When the diagonal sections alone are used, it is clear that the geometrical profile, No. 2., will not be the same as that formed by the oblique section of the cornice: this last must therefore be obtained from a plan and elevation of the mouldings as shown in No. 3.

2454. Instead of finding the square section made by the plane FNGO at the angle OG, it may be drawn on the plane TQM, where it is more readily found by producing the lines whereby the section TQM was obtained: so the lines TT", MO" are set out in perspective equal to the projection of the break of the building ON: moreover by the line TO" we may obtain the mouldings of the cornice on the face of the wall GH as produced or prolonged to TO", and conversely the cornice in perspective may be drawn from this imaginary section, if it be previously found.

2455. Our next care is to find the vanishing point of the raking mouldings, which may be found from what has already been said, and a perspective section must be made of these mouldings by means of any vertical plane where most convenient; but the best place is through the apex of the pediment, which, as it could not, for want of room, be done in the present example, is taken through the line oo, No. 2., passing through the extreme left angle of the tympanum of the pediment.

2456. As the mouldings of the pediment here are of the same depth and projection as in the horizontal parts, they will not, when inclined, coincide with the diagonal section of the horizontal cornice at OS; hence that section, if found in perspective at OS, cannot be used for drawing the perspective representation of the pediment cornice, except for the bead or fillet above the corona, which, from the construction of the pediment, will coincide at this mitre, as we may see in No. 2.; whence it may also be seen that the point a does not coincide with t. X'r cannot, therefore, in the perspective representation, be drawn through X, the point answering to t in the diagonal section NRX. OO' in the line OH is to be made in perspective equal to mo, No. 2., and the whole depth oo, and those of the several mouldings on the oblique section, being set upon EQ produced, they are to be transferred to OO' by means of the vanishing points. The distance O'I is the perspective distance of the projection qt of the cornice as before, and is most readily obtained from the section O"T", which is transferred to the plane O'I, and will be easily comprehended from the figure, the quantity of projection of each raking moulding of the pediment is equal to that of the same moulding where horizontal. Thus the perspective representation of an oblique section made by a plane passing through oo, No. 2., is obtained, and the mouldings are then drawn to the vanishing point through the various points, the line IX' cutting TX in the point corresponding to x, No. 2. As to the modillions, their representations are found with less confusion by planning them apart and using visual rays; but if no plan is used, the following method, invented by the elder Malton, may be adopted:

2457. Draw BC, the line intersecting the plane of the sofite of the corona, Nos. 2. and 3., through the proper point a in MQ at right angles to it, and draw ay to the vanishing point. Produce the line corresponding to A in No. 3. to A in xy, and transfer A to 1 in BC, so as to be proportional to it in respect of the whole extent. Then set off the proportional widths and intervals of the modillions, as shown on Nos. 2. and 3. on BC, and transfer them by means of the same proportioning point by which z was transferred to 1; and from the points 2, 3, 4, 5, 6, &c. in xy thus obtained, draw on the perspective of the sofite by the use of the vanishing point the lines representing the tops of the modillions corresponding to 2, 3, 4, &c., No. 2. The cymatium round them and the inner angle of the sofite may be drawn by the eye, or where great accuracy is required, the mitre or diagonal sections may be determined as for the principal mouldings already described. At the backs of the modillions the verticals are to be determined either by means of visual rays from a plan, or through the medium of intersections of the perspective lines of the upper parts of them on the sofite, which is as much as can be requisite for guiding us to a correct delineation. The same process is to be used for the modillions on the other

sides.

SECT. III.

SHADOWS.

2458. Sciography, or the doctrines of shadows, is a branch of the science of projection, and some preparation has been made for its introduction here in Sect. VI. Chap. I. (1110, et seq.) on Descriptive Geometry, which, if well understood, will remove all difficulty in comprehending the subject of this section.

2459. The reader will understand that in this work, which is strictly architectural, the only source of light to be considered is the sun, whose rays, owing to his great distance, are apparently parallel and rectilineal. It is moreover to be premised, that such parts of any body as may be immediately opposed to the rays of light are technically said to be in

But when one

light, and the remaining parts of such body are said to be in shade. body stands on or before another, and intercepts the sun's rays from the latter, which is thereby deprived of the action upon it of the rays of light, the part so deprived of the immediate action of the light is said to be in shadow. It seems hardly necessary to observe, that the parts of any body nearest the source of light will be the brightest in appearance, whilst those furthest removed from it will, unless under the action of reflected light, be the darkest.

2460. It has been the practice, in architectural drawings, to represent the shadows of their objects at an angle of forty-five degrees with the horizon, as well on the elevations as on the plans. The practice has this great convenience, namely, that the breadth of the shadow cast will then actually measure the depth of each projecting member which casts it, and the shadowed elevation may be thus made to supply a plan of the external parts of the building. Now, if in the elevation the shadows be cast at an angle of forty-five degrees, it will on a little consideration be manifest, that, being only projections of a more lengthened shadow (for those on the plan are at an angle of forty-five degrees), the actual shadow seen diagonally must be at such an angle as will make its projection equal to forty-five degrees upon the elevation; because all elevations, sections, and plans, being themselves nothing more than projections of the objects they represent, are determined by perpendicular, horizontal, or inclined parallel lines drawn from the points which bound them to the plane of projection, and similarly, a shadow in vertical projection, which forms an angle of forty-five degrees with the horizon, can only be the representation on such projection of an angle, whose measure it is our business now to determine.

2461. In the cube ABCDEFGH (fig. 838.) the line BD, forming an angle of forty-five degrees with the horizon, is a projection or representation of the diagonal AH on the vertical plane ABD; and our object being to find the actual angle AHB, whereof the angle ADB is the projection, we have the following method. Let each side of the cube, for example,

Fig. 838.

D

That is, 10 x 10 + 10 x 10=200= AH2, consequently AH-14.142100. As BAH is a right angle, we have by Trigonometry, using a table of logarithms, As AH (=1414142100) or Ar. Co. Log. 9.8494850 To tangent 45°

So AB (=10-00000000) log.

10.0000000
1.0000000

Hence it follows, that when shadows are projected on the plan as well as on the elevation, at an angle of forty-five degrees, the height of the sun which projects them must be

35° 16'.

2462. It is of the utmost importance to the student to recollect this fact, because it will be hereafter seen that it will give him great facility in obviating difficulty where confusion of lines may lead him astray, being, in fact, not only a check, but an assistance in proving the accuracy of his work.

2463. We now proceed to submit to the student a series of examples, containing the most common cases of shadowing, and which, once well understood, will enable him to execute any other case that may be presented to his notice.

2464. In fig. 839. we have on the left-hand side of the diagram the common astragal fillet and cavetto occurring in the

The

Tuscan and other pilasters, above in
elevation and below in plan.
right-hand part shows the same con-
rected with a wall, whereon a shadow
is cast by the several parts. LL is a
line showing the direction of the light
in projection at an angle of forty-five
degrees. It will on experiment be
found, by a continuation of the line,
or by one parallel to it, to touch the
side of the astragal at a, whence an
horizontal line drawn along it will

L

determine its line of shade. We here again repeat, to prevent misunderstanding, that in the matter we are now attempting to explain we are not dealing with reflected light, nor with the softening off of shadows apparent in convex objects, but are about to

The

determine the mere boundaries of shade and shadow of those under consideration. rest must be learned from observation, for the circumstances under which they are seen must constantly vary. This, however, we think, we may safely state, that if the bound. aries of shade and shadow only be accurately given in a drawing (however complex), the satisfaction they will afford to the spectator will be sufficient, without further refinement. But it is not to be understood from this that we discountenance the refinement of finish in architectural subjects; all that we mean to say is, that it is not necessary. To return to the diagram: it is manifest that if the boundary of shade be at a from that point parallel to the direction of the light a line ab will determine the boundary of shadow on the fillet at b, and that from the lower edge of such fillet at f a line again parallel to the direction of the light will give at c the boundary of the shadow it casts upon the shaft S. As, in the foregoing explanation, a was the upper boundary of shade, so by producing the horizontal line which it gave to a on the right-hand side of the diagram we obtain there a corresponding point whence a line aa' parallel to the direction of the light is to be drawn indefinitely; and on the plan a line aa, also parallel to the direction of the light, cutting the wall WW whereon the shadow is cast at a. From the point last found a vertical line from a, where the shadow cuts the wall on the plan, cutting aa' in a', will determine the point a' in the shadow. The point e, by a line therefrom parallel to the direction of the light, will determine similarly the situation e' by obtaining its relative seat on the diagonal cd, which perhaps will be at once seen by taking the extreme point d of the projection of the astragal, and therefrom drawing dd' parallel to the direction of the light. From the line dd, drawn similarly parallel to the direction of the light, and cutting WW in d, we have the boundary of the shadow on the plan, and from that point a vertical dd being drawn, the boundary of shadow of the extreme projection of the astragal is thus obtained. The boundary of shadow of the fillet on the right-hand side at b, similarly by means of bb, and by the vertical bb', gives the boundary point of the shadow from b. The same operation in respect of ce gives the boundary of shadow from e to c' in the latter point. We have not described this process in a strictly mathematical manner, because our desire is rather to lead the student to think for himself a little in conducting it; but we cannot suppose the matter will not be perfectly understood by him even on a simple inspection of the diagram.

It

2465. In the diagram (fig. 840.) is represented a moulding of common occurrence in architectural subjects, and, as before, the right-hand side is the appearance of its shadow on the wall WW on the plan. will be immediately seen that LL being the projected representation of the rays of light, the line aa determines the boundary of shadow on the ovolo, and that at b, the boundary of its shade, is also given by a line touching that point parallel to the rays, or rather projected rays, of light. On the right-hand side of the figure oo', drawn indefinitely parallel to the direction of the light,

Fig. 840.

W

and determined by a vertical from a", the intersection by a"a" with the wall, will give o'a", the line of shadow of oa'. The line aa determines the shadow on the ovolo, and this continued to a' horizontally gives also a like termination to a" in the shadow; b, the boundary upwards of the ovolo's shade,

cc on the

is represented to the right by b', and
to the right on the plan by b, whence
by a vertical cutting the line b'b" in
b", the boundary of shadow which
b' will cast is obtained.
plan is in projection the distance
of the line of shade c' from the
wall whereon the shadow is cast,
and its place in the shadow is at
c", ee"b" being the length of hori-
zontal shadow produced by the cir-

cumstances.

In fig. 841., which, it will be seen, is a common fillet and cavetto, LL is, as before, the direction of the

L.

Fig. $41.

CHAP. IV.

light, and aa gives the boundary of shadow, as well of the fillet's lower edge as of the lower edge of the cavetto itself. In respect of the right-hand side of the figure, a'a' is a line showing in profile the extent of projection of the fillet before the wall line WW, and from a' a line drawn indefinitely parallel to the direction of the light, and terminated by So is the intersection of a vertical from a' in a", will give the point a' in the shadow. bb found through a vertical from b on the wall, by a line drawn parallel to the direction of the light from b on the plan. The several points being connected by lines, we gain the boundaries of the shadow, wherein a'a"" is represented by a"a".

2466. Fig. 842. exhibits a fillet and cyma reversa or ogee, wherein, as before, LL is the direction of the light at a similar

angle to that used on the plan. From the lower edge of the fillet, parallel to the direction of the light, is obtained the point a on the ogee, and from b a similarly parallel line gives the boundary of shadow in c. A line from o in direction of the light, drawn indefinitely, intercepted by a vertical line from d', its projection on the plan in d determines o'd, the boundary of the shadow of the fillet on the wall WW. cc" is the line of profile of the projecting boundary in elevation, of the shade of the ogee before the wall, whereon its shadow is terminated from c and c"" by a vertical c"" c"". bb', the boundary of shade of the

Fig. 842.

ogee itself, is found in shadow by the line b'b"" drawn indefinitely parallel to the direction of the light, and terminated by a vertical from b', the point on the wall correspondent to b on the plan, the place of the shade's point in the elevation. By the junction of the It is here to lines so found, we shall have the outline of the shades and shadows cast. be observed, that the portion of light a'b' which the moulding retains is represented in the shadow by a"b"", all the other parts of its curved form being hidden, first by the projection of the fillet, and secondly by the line of shade bb", which acts in the same way as the fillet itself in producing the line aa', for the moment the light is intercepted, whether by a straight or curved profile, shadow must follow the shade of the moulding, whatever it be; and this is by the student to be especially observed.

2467. Fig. 843. exhibits the mode of obtaining the shadows and shade in the cyma LL is the direction of the

recta.

light, parallel whereto the line ab determines the line of horizontal shadow cast by the lower edge of the fillet upon the cyma, and ed that of the under part of the cyma itself upon the fillet at d. ce' is the upper boundary of the shade of the cyma, and e the point for determining the shadow of the lower fillet, the points abcd corresponding with abcd on the plan. WW on the right hand is the face of the wall, whereto the lines e'e", d'd", c'c", b'b", and a'a" are drawn parallel to the direction of the light. From e'd"c"b"a" vertical being drawn, cutting the indefinite lines oo', a'a", &c. parallel to the direction of the light in e", d'", c", b", and a", we have the

Fig. 813.

form of the shadow in elevation. The part from b' to c' of the cyma being in light, its shadow will be the curve c'b', wherein, if it be required on a large scale, any number of points may be taken to determine its form by means of correspondent points on the plan as for the parts already described.

2468. Fig. 844. is the plan and elevation of some steps, surrounded by a wall, and P in It will be seen that the line AB the plan is a square pillar standing in front of them.

corresponds with ab on the plan, as do the points E, F, G, H with efgh, from which verticals deter. mine them in the elevation. The projection of the plinth on the lower step is found by KI and a corresponding line and vertical, which, to prevent confusion, is not shown on the plan. The shadow of the square pillar P is found in a similar manner by the line CD corresponding to cd on the plan, the shadows on the steps being also determined by the points L, M, N, O, through the medium of verticals from 1, m, n, o. The left-hand side of the shadow of the pillar is determined in a similar way by the line pq, and QR in the elevation is given by qr in the plan, and is the line representing the back ps of the top of the pillar. It will be observed that we have not described any of the preceding diagrams in a strict way, neither shall we do so in those that follow, presuming that the reader has, from the perusal of the section on Descriptive Geometry acquired sufficient knowledge to follow the several lines.

2469. The fig. 845. is a sort of skeleton plan and elevation of a modillion cornice, but deprived

Fig. 845.

of a corona, so as to show the shadows of the modillions, independent of any connection with other parts of the assemblage. FG, HI, and AB parallel to the direction of the light determine, by means of verticals from d and i, the points of shadows from the correspondent points c, 1, the points D, L, and I, whereof L is the point of shadow of M.

2470. In fig. 846. we approach a little nearer to the form of a modillion cornice. The line EF determines the shadow of the corona, and AB by means of the lines cd, Ik, and the verticals dD, kK, the boundary of the side HL of the modillions. A line also drawn horizontally from B will give the under sides of their shadows. FG is a line representing the shadow of the corona.

2471. Fig. 847. gives the finished modillion, and the lines Aa, Bb, Cc, Dd will determine, by horizontal lines drawn from

them, the shadows which we are seeking. The auxiliary lines, to which no letters are attached, cannot fail of being understood; but if difficulty arise in comprehending them, it will be removed by planning the several points, and therefrom drawing on the plan, to meet what may be called the frieze, vertical lines to intercept those from the correspondent points in the elevation, and the operation will be facilitated, perhaps, by projecting the form of the curved lines (as seen in the figure) whereof the modillion is formed.