1462
THEORY AND PRACTICE OF ENGINEERING.
Boor II.
nation, which should form the arris of the section, and the remainder of the operation isperformed as in the preceding example, that is to say, with the arcs taken from thesection, and on the great circle whose diameter is the diagonal. The voussoir in per-spective is marked with letters corresponding with its position on the plan and elevation.The most convenient method of constructing either entire or segmental spherical vaultsis in horizontal courses : we have only described those constructed in vertical courses, tonotice the difficulties which they produce, as an assistance to those who prefer someexercise for their ingenuity.
Hemispherical Niches are so formed that they may be cut into two equal parts by a verticalplane passing through the centre, which would support themselves independently of eachother, or into four by vertical planes crossing each other at the centre, and each will supportitself. Hemispherical niches may be set out by three different methods: by horizontalcourses forming half circles or courses; by vertical courses, or in the form of a trompe.The niche has the trompillion, indicated by H; it is shown in front in fig. 2627., on plan,fin*. 2628., and profile, fig. 2629. The joints of the voussoir above, tending to the centreof the niche, are indicated by straight lines in fig. 2627., and by curved lines in figs. 2628.
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Fig. 2627. \
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and 2629. . . .
To find the curved projection of these joints, divide the thickness of the wall m fig. 2628.,in which they are comprised, into two or three unequal portions, by lines qr,$t, parallelto the face AC;these lines are ra-dii of the quartersof a circle, whichdivide the surfaceof the niche inelevation intoparts proportion-ate to those of theplan ; thus for thefirst joint a i ofthe elevation,lower the points1 and 2, ■wherethese quarters ofcircles cut thejoints of the pa-rallels, to the axisD C, common tothe two figures;these cut the linesof the plan qr,st,at the points V, 2',which will be twoof those of theprojection curve ofthis joint in plan,and should ter-minate at thepoints a, i, givingfour points bywhich it may betraced, and so onfor the others. Totrace the voussoirsof this niche,moulds may beused for all the
faces and joints, viz. one for the elevation, fig. 2627., which may serve for the two sidesby turning it from right to left; two for the joints, and one for the trompillion. Themoulds for the joints are shown at fig. 2631., placed one over the other, so that the lineindicating the arrises of the returns of the quoins, and the arris of the extracos of thekey, are common to all. As the hollow surface of this niche is supposed to le exactlyspherical, the curves cl, bh , ai, are equal arcs of circles described with the radius AC.Fig. 2630. represents the key, in perspective ; its arrises and principal angles are indicatedby letters corresponding in figs. 2627, 2628, and 2629.
A Niche situated in an Angle _Figs. 2636. and 2637. show the plan and elevation; the
divisions of the voussoirs which tend to the centre I are made on the semicircle abcdefgkof the elevation, the projection of which on the plan is shown by a straight line, with
fig. 26S9.
mt
HEMISPHERICAL HICHES.