Machine for Drawing the Perfect Egg-Oval. 333 



is ihen removed; the point of a pencil is inserted into the 

 groove or slot, and within the cord, which it is made to 

 tighten around the three remaining studs by drawing the 

 point of the pencil towards the moveable end of the lever, 

 which is then moved round upon its axis, the cord being 

 kept tight. The pencil will thus trace upon the board one 

 half of a perfect egg oval ; because the motion of the focus 

 at the end of the rack increases fluxionally the two radii of 

 the curve. Since this machine was made, I have invented 

 another, which, by means of two racks, will form both sides 

 of the oval by one continuous line, as shewn by this sketch 

 on the board. By this machine, therefore, the true oval or 

 egg form may be produced, but as yet its capabilities go no 

 farther ; and I have, therefore, adopted a more simple and 

 more practically useful process for producing a series of 

 figures of this kind applicable to the arts of ornamental de- 

 sign ; although the ellipses of which such figures are in reality 

 composed are not so perfectly blended as by the machine. 



These figures, 1 shall prove to you, are capable of infus- 

 ing into the ornamental arts, as connected with architectural 

 decorations, ornamental sculpture, the works of the artificer 

 in silver and other metals, and, especially, those of the pot- 

 ter, that refinement of beauty by which the ornamental 

 works of the best periods of ancient art are distinguished. 



My process is this : I first classify and arrange a series 

 of isosceles triangles agreeably to the harmonic ratios ; I then 

 arrange these in pairs of right-angled with acute-angled, 

 and obtuse-angled with acute-angled, as now explained by 

 the figure I shew you, and will be more fully so in a work 

 upon the subject which I have at present in course of publi- 

 cation. Of this process, I shall give you an example. I 

 unite this right angled isosceles triangle with another isosce- 

 les triangle, whose most acute vertex is 22° 30', having to the 

 right angle (90°) the ratio of 1 to 4. At the four vertices 

 of these compounded triangles, which form a figure having a 

 right angle subtending an acute angle, and two obtuse 

 angles subtending each other, I fix studs or pins at each 

 angle, and tie a cord tightly round them, with a knot that 

 will not slip, and I then remove the stud or pin at the vertex 



