plate V.), by means of flat tints. According to the position of the prism, as shown by its plan (fig. 1), the face a b c d (fig. 4) is parallel to the plane of projection, and therefore entirely in the light. This face should receive a uniform tint either of Indian ink or sepia. When the surface to be tinted happens to be very large, it is advisable to put on a very light tint first, and then to go over the surface a second time with a tint sufficiently dark to give the desired tone to the surface.

The face b g h c being inclined to the plane of projection, as is shown by the line b'g' in the plan (fig. 1), should receive a graduated tint from the line b c to the line g h. This graduality is obtained by laying on a succession of flat tints in the following manner :-First, divide the line b'g' (fig. 1) into equal parts at the points 1', 2′, and from these points project lines upon, and parallel to, the sides of the face b ghe (fig. 4). These lines should be drawn very lightly in pencil, as they merely serve to circumscribe the tints. A greyish tint is then spread over that portion of the face bg hc (fig. 2), between the lines b c and 1, 1. When this is dry, a similar tint is to be laid on, extending over the space comprised within the lines b c and 2, 2 (fig. 3). Lastly, a third tint covering the whole surface b c h g (fig. 4) imparts the desired graduated shade to that side of the prism. The number of tints designed to express such a graduated shade depends upon the size of the surface to be shaded; and the depth of tint must vary according to this number.

As the number of these washes is increased, the whole shade gradually presents a softer appearance, and the lines which border the different tints become less harsh and perceptible. For this reason the foregoing method of representing a shade or graduated tint by washes successively passing over each other is preferable to that sometimes employed, of first covering the whole surface bg he with a faint tint, then putting on a second tint b 2 2 c, followed, lastly, by a narrow wash b 1 1 c; because, in following this process, the outline of each wash remains untouched, and presents, unavoidably, a prominence and harshness which, by the former method, are in a great measure subdued.

The face ad fe is also inclined to the plane of projection, as shown by the line a' e' in the plan (fig. 1); but as it is entirely in the light, it should be covered by a series of much fainter tints than the surface b g h c, which is in the shade, darkening, however, towards the line ef. The gradation of tint is effected in the same way as on the face b g h c.

Let it be proposed to shade a cylinder (fig. 12), by means of flat tints: In shading a cylinder, it will be necessary to consider the difference in the tone proper to be maintained between the part in the light and that in

the shade. It should be remembered that the line of separation between the light and shade a b is determined by the radius O a' (fig. 5), drawn perpendicular to the rays of light R O. That part, therefore, of the cylinder which is in the shade is comprised between the lines a b and c d. This portion, then, should be shaded conformably to the rule previously laid down for treating surfaces in the shade inclined to the plane of projection. All the remaining part of the cylinder which is visible presents itself to the light; but, in consequence of its circular figure, the rays of light form angles varying at every part of its surface, and consequently this surface should receive a graduated tint. In order to represent with effect the rotundity, it will be necessary to determine with precision the part of the surface which is most directly affected by the light. This part, then, is situated about the line e ¿ (fig. 12), in the vertical plane of the ray of light RO (fig. 5). As the visual rays, however, are perpendicular to the vertical plane, and therefore parallel to V O, it follows that the part which appears clearest to the eye will be near this line V O, and may be limited by the line T O, which bisects the angle V OR and the line R O. By projecting the points e' and m', and drawing the lines e i and m n (fig. 12), the surface comprised between these lines will represent the lightest part of the cylinder.

This part should have no tint upon it whatever if the cylinder happen to be polished: a turned iron shaft or a marble column for instance; but if the surface of the cylinder be rough, as in the case of a cast-iron pipe, then a very light tint-considerably lighter than on any other part-may be given it.

Again, let us suppose the half-plan of the cylinder f' m' a' c' (fig. 5), to be divided into any number of equal parts. Indicate these divisions upon the surface of the cylinder by faint pencil lines, and begin the shading by laying a tint over all that part of the cylinder in the shade a c d b (fig. 6). This will at once render evident the light and dark parts of the cylinder. When this is dry, put on a second tint covering the line a b of separation of light and shade, and extending over one division, as shown in fig. 7. A third tint should be spread over this division, and one on each side of it, as in fig. 8. Proceed in this way until the whole of that part of the cylinder which is in the shade is covered. The successive stages of this process may be seen in figs. 9, 10, and 11.

Treat in a similar manner the part feig, and complete the operation by covering the whole surface of the cylinder-excepting only the division emni (fig. 12)-with a very light tint; the cylinder will then assume the appearance presented by fig. 12.

Shading by softened tints.-The great advantage which this method possesses over the one just described, consists in imparting to the shade a much softer appearance; the limitations of the different tints being imperceptible. On the other hand, it is considerably more difficult, requiring longer practice, and greater mastery over the movements of the brush to accomplish it with tolerable precision.

Let it be proposed to shade by this method the segment of the hexagonal pyramid (fig. 8, plate VI.)

The plan of this figure is similar to that of the prism (fig. 4, plate V.) Its position in reference to the light is also the same. Thus the face a b c d should receive a unform flat tint. If, however, it be desired to adhere rigorously to the preceding rules, the tint may be slightly deepened as it approaches the top of the pyramid, seeing that the surface is not quite parallel to the vertical plane.

The face bg hc being inclined and in the shade, should receive a dark tint. The darkest part of this tint is where it meets the line b c, and gradually becomes lighter as it approaches the line g h. To produce this effect, apply a narrow strip of tint to the side b c (fig. 6), and then, qualifying the tint in the brush with a little water, join another strip to this, and finally, by means of another brush moistened with water, soften off this second strip towards the line 1, 1, which may be taken as the limit of the first tint. This is shown in fig. 6.

When the first tint is dry, cover it with a second, which must be similarly treated, and should extend beyond the first up to the line 2, 2 (fig. 7). Proceed in this manner with other tints, until the whole face bg hc is shaded, as presented in fig. 8.

In the same way the face e a df is to be covered, though with a considerably lighter tint, for the rays of light happen to fall upon it almost perpendicularly.

It may be observed, that consistently to carry out the rules we have laid down, the tint on these two faces should be slightly graduated from e a to fd, and from c h to b g. But this exactitude may be disregarded until some proficiency in shading has been acquired.

It is now proposed to shade the cylinder (fig. 4) by means of softened tints. The boundary of each tint being indicated in a manner precisely similar to that shown by fig. 5, plate V., the first strip of tint must cover the line of extreme shade a b, and then be softened off on each side, as shown in fig. 13. Other and successively wider strips of tint are to follow, and receive the same treatment as the one first put on. The results of this process are shown in figs. 2, 3, and 4.