4 0 Of N I C H E S.
(4J An elliptical headed Nich, may be form- hz 8. . Divide the Semidiameter z 1 6 , in eighted in the fame Manner, as the preceding ; if Parts, and through them draw the Lines h p, i q,Semi-Ellipsisses are described on the Surfaces of k r, &c. and on the Points 9, 10, n,&V. with
the Thicknesses ; as the Semicircles aforesaid.
To find the long Diameter of the several Semi-El-lipfijfes.
As they diminish from the Base of the Nichto its Zenith •, describe an Ellipsis equal to thePlan, or Face of the Nich ; divide its Heightinto Thicknesses, and drawing Lines through theseveral Points of Divisions, parallel to its longestDiameter, until they meet the Curve of the Front,in the same Manner, as in the preceeding Fig. K;they will be the long Diameters required.
To find their respective semi-Jhort Diameters.
Describe a Quadrant, whose Radius is equal tothe Height of the lemi-elliptical Head of theNich. Divide one of its Sides, into the sameNumber of Parts, as the Number of Thicknessesin the Height. From those Parts or Divisions,draw Ordinates to the Limb ; which are the se-mishort Diameters, respectively proportionate tothe long Diameters before found.
The Heads of Niches are sometimes, formedby Ribs, as Fig. IV, where A is the Plan, andB, the Elevation, of the Ribs, for a semi-circu-lar headed Nich. '
The Mould, by which, these Ribs are made,is the Arch of a Quadrant, as a h, Fig. III ; orthe Arch ah, the half Front of Fig. B. Whenthe Heads of Niches are thus formed, they areeither lath’d or plaister’d within Side, or lin’dwith thin Deal or Wainscot; which last if per-formed in a neat Manner ; has a very good Ef-fect, and may be thus performed.
To cut out the Lining, for the Head of a semicircu-lar Nich. Fig. I. Plate LVIII.
Let the Semicircle h 48, represent the Planof the Head of a semicircular headed Nich, whichdivide in 16 Parts, and through every other Partdraw the Lines A z, B z, C z, LA. makingtheir Lengths B a, &c. equal to the Length ofthe Arch h 4 -, or half the Circumference of theNidi's Head.
Complete the Circle 1 6 b, 4 p, and draw thejjumeter 416, at right Angles to the Diameter
the Radius 97,; 10 q -, 11 r ific. describe Semi-circles, as 0 g 10 w ; nfzv, &c. and divide afourth Part of each, as F 10; /z, &c. into 4equal Parts. On the Point G, with a Radiusequal to the Length of the Arch 0.16, or 1 6w,describe the Arch a 17 b, also with Radius’sthe Lengths of the Arches 16 » ; 16 m 16 I ,
1 6 k •, 16/'; 16 h •, describe the Arches d 18 ce x9/; hiog-, k 21 i, &c. On the Archesah, d c, es, &c. set off one fourth Part of theArches g 10, f z, &c. from the Points, 17, 18,19, &c. to the Points ah-, d c 5 es ; b g\ki\&c. through which, Lines being traced, from thePoint G, to the Points 6 and 7 ; the Part G 6 7.will be an eighth Part compleated. In the fameManner complete the'other 7 Parts, ABC, &c.and when bent into their Places, they will exact-ly complete the Lining of the Head of the Nich,as required.
Note, In very large Niches, the Number ofParts may be encreascd from 8 to 12, 16, 20,&c. at Pleasure.
Fig. II. is the Plan of the Head of a scmi-el-liptical Nich, composed of Ribs for Lath andPlaister, whose Bases are represented by a h c des. The Front of this Nich, is the very fameSemi-Ellipsis, as the Plan a f g. But the seve-ral Ribs, which stand on the Plan to form theHead, are different, as being all Quarter Parts ofEllipsis’s, whose longest Diameters are less ; ex-cepting the Front Rib, that stands over the Base/ h, which is the fourth Part of a Circle, whoseRadius is fh.
To form the Curves of the Ribs, to stand onthe Parts bede, consider their Bases b h, c h, dh,and eh, as half the long Diameters of so manyOvals and s h is half the short Diameter to eve-ry of them in general. Then by the Rule gi-ven in Plate LIV, to describe an oval lar Win-dow of any Breadth and Height; describe theCurves for the several Ribs required ; which areno more than the Quarter Parts of so many com-plete Ovals.
Plate LIX, LX.
Eight Designs for Marble Cisterns, for Buffets,Side Board Tables, &c.
Plate