Lr.'/FIIJNG AND LAIIXG OUT. 



155 



in mind concerning them is, that the length must always correspond with the 

 width. In cases where both length and breadth are given, the easiest way to 

 proceed is as follows :— Make the line for the lergth, and another for the 

 width perpendicular to it. Then take a distance one half the entire length 

 of the oval, and place the stake or compasses at an equal dibtance on each 

 side from the cen+re, and cut the base-line from each extremity of this line 

 diagonally to the point where the oval inclines to its centre. Then insert two 

 strong stakes at the front of the base-line ; place a garden-line round them ; 

 draw it tight, and it will slip round the stakes and define the ellipsis. Ovals 

 can also be formed by the aid of two, three, or four circles, as shown below. 



364. In fig. 1, three circles are formed on the centre line of the oval, whose 

 length is given. The outer edge of the two end 

 cu'cles forms the end of the eUipsis. Then draw 

 the lines, he, of, ec, and ag, and, where they 

 cut the centre of the figure is the point for 

 describing the sides of the oval. Placing a stake, 

 or one leg of the compasses, at a, describe the 

 line gf ; then move to c, and describe he, and the 

 ellipsis is completed. 



365. To make fig. 2, form two cu'cles, II, I, whose circumferences will touch 

 each other. Take the diameter of one, place the 

 compasses in the centre of the circle II, already 

 formed, and sweep upwards to a, and downwards 

 to h ; place them in the opposite circle, and sweep 

 in the opposite direction. Where these lines in- 

 tersect each other, draw two more circles of the 

 same diameter, and those will form the end of the 

 oval. Then place one end of the compasses at I, 

 and describe the side from B to H ; remove to II, 

 and draw F to C, and the figure is complete. These 

 circles may all be formed by means of a stake, to 

 which a string is attached. 



366. Fig. 3 is still more simple : divide the length into three equal parts ; 

 let the two j)oints thus found be the centres of 

 two circles, whose outside edges will form the ends 



r--. of the ellipsis. Where 



they intersect each 

 other in the centre of 



^ the figure will be points 



^ from which to complete ^^9- 3- 



the segments of its sides. I suppose every one knows how to erect one line 

 perpendicular to another :— Let ah be a straight Hne from which a perpendi- 

 cular Hue is passed at c. Measure any distance on each side of c, the same on 

 both sides ; place the compasses in each of the points thus formed, describe the 

 lines at d ; the point of intersection will be perpendiciUar to c. There is no 



