This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

Let a b (Fig. 97) be the base, and b c the height. Bisect a b at d, and divide a d into 100 equal parts; of these give de 26, ef 18 1/4 1/2,fg 12 1/4, 12 1/4, h i 10 3/4, ij 9 1/2, and the balance, 8 3/4, to ja; divide be into 8 equal parts, and from the points of division draw lines parallel to a b, to meet perpendiculars from the several points of division in a b, at the points o, o, o, etc. Then a curve traced through these points will be the one required.

239. - Small Domes over Stairways: are frequently made elliptical in both plan and section; and as no two of the ribs in one quarter of the dome are alike in form, a method for obtaining the curves may be useful.

Fig. 98.

Fig. 99.

To find the curves for the ribs of an elliptical dome, let abcd (Fig. 98) be the plan of a dome, and ef the seat of one of the ribs. Then take ef for the transverse axis and twice the rise, og, of the dome for the conjugate, and describe (according to Arts. 548, 549, etc.) the semi-ellipse egf, which will be the curve required for the rib egf. The other ribs are found in the same manner.

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