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Description of a Machine for Drawing the perfect Egg-Oval; 

 and of a Method of producing Curvilineal Figures, on a prin- 

 ciple whereby Beauty of Form may be imparted to Orna- 

 mental Vases and Mouldings in Architecture, — to the Works 

 of the Silversmith, Brazier, and Potter, — equal to such 

 Works of the Ancients. Invented by D. R. Hay, Esq., 

 F.R.S.S.A. Communicated by the Royal Scottish Society 

 of Arts.* 



Finding that throughout all nature the elements of every 

 species of beauty are reducible to three orders or classes, 

 namely, a primary, a secondary, and a tertiary, I have adopted 

 the same principle in regard to curvilineal forms. The circle I 

 have taken as the primary, the ellipse as the secondary, and 

 the oval as the tertiary, the first having one focus, the se- 

 cond two, and the third three foci. 



The curve of the circle is unform in all its parts, and is, 

 therefore, devoid of variety, its arcs being all identical. The 

 ellipse may be divided into four uniform parts, each of which 

 possessing the elements of variety. Its variety, therefore, is 

 to its uniformity as 4 to 1. But the oval form, being divisible 

 into two similar parts only, has its variety to its uniformity in 

 the simple ratio of 2 to 1 ; and, consequently, its beauty is 

 the most perfect. 



This species of beauty is a distinguishing quality in the 

 human figure, which, as viewed in full front, presents two 

 identical halves, each of which are distinguished by infinite 

 variety in the parts of which they are composed. 



The circle belongs to the perfect square, which it harmo- 

 nically inscribes ; the ellipse to the oblong rectangle, either 

 as horizontally or vertically considered ; and the oval to the 

 isosceles triangle. In treating of the nature of beauty, Mr J. 

 D. Harding, in his excellent work, " The Principles and Prac- 

 tice of Design," thus speaks of the curve of the oval. " In 

 the circle we see and feel, without preparatory education, 

 and without difficulty, its sameness, and, therefore, its want 



* Read before the Society on 9th March" 1846. 



