When an arch is formed by the intersection of a cylin dric vault with a spheric vault, and the spheric portion being of gecatel height than the cy lindrie portion, the loch is called a sphero-cylindrie arch.
When an arch is formed by the intersection of a cylin dric %atilt with a spheric Ninth, and the spheric portion is of less altitude than the cylindric portion, it is called a cylindro-spherie arch.
'When one conic vault pierces another of greater alti tude, the arch funned by the intersection is called a collo conic arch.
Ilistory Qf Groins.
The invention of groins must have been subsequent to that of simple vaulting, and has probably originated from arched passages, when it was necessary to occupy the whole height. At what time they were first introduced in architecture is uncertain : the remains of antiquity slim that they are of very remote date, which, however, cannot be traced beyond the times of Roman power and grandeur. Use or necessity was no doubt the occasion of their invention ; but in process of time they were used as ornaments, and became fashionable at the decline of the empire. They arc to he found in the amphitheatre at Rome, formed at the intersections of the radiating and elliptic passages. In the temple of Peace, and baths of Dioclesian, at the same place, instead of massive piers, they are supported upon columns, the most feeble of all supports, and which would be incapable to resist the lateral pressure of the arches, were it not for the auxiliary support of the walls immediately behind them at the sides and angles of the building.
Groins continued to be used at the declioc of the Roman empire in ecclesiastic structures ; and where ever grandeur or decoration was required, they were never omitted. They became the most principal orna ment of the times, and formed the most conspicuous features in the edifices in which they were employed. At first they were used in the same manner as by the Romans.
In after times the groins were supported upon ribs which sprung from cylindrical or polygonal pillars, with capitals of the same form. This produced a necessary change in the figure of the vaulting, as the bottom of the ribs rise from the circumference of a circle, instead of the angles of a square, with its sides parallel to the walls ; and as the spaces between and over the ribs were vaulted in a twisted or winding surface, so as to coincide in every part with a straight line, level between the ribs; the angles of the groined surface were thus very obtuse at the bottom, but diminished continually upwards, and ended in a right angle, at the summit of the ceiling. Afterwards, when the pillars were formed
upon a square plan, diagonally placed with regard to the sloes of the bnitding, and decorated with vertical mould ings, or small attached columns, and the number of ribs increased, tile lirst idea of fan work would be presented at the of the ribs. But in this the architects would soon perceive an incongruity of form in the sur face : as it approactied the summit of the vaulting, the ribs would be formed all of equal radii, and disposed around to support a concavity which might be generated by revolving a curve round an axis which was in the centre of the pillars ; and being accustom( d to groins meeting in lines crossing each Other, it was n. on al to suppose they would at first permit the ribs to run Out and meet each other, which would then be of unequal maths. If the difference between the openings wan not %try gal at,lhe lines thus formed, by the meeting of the opposite sides of the x;. lilting, would not differ materially from straight lines, but would not be parallel to the horizon, as they would run upward:, towards the centre of the groin ; lint this would dcplIgi oil the angle forint d by tit o opposite ribs in the same plane. Tilos if tie, tatlpylitS ZA. the vertex of the opposite curves an angle of 120 degrees, the apex line on the ceiling would form a curve, in receding from the vertical angles of said ribs, of a very decided convexity ; but ill going progressiNely forward, toe cur vature would change into a concavity, and then would begin again to descend. The idea of mute rseetiog the ribs thus disposed in vertical planes around a common axis, by circular horizontal ribs, waa natural ; and tl.is again would generate another idea, of supporting the upper ends of the ribs by a circular ritaa, concentric with the axis of a pillar ; and thus being done f•ifin four pillars, would leave a space inclosed by our convex arcs of circles. Nothing farther was 'Aaiun cd to com plete this system of vaulting than to lid up the spare, and the whole would be keyed together. In this man ner, by slow and imperceptible changes, a species of vaulting was invented very different from that of the Greeks and llomans. Instead of clo,ing the space, if Ave suppose another ring forming a complete circum ference to he built interiorly to touch the former arcs, and the four triangular curved spaces closed and wedged together with masonry, the whole will stand equally firm as if the middle had been solid ; and thus an aperture for light will be formed the same as in dome vaulting.