The line A B represents the full height of this structure. The line A C, which makes an angle of (²⁄₉) with the vertical, determines the width of the design, the tops of the aisle windows, and the bases of the pediments on the inner buttresses; A G, (¹⁄₅) with the vertical, that of the outer buttress; A F, (¹⁄₉) with the vertical, that of the space between the outer and inner buttresses and the width of the great centre window; and A E, (¹⁄₁₂) with vertical, that of both the inner buttresses and the space between these. A H, which makes (¹⁄₄) with the vertical, determines the form of the pediment of the centre, and the full height of the base and surbase. A I, which makes (¹⁄₃) with the vertical, determines the form of the pediment of the smaller gables, the base of the pediment on the outer buttress, the base of the ornamental recess between the outer and inner buttresses, the spring of the arch of the centre window, the tops of the pediments on the inner buttresses, and the spring of the arch of the upper window. A K, which makes (¹⁄₂), determines the height of the outer buttress; and A Z, which makes (¹⁄₆) with the horizontal, determines that of the inner buttresses. For the reasons already given, I need not here go into further detail.[11] It is, however, worthy of remark in this place, that notwithstanding the great difference which exists between the style of composition in this Gothic design, and in that of the east end of the Parthenon, the harmonic elements upon which the orthographic beauty of the one depends, are almost identical with those of the other.

On the Curvilinear Forms and Proportions of Architecture.

Each regular rectilinear figure has a curvilinear figure that exclusively belongs to it, and to which may be applied a corresponding terminology. For instance, the circle belongs to the equilateral rectangle; that is, the rectangle of (¹⁄₂), an ellipse to every other rectangle, and a composite ellipse to every isosceles triangle. Thus the most simple elements of beauty in the curvilinear forms of architectural design are the following three figures:—

I find it necessary in this place to go into some details regarding the specific character of the two latter figures, because the proper mode of describing these beautiful curves, and their high value in the practice of the architectural draughtsman and ornamental designer, seem as yet unknown. In proof of this assertion, I must again refer to Mr Penrose’s great work published by the “Society of Dilettanti.” At page 52 of that work it is observed, that “by whatever means an ellipse is to be constructed mechanically, it is a work of time (if not of absolute difficulty) so to arrange the foci, &c., as to produce an ellipse of any exact length and breadth which may be desired.” Now, this is far from being the case, for the method of arranging the foci of an ellipse of any given length and breadth is extremely simple, being as follows:—

Let A B C (figure 1) be the length, and D B E the breadth of the desired ellipse.

Fig. 1.

Take A B upon the compasses, and place the point of one leg upon E and the point of the other upon the line A B, it will meet it at F, which is one focus: keeping the point of the one leg upon E, remove the point of the other to the line B C, and it will meet it at G, which is the other focus. But, when the proportions of an ellipse are to be imparted by means of one of the harmonic angles, suppose the angle of (¹⁄₃), then the following is the process:—

Let A B C (figure 2) represent the length of the intended ellipse. Through B draw B e indefinitely, at right angles with A B C; through C draw the line C f indefinitely, making, with B C, an angle of (¹⁄₃).