OBSERVATIONS ON VAULTS.

(Fig. 13.) surfaces cutting vaults vertically. Thelines of intersection are termed Welch groins, roundwhich, in practice, are constructed what are termedWelch arches : upon these arches the superior partsof the vaults are supported. The principle is appli-cable to all forms of vaults, simple or complex, plainor ribbed, Fig. 7* 12. 13. &c.

The angles of a dome, being a convex pyramidalvault (Fig. 16.), are similar to the groins of a groinedvault; or the vault may be considered to be composedof as many similar and equal triangular pieces of acylindrical or cylindroidal vault, as there are sides inthe polygon, Fig. 15. 16. 17. &c.

The simplest rib vault is that which is called ArcDoubleau ; by which is understood a vault where atcertain intervals a concentric arch is supposited, orthe vault itself at certain places is of double or greaterthickness than at others.

The forms of ribs in groined rib vaults (Fig. 18.and 19.) are generated from the curves over the sidesof the plan of the space to be covered. As manyradii as there are to be ribs, are to be drawn from theangles of the plan, until they mutually intersect. Thecurvature of each rib will be an elongation of thegiven semi-curve, in proportion to the intersectedradius over which it is to be vertical, (Fig. 18. and19.)

The forms of rib vaults by ribs of the same curv-ature, are composed of parts of an inverted conoid.The ribs are either continued in these forms untilthey intersect each other (Fig. 20.), or are intersectedwholly, or in part, by a polygon with sides curvinginwards with the curvature of the base of the invertedfigure, and performing the office of a key-stone. This

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