30

OF DOMES.

land bird. The churches of Saint Genevieve , In-valids, Sorbonne, and Val de Grace, resemble SaintPeter’s in this part of their structure. The vaults inthe naves and transteps of Saint Genevieve have a re-semblance to the vault of Saint Sophia; also those inthe church of Saint Philip of Neri , at Naples, thosein the naves and isles of Saint Paul’s, and thosein the new rooms at the Bank of England .

Cylindrical vaults, crossing a spherical dome, mustintersect it in vertical planes; and the lines of inter-section will be arcs of circles, (Fig. 7- S. 9. 10.) Butit is manifest that the stability of these domes de-pends equally on the abutting cylindrical vaults as onthe piers; and that the pendent domes (Fig. 70 ofSaint Sophia, (Fig. 8 and 9.) of Saint Peter and SaintPaul, could not exist without resistance, as well assupport, from the vaults of the naves. In like man-ner .when hyperbolic vaults cross a cone, (Fig. 14.)The lines of intersection are hyperbolas, and in ver-tical planes, and the pendent cone must be supportedand resisted by the crossing vaults. 9

This is not the case when an ellipse, or other curve,crosses a dome; for then Welch arches must be con-structed in the pendent dome, which discharge thethrust wholly on the piers (Fig. 12.), and render itindependent, and it can stand alone. Sir ChristopherWren has either availed himself of this principle inthe transverse crossing vault of the naves, to dis-charge the thrust of the small domes from the upperwalls (Fig. 11.), or a necessary proximity of the piersreduced him to this expedient. Whatever vaultscross a cylindrical or cylindroidal vault of greaterheight (Fig , 13.), Welch arches necessarily are con-