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corresponds with ab on the plan, as do the points E, F, G, H with efgh, from which verticals determine 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

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Fig. 845.

Fig. 846.

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 ed, 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.

Fig. 847.

2472. Fig. 848. will scarcely require a description. It is a geometrical elevation of the

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Doric triglyph and frieze, with the usual accessories. AB gives the boundary of shadow on the femora of the triglyph, AC the boundary of shadow on the light sides of the glyphs, and AD of the shadow of the corona on the frieze.

2473. Fig. 849. is a skeleton representation of a three-quarter column, forming part of an

Fig. 849.

arcade. The abacus is the mere block of material AK. In the plan ab shows the length of the line of shadow AB, and is determined by the vertical bB. In the same way, CD is found by ed and the vertical dD. KG is the representation of kg on the plan, and by a vertical from g the line GH is also determined; H giving also by the horizontal line FH, in which H is already found, the situation of shadow of the point E of the abacus, as also by a vertical from f. LMN are places of the shadow of the column on the impost moulding of the arch, whereof two correspondent points are seen in 1 and n.

2474. The form of shadow of the console in fig. 850. will be seen on inspection to have been found from the lines aa, cc, dd, &c. on the elevation, corresponding with aa, cc, dd, &c. on the section, all which are parallel to the direction of the light, and sufficiently explain themselves.

2475. Fig. 851. is the elevation and section of a hemispherical niche, wherein are shown the shadows cast thereon by the vertical wall in which it is placed. Through the centre O draw DD at right angles to the direction of the light, and from O draw OA parallel to the direction of the light: A will be found the point in the wall casting the longest shadow. Produce AO indefi.. nitely; and from a, the corresponding point in the section to A on the elevation, draw aa', parallel to it, which will cut the surface of the niche in a'. Draw the horizontal line a' a" cutting AO produced in a"", and all will represent in the shadow the point A in the circumference. Take any other

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Fig. 851.

Fig. 850.

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point B in the edge of the niche, and by means of a line drawn therefrom horizontally we have the correspondent point b of B in the section. From B draw in the direction of the light the line Bb" b', cutting DD on the diameter in b'"; transfer the point b"" in the elevation to b in the section, and draw bb' in the direction of the light indefinitely. Then with Bb" as a radius from b as a centre, describe an arc cutting bb' in b'; and from b' draw the horizontal line b' b', cutting Bb" produced in b", and b" will be the point in the shadow corresponding to B in the elevation. To avoid the confusion which

would follow the description of the remainder of the operation, we have not encumbered the diagram with more letters of reference; the lines showing, on inspection, similar applications of the process for all parts of the curve. The fact is, that the whole of the shadow may be completed by taking the line DD as the transverse axis of an ellipsis, and finding the semi-conjugate axis Oa by the means above described, for Da"D is a semi-ellipsis in form, inasmuch as it is the projection of a section of a hemisphere. This example is applicable to the shadow of a cylindrical niche with a hemispherical head. The line NN shows the shadow of the portion of the head, and the remainder is obtained by the mere intersection of lines in the direction of the light from different points to the left of N, of which enough has been already given in the previous examples to make the application intelligible.

2476. Fig. 852. is the representation of a pediment wherein the section A is that of the

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mouldings of the pediment at its apex. In the section, ab drawn from the projection a of the corona in the direction of the light, determines the point b therein, wherefrom the horizontal line intercepted by the line ab in the elevation, also drawn parallel to the direction of the light, gives the point b in the elevation. A line from b, parallel to the inclined sides of the pediment on the left, will give the shadow of the corona on the tympanum on that side, and similarly the line of shadow from b on the right side. cd determines the line of shadow on the frieze, and B is the section of the shadow of the assemblage of mouldings on the right.

2477. In fig. 853. is given the plan, elevation, and section of a square recess, covered with a cylindrical head. The lines AA, BB, CC of the elevation are determined by aa, bb, and cc of the plan; and in the section c'e' is the representation of the line cc of the plan. D, the point at which the direction of the light begins to touch the circular head, is d' in the section.

2478. Fig. 854. is the elevation of an arch, below which is its plan and the shadow cast by it on the plane upon which it stands. AA is shown by aa on the plan, the corresponding points in the rear of the arch being a' a', and a" a" the points in the shadow. In a similar way, by BB corresponding with bb' on the plan the points b"b" are obtained in the shadow.

2479. Fig. 855. is the plan and elevation of the upper part of a house,

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wherein the upper story is occupied by an attic in the centre, against which, on each flank, the sloping roof is terminated. aa on the plan in the direction of the light, produced to intersect the hip at b, gives, by a vertical to B on the elevation, the direction BB of the shadow thereon; and BB cut by AA in the direction of the light, the length BA of the line of shadow, which may, by letting fall the vertical Aa, determine the length aa on the plan. The line of shadow ac is determined by letting fall a vertical from C, where the line of shadow is intercepted by the hip of the roof; and from c the shadow will be found on trial to return as shown in the diagram.

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E

and D on the elevation are found,

Fig. 855.

as seen in previous examples, in ee, and d on the plan, and their shadows at e'e' and d'. 2480. What is called an attic base is given in plan and elevation by fig. 856. The me thod of obtaining the shadows thereof

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in plan and elevation is now to be explained. It is an example which constantly occurs in architectural subjects, and should be well studied and understood. The operations requisite for obtaining a representation of the lines of shadow of the different mouldings in this example depend upon the principles developed in the preceding subsections. The lower portion of the figure exhibits the plan, and the middle portion the elevation of the attic base in question. The uppermost portion of it presents three sections of the mouldings of the base in question cut in three different places parallel to the direction of the light. This last portion of the figure is not absolutely necessary, inasmuch as the profiles in question might have been obtained upon the elevation; but we have preferred keeping it separate to prevent a confusion of subsidiary lines. There is moreover another advantage in thus separating the parts from each other, namely, that of immediately and more distinctly seeing the lines at each selected place, in which the rays of light separate the parts actually in light from those in shadow; and where the student is likely to meet with matters of perplexity, nothing should be left untried to save his time, and, what is often more important, his patience. The mode to be adopted is as follows:

Fig. 856.

Make on the plan any number of sections a'a'a'a', b'b'b'b' in the direction of the light, and draw on the elevation the corresponding sections aaaa, bbbb. LL being the direction of the light, draw parallel thereto tangents to the curves of the convex mouldings, and the boundaries of their shades will be obtained, as will also those of their shadows, by continuing them from such boundaries till they cut the other parts in each section, as will be more especially seen at cc. It will be recollected that in our first mention of the projected representation of the line of light and shadow we found that it was an angle of 54° 44' of the diagonal of a cube. This angle is set out in xyz on the plan. We have therefore another mode of finding the boundaries of shade and shadow on the moulding, by developing the sections a'a'a'a', b'b'b'b', &c., as at A, B, and C, and drawing tangents yz to the convex mouldings for

boundaries of shade thereon, and continuing them, or otherwise, for the other parts, as shown in the diagram.

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mences, a curve line of an elliptical nature connects the points found. If the drawing to be made be on a large scale, it may then be worth the architect's while to increase the number of points wherefrom the shadow is to be projected, so as to produce the greatest possible accuracy in the representation.

2482. The shadows of an Ionic capital are given in fig. 858. The shadow of the volute on the column is obtained by any number of lines AA, BB, CC, &c. from its different

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parts and verticals from their corresponding ones aa, bb, cc, &c. on the plan, and similarly the shadow of the capital on the wall. In this example, as in those immediately preceding, the employment of sectional lines parallel to the direction of the light is again manifest. The use of them is most especially seen in the example of the Corinthian capital which follows. As a general rule, it may be hinted to the student of sciography, that in the difficulties that may occur, they will be most expeditiously and clearly resolved by the use of the sectional lines, whereon we have thought it proper so much to dilate.

2483. The Corinthian capital in fig. 859. will require little more than inspection to understand the construction of its sciography; and all that we think necessary to particu larise are the developed projections A, B, C, D, E, F of the abacus and the leaves, whereon the termination of the shadows at angles of 54° 44', as explained in fig. 856., give their respective depths on the elevation.

There is another method of arriving at the result here exhibited, by drawing sectional lines parallel to the direction of the light through the different parts and leaves of the

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