MOO

THEORY AND PRACTICE OF ENGINEERING.

Book II.

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dicated by the angles made with the arcs taken on projection. If, according to these line9and those traced on the two straight joints with the mould 5 b, c 6, the stone which iswithout be levelled, using the rule, for the joints 6 c, 5 b, and cutting out the convexparts for the arcs 5, 6, and b,c of the profile, the voussoir will be indicated with correctness.

Fig. 2619. represents the section andhorizontal projection of a spherical vault,the courses of voussoirs of which formin elevation vertical arches, and on theplans open squares inscribed in eachother, like the vault of an arc de cloitreon a square plan; this arrangementpresents at the bottom four niches form-ing together a square.

This is appropriate for niches instraight walls, but objectionable when ap-plied to a spherical vault, on account of the triangularvoussoirsrequired by the union of the four vaulted parts of niches;those parts which rest on acute and fragile angles aremore difficult in execution, and less solid, than where thecourses are arranged horizontally, because the parts are notso well bonded together, and occasion a thrust which tendsto spread outwards.

In fig. 2619., B, C, D, show the moulds for the stones ofthe soffite which are applicable to this arrangement, it beingunderstood that the surface of each course is formed by aportion of a truncated cone, the axes of which are perpen-dicular to the centre of the lines, expressing in plan theprojection of these slices of a cone; whence itresults that each of the hollow squares consistsof four parts ofsimilar cones, theaxes of which crossin the centre, andmeet at the diagonalsof these squares. As/ the direction of thesesurfaces in a rightline is to the summitof each cone, that o.the parts which uniteon the diagonal tend-ing to two differentpoints should form an angle, whichprevents the development of thesoffites, corresponding to the angle ofa single piece, that is to say, thosetriangular parts which are at the com-mencement in the angles.

A, fig. 2619.., represents the voussoirjoining the key in perspective: the joints answering to the lines of the plan, which arevertical, may be traced on the contiguous face of the prism with a square base, in whichthis voussoir is comprised, with the mould taken from the section.

For the voussoirs of the lower angles a stone must be selected large enough to hollowout a segment of a sphere, capable of containing the soffite of the voussoir, and somethingmore, for the projection, as shown in fig. 2620. ; it is then only required to cut out thestone, according to the figure of the soffite traced with curves, and to form the joints withbevels, which give the angles of the soffites, with the sections, and which should all tend tothe centre of the sphere: this method consumes more stone, but it is more simple and

Fig. 2619

Fig. 2629.

accurate.

Vaults formed of a portion of an hemisphere , where the Plan is a Square , constructed in hori -zontai Courses, agreeing with the preceding examples in every other particular, exceptingin the addition of the pendentives; it Is the portion of a sphere whose diameter is thediagonal of a square; the parts cut off by the walls form semicircles on their interiorsurfaces, whose diameter is equal to the inner length of the walls; the section of a sphereby any plane is always a circle.

In the section the arc N I is a portion of a semicircle described with the semi-diagonalCE. The quarter circle AD indicates the re-entering arm formed by the intersection of