To describe the ovolo, supposing the extremity of the conjugate axis to be at the point of contact a, Fig. 12. Join a b, which bisect in e, and draw c ef: make aft k perpendicular to the tangent a c, then the point f will be the centre of the ellipsis: draw /Ili parallel to a c ; take the distance f a, and from the point b cross the line fiat ; produce b h to 1, and make f i equal to b 1; then with the semi-transverse fi, and the semi-conjugate fa, de scribe an ellipsis, and the portion of the curve contained between the extremities a and g, will be the contour of the moulding required. This method is recommended as producing the most graceful form of an ovolo, as the lower extremity of the curve hegins at the point of con tact. From the large projection here given, the mould ing is adapted to Doric columns.
To describe the hyperbolical ovolo, as used in Dot ic capitals, the same things being given as before, Fig. 13. Erect adefg perpendicular to the horizon, and draw c d and b e at right angles to a d efg : make e g equal to a e, and e f equal to a d; join bf, divide bf and b c in to the same number of equal parts, and draw lines from g through the divisions of bf, also lines from a through the divisions of b c: Each corresponding pair meeting as before, will give the points in the curve of the hyperbo lical moulding. This is the general form of the ovolos in the capitals of the Grecian Doric.
To describe a scoria, Fig. 14. Join the extremities a and 6 of the moulding; bisect a 6 in c; draw cc d paral lel to the horizon; make cd equal to the recess of the curve, and c e equal to cd ; then with the conjugate dia meters and describe the curve ad 6, which will be the contour of the moulding required.
Fig. 15. represents the form of the annulets as applied in Fig. 13. where the receding parts arc in the tangent at the buttons of the curve of the ovolo.
Fig. 16. represents another kind of aunulet, which has a vertical position. This form is only to be found in the Doric portico at Athens.
Fig. 17. represents a curious Grecian moulding, to be found under coronas.
To diminish the shaft of a column, Plate CLXXXI1I. Fig. I. Let AB he the altitude of the column, and BC the diminution at the upper end of the shaft; divide AB into any number of equal parts, and divide the projection BC into the same number; draw the lines 16, 2d, 3c, &c. at right angles to the altitude ; and draw other lines from the points 1, 2, 3, &c. in BC towards A, to intersect with the former parallel lines at the respective points 6, c, d; then A bcdefC, will be the curve line of the sec tion of the column.
But suppose it were required to give less swell to de: column, as in Fig. 2. Divide All as before, and DC
into two equal parts at D; divide DC into as many equal parts as All; then proceed as in Fig. I. Or thus: sup pose El' to be the axis of the column, EG, EA, the semi diameters at the bottom, and FN, FC, the semi-diame ters at the top ; on AG, as a chord, describe the seg ment AOPG of a circle, proportionably less than a se micircle, as the swell is intended to be less; draw NP parallel to FE; divide the arc GP into any number of equal parts, and divide the altitude EF into the same number of equal parts : through the points of division draw the lines a h, 6 i, c k, d 1, c m, parallel to AG ; also draw G 1 h, 2 f, 3k, 4/, 5 m, PN, perpendicular to A ; then through the points G, 1,, i, k, 1, at, N, draw a curve, which will be the contour required.
To describe the flutes of a column without fillets, Fig. S. Let All, No. I. be the diameter, which bisect in G ; draw AD and BC perpendicular to All, and describe the semicircle A EFB ; draw DC to touch the circle, and DEG and CFG to the centre G ; divide the arc El' into five equal parts, and run the same part on the arcs EA and F13, so that the whole 101 be divided into nine equal parts, and two half parts at each extremity; then the points of division will mark the arris of the flutes. Their concality will be found by an arc described from the summit of an equilateral triangle. The fluting at the upper end of the shaft, shown in the concentric cir cle, is described in the same manner. No. 2. represents the bottom elevation, and No. 3. the top elevation of the shaft, as drawn from the section.
To describe flutes with fillets on the shaft of a column, Fig. 4. Supposing every thing is done as in Fig. 3. be fore the division of the circle. Divide EF into six equal parts, and run the chord upon the arcs EA and F11, each of which will contain it three times, so that the whole send-circumference will be divided into twelve equal parts, the points of division marking the centres of the flutes: divide the chord of one of these small arcs into five equal parts; then with three of these parts as a radius, from each of the aforesaid centres describe a se micircle, which will be that representing the section of the flute. Those of the interior circle, representing the top of the shaft, arc found by drawing the lines to the centre, as appears sufficiently by the figure. No. 2. the elevation of the fluting at the bottom of the shaft, as in the temple of Vesta at Rome. No. 3. the elevation of the fluting, as in the temple of Bacchus at Teos. No. 4. and 5. the common way in which the flutings of columns are terminated at the bottom and top of the shaft.