317. - Roman Mouldings: are composed of parts of circles, and have, therefore, less beauty of form than the Grecian. The bead and torus are of the form of the semicircle, and the scotia, also, in some instances; but the latter is often composed of two quadrants, having different radii, as at Figs. 206 and 207, which resemble the elliptical curve. The ovolo and cavetto are generally a quadrant, but often less. When they are less, as at Fig. 210, the centre is found thus: join the extremities, a and b, and bisect a b in c; from c, and at right angles to a b, draw c d, cutting a level line drawn from a in d; then d will be the centre. This moulding projects less than its height. When the projection is more than the height, as at Fig. 212, extend the line from c until it cuts a perpendicular drawn from a, as at d; and that will be the centre of the curve. In a similar manner, the centres are found for the mouldings at Figs. 207, 211, 213, 216, 217, 218, and 219. The centres for the curves at Figs. 220 and 221 are found thus: bisect the line a b at c; upon a, c and b successively, with a c or cb for radius, describe arcs intersecting at d and d; then those intersections will be the centres.
318. - Modern Mouldings: are represented in Figs. 222 to 229. They have been quite extensively and successfully used in inside finishing. Fig. 222 is appropriate for a bed-moulding under a low projecting shelf, and is frequently used under mantel-shelves. The tangent i h is found thus: bisect the line ab at c, and be at d; from d draw de at right angles to eb; from b draw bf parallel to ed; upon b, with b d for radius, describe the arc df; divide this arc into 7 equal parts, and set one of the parts from s, the limit of the projection, to o; make o h equal to o e; from k, through e, draw the tangent hi; divide bh, he, e i, and ia each into a like number of equal parts, and draw the intersecting lines as directed at Art. 521. If a bolder form is desired, draw the tangent, i h, nearer horizontal, and describe an elliptic curve as shown in Figs. 191 and 224. Fig. 223 is much used on base, or skirting, of rooms, and in deep panelling. The curve is found in the same manner as that of Fig. 222. In this case, however, where the moulding has so little projection in comparison with its height, the point e being found as in the last figure, h s may be made equal to s e, instead of o e as in the last figure. Fig. 224 is appropriate for a crown moulding of a cornice. In this figure the height and projection are given; the direction of the diameter, ab, drawn through the middle of the diagonal, e f is taken at pleasure; and dc is parallel to ae. To find the length of dc, draw b h at right angles to ab; upon 0, with of for radius, describe the arc, fh, cutting bh in h; then make oc and od each equal to b h* To draw the curve, see note to Art. 551. Figs. 225 to 229 are peculiarly distinct from ancient mouldings, being composed principally of straight lines; the few curves they possess are quite short and quick.
Figs. 230 and 231 are designs for antae caps. The diameter of the antae is divided into 20 equal parts, and the height and projection of the members are regulated in accordance with those parts, as denoted under H and P, height and projection. The projection is measured from the middle of the antae. These will be found appropriate for porticos, doorways, mantelpieces, door and window trimmings, etc. The height of the antae for mantelpieces should be from 5 to 6 diameters, having an entablature of from 2 to 2 1/4 diameters. This is a good proportion, it being similar to the Doric order. But for a portico these proportions are much too heavy: an antae 15 diameters high and an entablature of 3 diameters will have a better appearance.
* The manner of ascertaining the length of the conjugate diameter, dc, in this figure, and also in Figs. 191, 241, and 242 is new, and is important in this application. It is founded upon well-known mathematical principles, viz.: All the parallelograms that may be circumscribed about an ellipsis are equal to one another, and consequently any one is equal to the rectangle of the two axes. And again: The sum of the squares of every pair of conjugate diameters is equal to the sum of the squares of the two axes.