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circles being taken as a base line, and lines drawn from its 
extremities througb the intersections of the circles, an equila- 
teral triangle is produced. By bisecting the radii of the two 
outer circles, and from these points, as the diameter, striking 
a fourth circle, the intersection of this last circle with the 
sides of the triangle, gives the centres of the upper limbs of 
the trefoil head, which it will be perceived approaches very 
nearly to a portion of a single circle. The lines of the label 
mouldinof over this trefoiled arcade are also struck from the 
centres of the two outer circles first-mentioned, so that by 
reference to the diagram, it will be seen that every point 
arising from the various intersections is of practical utility. 
Having measured this example myself, I can vouch for its 
correctness ; and I would mention, that the mouldings of this 
arcade, which have an excellent effect, are produced by 
strictly geometrical forms of a very complicated character, 
(but which could not be reduced to the size of the plate.) 
The next example is from York Cathedral, (plate 3, No. 
7.) Here, by a slight variation, the head becomes equally 
foiled. The base line at the springing, is the diameter of a 
circle, and by striking two other circles of equal radius, from 
the extremities of the diameter, and forming two spherical 
equilateral triangles, the lower limbs are obtained : the points 
of intersection of these circles give the base of a third equi- 
lateral triangle, and are the centres from which the upper 
limbs are struck ; so that the inscribed line of this niche or 
arcade is an equilateral triangle exactly. 
The third example is from Lincoln Cathedral, (No. 6, plate 
3,) which, although very different in appearance from that of 
Stone Church, differs only in one respect, viz., that the apex 
of the equilateral triangle is a centre from which both limbs 
of the upper foil are formed. 
The fourth example is by far the most interesting ; it is 
from Kirkstall Abbey, (No. 5, plate 3,) Had I not actually 
