214 MATHEMATICAL MODES OF 



In order not to involve what was undeniable in Mr. Hay's 

 theory in any hypothesis and those who had studied Mr. 

 Hay's works would know that much in them was based on 

 harmonical theories these last should be kept out of view. 

 What might be shown was, that the artist accustomed to draw 

 the outline of the figure could do so, and would thereby find 

 his figure better proportioned, nor would he be liable to com- 

 mit those glaring blunders, which, however good figures might 

 be artistically, were offensive to the critical anatomical eye. 



The first diagram in Mr. Hay's book* was that of a female 

 figure seen in front with the arms by the side. Mr. Hay first 

 drew a line which represents the full height of the figure. 

 From the upper extremity of this line he drew lines making 

 with it respectively angles equal to l-3d, l-4th, l-5th, and 

 l-6th of a right angle ; and from the lower extremity a line 

 making l-8th of a right angle. The point in which the two 

 last lines, making respectively l-6th and l-8th of a right 

 angle, intersect one another determines the semi-breadth of 

 the figure. Passing through the upper extremity of the ver- 

 tical line, a circle and three ellipses were described the line 

 which joins the extremities of the axes major and minor of 

 the first ellipse being the first of the lines above drawn, and 

 that which joins the extremities of the axes of the second 

 being the third of the said lines. These give the skull, 

 face, and neck. A third ellipse, similar to the first of these, 

 but larger, represents the body. The other lines are few and 

 simple in their relations, the characteristic being that they make 

 an angle of l-3d and l-5th of a right angle with the vertical 

 line. It will be seen that the ruling feature in Mr. Hay's 

 theory is that 'position is determined ly direction, not ly distance. 



The diagrams show how, in the very simplest way, by 

 integral divisions of a right angle, a succession of lines had 

 been attained which corresponded precisely to the position of 



* Natural Principles of Beauty, Plate I. Figs. 1 and 2. 



