When the portion of a sphere, or cupo la, springs from a wall on a polygonal plan, and the vertical axis of the sphere passes through the middle of the plan, then the spandrels, or triangular spheric partials, comprehended between the springing lines and a horizontal plane passing through the different summits of the walls, are called pendentives.
When two or more plain vaults pene trate or intersect each other, the figure ofthe inwados formed by the severalbran dies is called a groin, or cross vault.
When two opposite equal branches meet other tu-o opposite equal branches in two intersecting vertical planes, pass ing through the diagonal lines, joining the four exterior angles of the plane, the groin may be called an equal pitched quadrilateral groin.
If two opposite branches of an equal pitched grain have cylindrical intradoes, and their 'plan of less breadth than that of the other two branches, the groin may be called cylindro-cylindroiclal, or cylin droido cylindric groin, accorcling as the cylindric branches or the other two are of the greatest breadth.
When a groin consisting of four bran ches is made by two equal portions of' cylindric surfaces, with the axis of the one cutting that of the other, it is called an equal pitched cylindric groin.
When two opposite branches of a cylin dric g-roin are of less breadth than the other two, it may be called an unequal pitched cylindric groin. This is called by workmen a Welsh groin.
When the branches of a cylindric groin are of equal breadth in the plan, the groin may be called an equilateral cylindric It is not easy to give a geometrical de finition that will extend to all properties of vaulting, called, by writers of the first eminence, groins. The first given is al most universal. It applies not only to plain vaults intersecting- each other, but also to those that are annular, or in the form of semi-cylindric rings, intersected by cylindric or cylindroidal plain vaults, the axis of which tends to that of the an !lulus. It does not, however, comprehend that species used in King Henry I'll's chapel, IVestminster, and King's College chapel, Cambridge.
This species of groins, instead of the horizontal sections of the curved surfaces presenting exterior right angles, as 1H ge nerally the case, present convex arches of circles. There is yet one property that is coinmon to every species of groins, that is, the several branches intersect and form arches upon each inclosing wall, and the perpendicular surface of thc wall upon each side is continued till it is inter cepted by the intradoes of the arches; consequently the upright of each wall is equal in height to the summit of the arch es. Hence the difference between groins and domes. A groin is a branched vault, and each branch terminates against the enclosing walls ; whereas a dome is a vault without branches, and the curves spring from the wall, or walls, from all points around its bottom circumference, whether the walls stand upon a polygonal, circular, or elliptic plan.
The Greeks, it would appear, had few or no arches or vaults much prior to the reign of Augustus, from which time they sometimes employed plain vaults with cylindrical intradoes ; we Aso find that they used quadrilateral, equal pitched grouted vaults, with cylindrical or cylin droidal intrad.oes, or mixed of both, over the pa.ssages of the theatres and gym nasia.
The Romans, as would appear also, did not empoly vaults more early than the Greeks. The Pantheon, one ofthe earli est remaining- structures with arches, wa.s praably built by Agrippa, the son-in-law of Augustus, thoug-11 some maintain that he only added the portico ; but of this there is no proof, as no mention is made of this celebrated building b efore his time.
We find from l'itruvius (lib. iii. c. 3,) that the floors of temples were frequently sup. ported by vaults, and (lib. v. c. I,) that the roofs of basilicas were vaulted of the tortoise form, which be distinguishes by the name of testudo. This form of vault ing is very flat, with four curved sides springing from each of the four walls, and it approaches nearly to that of a flat dome upon a rectangular plan.
We also find, from the remains of Ro man buildings, the ceiling:8 of their apart ments vaulted. The side apartments, or chapels, of the Temple of Peace, and of the baths of Dioclesian, have vaults with cylindrical intradoes, while the great rec tangular apartment in each of thesp edifi ces is vaulted in the groined form ; and it is remarkable that the groins are not formed by the intradoes of the vaults in the chapels, fbr the summits of the vaults in these rise but a small distance above the springings of the middle groins. It may also be remarked, that the piers be tween the chapels have small arcades, the summits of which are considerably below the cylindrical intradoes of the side vaults. This circumstance is not peculiar to these buildings, as is to be found in many others. This is to be seen distinctly- in the plates of the Temple of Peace, by Desgodetz. The Romans em ployed annular vaults, as in the temple of Bacchus ; and in this, as in the temple of Peace, and the baths of' Dioclesian, the summits of the arcades supporting the cylindric wall and dome of the central apartments do not interseet the annular intradoes, but the convex side of the cy lindric wall which supports this annular intrados, and consequently- do not form groins. The intradoes of the Roman dotnes are of a semicircular section, as may be seen in the Pantheon, the temple of Bacchus at Rome, the temple ofJupi- ter, and vestibule of the palace of Dioele slan, at Spalatro, in Dalmatia, while the vertical section of the extradoes through the axis is a much less segment, as the Pantheon at Rome, and the vestibule and palace of' Dioclesian, exhibit. We have no instances among the Roman or Grecian buildings of' pendentives or spandrels which are supported by fonr pillars, or by quadrangular or polygonal walls, and which support themselves on a spheric dome or cylindrical wall. Pendentives ri sing from four pillars, and a dome from the top of the pendentives, were first put in practice, it is said, in the celebrated church of Sancta Sophia at Constantino ple.
In the rectangular buildings of the mid dle ages, quadrangular, equal pitched groins were generally used ; and in cir cular buildings we have annular groins, as in the Church of the Holy Sepulchre at Cambridge, and Temple Church, Lon don. Welipe also mentioned those cu rious groitir which are exhibited in the ceilings of King's College Chapel, Cam bridge ; St. Georg-e's Chapel, Windsor and King Henry the Seventh's Chapel, Westminster, of modern invention.
In the present (Lay, every species of vaulting, that were either used by the an cients or throughout the middle ages, are employed, both for the sake of variety, and for elegance.
It does not appear that the ancients we re acquainted with cylindrical, unequal pitched groins, at least by way- of orna ment ; this form is, however, very beauti ful, as the arcades above the passage through the front of Somerset-House clearly- exhibit.