the ground line.

Figs. 1, 2.-In delineating the pyramid, it is necessary, in the first place, to construct the plan. The point S', where the line Z Z' intersects the line M N, is to be taken as the centre of the figure, and from this point, with a radius equal to the side of the hexagon which forms the base of the pyramid, describe a circle, cutting M N in A' and D'. From these

points with the same radius, draw four arcs of circles, cutting the primary circle in four points. These six points being joined by straight lines, will form the figure A'B'C' D' E' F', which is the base of the pyramid; and the lines A' D', B' E', and C' F', will represent the projections of its edges fore-shortened as they would appear in the plan. If this operation has been correctly performed, the opposite sides of the hexagon should be parallel to each other and to one of the diagonals; this should be tested by the application of the square or other instrument proper for the purpose.

By the help of the plan obtained as above described, the vertical projection of the pyramid may be easily constructed. Since its base rests upon the horizontal plane, it must be projected vertically upon the ground line; therefore, from each of the angles at A', B', C', and D', raise perpendiculars to that line. The points of intersection, A, B, C, and D, are the true positions of all the angles of the base; and it only remains to determine the height of the pyramid, which is to be set off from the point G to S, and to draw S A, S B, S C, and S D, which are the only edges of the pyramid visible in the elevation. Of these it is to be remarked that SA and S D alone, being parallel to the vertical plane, are seen in their true length; and moreover, that from the assumed position of the solid under examination, the points F' and E' being situated in the lines B B' and C C', the lines S B and S C are each the projections of two edges of the pyramid.

Figs. 3 and 4.-To construct the projections of the same pyramid, having its base set in an inclined position, but with its edges S A and SD still parallel to the vertical plane.

It is evident, that with the exception of the inclination, the vertical projection of this solid is precisely the same as in the preceding example, and it is only necessary to copy fig. 1. For this purpose, after having fixed the position of the point D upon the ground line, draw through this point a straight line D A, making with L T an angle equal to the desired inclination of the base of the pyramid. Then set off the distance D A, fig. 1, from D to A, fig. 3; erect a perpendicular on the centre, and set off G S equal to the height of the pyramid. Transfer also from fig. 1 the distance B G and C G to the corresponding points in fig. 3, and complete the figure by drawing the straight lines A S, BS, CS, and DS.

In constructing the plan of the pyramid in this position, it is to be remarked, that since the edges S A and S D are still parallel to the vertical plane, and the point D remains unaltered, the projection of the point A will still be in the line M N. Its position at A' (fig. 4) is determined by