Garden Surveying, Levelling, and Mensuration 223 



Circles. The diameter of any circle being known, the circumference 



22 



is obtained by multiplying it by 31416 or -=- . Thus, a circle with a 



diameter of 12 in. would have a circumference of 37 '6992 in. The radius 

 of a circle is half the diameter. The area of a circle is obtained either 

 (1) by squaring the diameter and multiplying by '7854 or (2) by multi- 

 plying the square of the radius by 3'1416. The following are useful 

 formulae relating to the circle: 



3183 = diameter. 

 15915 = radius. 

 1'2732 = square of diameter. 



square of the circumference. 



= side of an inscribed equilateral triangle. 



diameter. 

 = radius. 



Circumference of circle X 

 X 

 X 



X 12-5663 

 X -2756 

 + 3-1416 

 -=- 6-2831 



Fig. 406. Showing how an Oval Bed is struck 

 from 2 circles, and how the intervening space may 



Oval, Ellipse. These are two com- 

 mon shapes for flower beds in gardens. 

 The methods used for striking ovals 

 and ellipses in gardens are shown in 

 the accompanying diagrams (figs. 406, 

 407). In the first one it will be seen 

 that two intersecting circles are made, 

 one with the centre at D, the other at C 

 both equal. The gap between the 

 two is filled in by freehand. To find 

 the area of an ellipse multiply the 

 long axis by the short axis, and the 



product by '7854. The same result may be secured by multiplying half the 

 long or main axis by half the short axis, and the product by 3'1416. 



Having decided on the length of an elliptical bed, the most simple 

 method of striking the 

 figure is to fix two pegs 

 at equal distances in 

 from the ends of the 

 long axis. Then make 

 a string loop equal to 

 the entire length of the 

 long axis and place to 

 enclose the two pegs. 

 By stretching the loop 

 tightly with a pointed 

 stick, and working right 

 round from one end of the long axis to the starting point, the form of 

 an ellipse may be traced on the ground. 



Cone. The area equals half the product of the circumference of base 



Fig. 407. Showing how to make an Elliptical Bed 



