S78 On the Kaleidoscope. 



or fortifications. As for example ; in the second figure, we sec 

 a circle divided into six parts, and upon the division marked 

 A is drawn part of a design for a garden. Now to see that de- 

 sign entire, which is yet confused, we must place our glasses ujjoii 

 the paper, and open them to the sixth part of the circle, i. e., one 

 of them must stand upon line b to the centre, and the other 

 must be opened exactly to the point c ; so shall we discover an 

 entire garden plat in a circular form (if we look into the glasses) 

 divided into six parts, with as many walks leading to the centre, 

 where we shall find a basis of an hexagonal figure. 



" We may more plainly see how the glasses ought to be placed 

 upon the design by viewing the third figure. The line A, where 

 the glasses join, stands immediately over the centre of the circle: 

 the glass B stands upon the line drawn from the centre to the point 

 C, and the glass D stands upon the line leading from the centre 

 to the point E. The glasses being thus placed, cannot fail to 

 produce the compleat figure we look for : and so whatever equal 

 part of a circle you mark out, let the line A stand always upon 

 the centre, and open your glasses to the division you have made 

 with your compasses. If instead of a circle you would have the 

 figure of an hexagon, draw the straight line with a pen from the 

 point c to the point d in the second figure ; and by placing the 

 glasses as before, you will have the figure desired. 



" So likewise a pentagon may be perfectly represented by 

 finding the fifth part of a circle, and placing the glasses upon 

 the outlines of it, and the fourth part of a circle will likewise 

 produce a square by means of the glasses, or, by the same rule, 

 will give us any figure of equal sides. I easily suppose that a 

 curious person by a little practice with these glasses may make 

 many improvements with them, which perhaps I may not yet 

 have discovered, or have for brevity's sake omitted to describe. 



" It next follows that I explain how by these glasses we may, 

 from the figure of a circle drawn upon paper, make ati oval ; and 

 also by the same rule, represent a long square, from a perfect 

 square. To do this, open the glasses and fix them to an exact 

 square : place them over a circle, and move them to and fro till 

 you see the representation of the oval figure you like best; and 

 so having the glasses fixed, in like manner move them over a 

 square piece of work, till you find the figure you desire of a long 

 square. In these trials you will meet with many varieties of 

 designs. As for instance, the fourth figure, although it seems 

 to contain but a confused representation, may be varied into 

 above 200 different representations by moving the glasses over 

 it, which are opened and fixed to an exact square. In a word, 

 from the most trifling designs, we may by this means produce 

 sftme thousands of good draughts. 



'^ But 



