Chap. XXI \.
14-17
every imaginable diversity of figure : there can be no doubt that the Homans practisedthe various methods of groining in concrete adopted after the introduction of pointedarchitecture, with the omission of the rib, although there are several instances of itconcealed in the thickness of their vaults ; the flat tile is found built up in ribs, of whichthere are several remains in the springing of the vaults in the Temple of Peace at Rome .
Circular Faults, with double Groining . — The primitive vault, from whence we commencesetting out the voussoirs, is a semicircle; the others are ellipses formed from its ordinateslines are let fall until they meet the diagonals, as is described in a former diagram ; othersare then drawn at right angles to them, to enable the setting out of the greater vault.The double groin is then drawn to the points of the right lines which cross the centre ofthe figure on the plan, at pleasure; where the perpendiculars are crossed by these groins,they are united at their points by other lines; these show the joints of the stones at thedouble groins. The four first voussoirs are at the side, and above is the vault, and onthe right is the third voussoir, both in perspective.
The stones which composevaults of this description areterminated by both plane andcurved surfaces: some exhibitmerely a point and two surfaces;others, one curved and one flat,the junction or meeting of whichproduces either a circular orelliptical arris common to both :such figures are very difficultto project, and must be con-sidered as cones, which requireseveral points to be laid downfor the curvature forming theirbases. A pyramid with anelliptic or circular base mayserve to facilitate the projectionof a polygon, and advantagewill always be derived from aknowledge of the regular solids,when there is a necessity forsetting out any curved lines,whether vertically or hori-zontally placed. In the workof Le Croix, the “ Complementdes Elemens de Geometrie, ” thebest method for projectingfigures of this kind is laiddown; and their careful studycannot be too strongly recom-mended to those desirous ofarriving at excellence in theart of stone-cutting, which isdecidedly much better under-stood on the Continent than inthis country.
When vaults of large dimensions are to be constructed, there is a considerable saving ofmaterials as well as expense by the engineer making his contract with the proprietors ofthe stone quarry for the delivery of blocks of certain forms and dimensions, for whichpurpose a sketch of the forms of the stones will be required, with the several dimensions ;and after the quarryman has roughed them out, he puts numbers upon them correspondingwith those of the drawing ; each stone being thus dressed somewhat to its intended shape isreduced in weight, and expense of transport is considerably lessened : the numbering uponthe stones should commence with those to be first used, and be regularly proceeded withto the last. Where a series of arches is to be constructed, the voussoirs may all be gotout of the quarry in the same manner, and much of the after labour be dispensed with : nogeneral rule can be given for the dimensions of the various stones to be used, but theblocks should be as large as possible, as the strength of all masonry depends as much uponthe weight as upon the quality of stone ; large and heavy stones with few mortar jointsconstitute the best construction. We have already observed that the Egyptians andPhoenicians used stones of greater size than are to be found in any modern buildings, andour astonishment is naturally excited to the manner in which they were enabled to movethem to the situations in which they are placed: whenever great strength is required, solid
4 z 4
Fig. 2559. circular vaults,