470 APPENDIX, 23

an infinite number of chamfers to be struck between B C and p p, from every point in Q A produced to infinity; thus we have infinity multiplied into infinity, to express the number of possible chamfers of this species, which are peculiarly Italian chamfers; together with another singly infinite group of the straight chamfers, a b, e f, etc., of which the one formed by the line a b, passing through the centre of the circle, is the universal early Gothic chamfer of Venice.

Again. Either on the line A C, or on any other lines A l or A m, radiating from A, any number of centres may be taken, from which, with any radii not greater than the distance between such points and Q, an infinite

number of curves may be struck, such as t u, r s, N n (all which are here struck from centres on the line A C). These lines represent the great class of the Northern chamfers, of which the number is infinity raised to its fourth power, but of which the curve N n (for Northern) represents the average condition; the shallower chamfers of the same group, r s, t u, etc., occurring often in Italy. The lines r u, t u, and a b may be taken as approximating to the most frequent conditions of the Southern chamfer.

It is evident that the chords of any of these curves will give a relative group of rectilinear chamfers, occurring both in the North and South; but the rectilinear chamfers, I think, invariably fall within the line Q C, and are either parallel with it, or inclined to A C at an angle greater than A C Q, and often perpendicular to it; but never inclined to it at an angle less than A C Q.

[Version 0.04: March 2008]