If the section of the moulding be the two sides of right angles, the one vertical, and the other of course horizon tal, it is termed a fillet, band, or corona. A fillet is the smallest rectangular member in any composition of mouldings. Its altitude is generally equal to its projec tion ; its purpose is to separate two principal members, and it is used in all situations under such circumstances. The corona is the principal member of a cornice. The beam or facia is a principal member in an architrave as to height, but its projection is not more than that of a fillet.
In the following descriptions, the projections and heights are always supposed to be given in position to the extremities of the curve.
To describe the torus, Plate CLXXXII. Fig. 1. Let a b be the vertical diameter whence the torus projects ; bisect a b in c ; from c, with the radius c a or c b, de scribe the semicircle b d a, which will be the profile of the torus.
To describe the ovolo, the height and projection being given, Fig. 2. First, let the height and the projection be equal to each other. Draw a b equal to the height, and b cat a right angle with, and equal to, a b, for the pro jection ; then with the radius b a or b c describe the arc a c, which is the contour of the ovolo. But if the pro jection is not equal to the height, but less, as in Fig. 2. draw a b and b c forming a right angle as before, a b being made equal to the height, and b c equal to the projec tion; from the point of recess a, with the height a b, des cribe an arc b d; and from the point c of projection, with the same radius, describe another arc cutting the former at d ; lastly, from d, with the radius d a or d c, describe the arc a c, which is the contour required.
The methods of describing the cavetto, Fig. 3. and 4. are the same as that for describing the ovolo, the one being the same as the other reversed.
To describe the cima-recta, Fig. 5. Join the point of recess a to the point of projection b by the line a b ; bisect a b in c, with the distance b c from the points c b; describe the intersection e, and from the points a c, with the same distance, describe the intersection d; from d, with the distance d a or d c, describe the arc a c ; and from c, with the distance e b or e c, describe the arc b c ; and a c b will be the contour of the cima-recta required. If the curve is required to be made quicker, we have only to use a less radius than that of or c b, in order to de scribe the two portions of its contour.
The same description applies to the cima-rcversa, Fig. 6. by the same letters of reference.
To describe the apophygc, Fig. 7. the projection be ing given. Let a b be the projection, and a c c a line which it is required to touch. Make a c equal a b, and
with the distance ac or a b from the points b and c de scribe the intersection d ; from the point d, with the ra dius d b or d c, describe the arc b c, which is the contour of the apophyge: To describ. the apophyge so as to touch a right line given in position at the point of projection, Fig. 8. Let be be the right line ; and a b the projection of the moulding; draw a c df at a right angle with a b; make c d equal to c b; draw b e perpendicular to b c, and d e perpendicular to c d ; from the point e describe the arc b d, which is the contour of the moulding.
To describe the scotia, Fig. 9. the extremities a and b of the curve being given. From the projecting point b erect b d e, and from the receding point let fall a g c per pendicular to b c, the horizontal of the moulding ; add the half of a c and two-thirds of b c into one length, which set from b to d ; from the centre d, with the dis tance d b, describe the semicircle bf c ; draw the straight line e af, and d gf; from the point g, with the distance g a or gf, describe the arc af: then will of b be the con tour of the scotia required.
To describe an ovolo, the tangent a c at the receding extremity a, and its projection at b being given, Fig. 10. and 11. Draw the vertical line c bd; draw be parallel to c a, and a e parallel to c b ; produce a c to f, making ef equal to e a ; divide e b and b c each into the same number of equal parts; from f, and through the points of division in a b, draw right lines ; also from a, and through each of the divisions in b c, draw another sys tem of lines, and the corresponding intersections of each pair of lines will be as many points in the curve as there are pairs ; then a curve being drawn through the points, will be the greater part of the contour. The remaining part b g may be found in the same manner, hy drawing lines front a through the points in b c instead of f, and drawing lines front b d to f, instead of b c to a. The curve drawn in this manner is a portion of an ellipsis, something greater than the quarter of the whole. The recess of the moulding at its projecting point is denominated the quirk. Fig. 10. is adapted for entablatures; and Fig. 11. having a large projection, to capitals of Doric columns, such as may be seen in the temple of Corinth, and in the Doric portico at Athens. This method, though easy, gives the extremity of the conjugate axis, between the rece ding extremity a, and the point of projection b; but the following method gives the extremity of the shorter axis, where the tangent commences, at the receding extre mity of the contour of the ovolo.