^{page 2 note a} De Non Voyage en Egypt, pl. 20. B.

^{page 2 note b} Barrow's Travels in China, p. 337.

^{page 2 note c} Vaulting is a general term for arches covering a void space between walls: in that species which is the subject of this paper, it is constituted of two essential parts, viz., continued vaulting or shell as it is sometimes called, and the arched ribs which are placed beneath it.

Vault has been used in the same sense as vaulting; but vault is now more commonly applied to mean a subterranean cellar.

^{page 3 note d} An arch of cut stone is said to be regular when, in the circular curve, the lines of the joints, if produced, converge to one centre: and in all cases a regular cut arch is constituted by the joint being perpendicular to the tangent at the same point of the curve. When the joint is inclined more or less to the tangent, it forms a scheme arch. The first kind is alluded to in this relation, and may be termed the radiated arch.

^{page 3 note e} This description applies to such groins as are produced by vaultings which cross each other at right angles.

^{page 3 note f} See Appendix (A).

^{page 3 note g} On account of the ambiguity that occurs in writings on this subject, by authors having indiscriminately applied the same term to different parts, it may be necessary to explain that here, and throughout this discussion, when speaking of the diagonal or transverse direction of the arch-ribs, &c. the horizontal plan of them is alluded to; and that the terms transverse and diagonal relate to the linear direction of the columns, piers, and walls on the ground. In a quadrangular space covered with a groined arch, the diagonal ribs are those which, resting on the four angles, cross each other in the middle of the space. The transverse ribs are those which pass over the sides of the quadrangular space.

^{page 4 note h} See Appendix (B).

^{page 4 note i} The vertex of the arch is, in technical language, called the crown; the side of the arch contiguous to the part whereon it rests, is called the springing; and some part between the vertex and the springing, is called the haunch: but how far each of these parts extends, is nowhere, that I know of, explained. It will be convenient to consider each half of the whole arch, from the base to the summit, as divided into four equal parts; of which the lowest one will be called the springing, the next two the haunch, and the uppermost the crown: and this may always be understood to relate to the inside, or sofite of the arch, unless the word outer be added. The whole line of an arch, whose sides rest on the same level base, will in this way be divided into eight equal parts, whereof two belong to the springings, four to the two haunches, and two to the crown.

^{page 4 note k} See Appendix (C).

^{page 5 note l} A bay is the quadrangular space over which a pair of diagonal ribs extend, that rest on the four angles. The same term is also used for the horizontal space comprised between two principal beams.

^{page 5 note m} See Appendix (D).

^{page 6 note n} See Appendix (E).

^{page 6 note o} See Appendix (F).

^{page 7 note p} See Appendix (G).

^{page 7 note q} In the third class, over the part where the ridge-band was afterwards introduced, it is not uncommon to find the shell of the vaulting curved from the top of the diagonal to the top of the transverse rib,

^{page 7 note r} See Appendix (H.)

^{page 8 note s} In narrow ailes, the diagonal ribs were frequently much elevated, with pointed tops,— The ridge-band often inclines downwards from the top of the diagonal to the top of the transverse ribs; which along the middle division of churches (where the breadth between the walls usually makes the longest side of a bay) is scarcely perceptible from the floor. This inclination of the ridge-band is caused by setting up the transverse rib, so as to preserve the centre of the curve's circle (being the same curve as that of the diagonal rib) on a level with the base of the springing of the arch. When one side of a bay is very much contracted in proportion to the other side (as sometimes happens against the side walls of the middle division of churches) the great inclination of the ridge-band, which would be occasioned by this procedure, is in several cases avoided by making a portion of the transverse rib, on the narrow side, a perpendicular line for some height above the base of the other ribs. As builders became more expert in the execution of point-arched vaulting, other means were afterwards practised, to procure a better accordance of lines, by a little variation in the curves of the ribs.

^{page 8 note t} Sir Christopher Wren observes (Parentalia, p. 297), that in the English buildings before the Norman period. “the windows were very narrow and latticed.”

^{page 9 note u} This subject is discussed at considerable length in Bentham's History of Ely Cathedral, page 15 et seq.

^{page 10 note x} See Appendix (I).

^{page 10 note y} The common terms for arched tops to apertures are, flat arched, round arched, sharp arched, and point arched; round arched usually implying a semicircle; and sharp arched a curve verging more towards an angle.

^{page 10 note z} See Appendix (K).

^{page 11 note a} See Appendix (L).

^{page 11 note b} See Appendix (M).

^{page 11 note c} Parentalia, p. 297, 298. 306.

^{page 11 note d} Shaw's Travels, p. 218, edit. 1757.

^{page 11 note e} Note on Pope's Epistle to the Earl of Burlington, vol. III. p. 266 et seq. edit. 1751 of Pope's Works.

^{page 12 note f} Comm. to the Antiq. Soc. Archaol. vol. IX. p. 110.

^{page 12 note g} Edinb. Roy. Soc. Trans. 1798. vol. IV.

^{page 12 note h} Carter's ancient Architecture of England, part I. Note at the end of the Preface. Milner's History of Winchester, vol. II. p. 163. Sir R. C. Hoare's Gir. Cam. vol. II. p. 415. 428. Bentham mentions (Hist, of Ely Cathedral, p. 37) tbe same opinion to have been entertained when he wrote.

^{page 12 note i} Smirke comm. to the Antiq. Soc. Archæol. vol. XV. p. 363. 373.

^{page 12 note k} Bentham's Hist, of Ely Cathedral, p. 37. Swinburne's Travels through Spain, vol. II. p. 262, etseq. edit. 1787. And see Appendix (N).

^{page 12 note l} Plates of “Antiguedades Arabes de España.” Swinburne's Travels through Spain, vol. I. p. 140; vol. II. p. 262, edit. 1787.