144 FARM AND SCHOOL PROBLEMS. 



The Rectangular or Square system is used more than any 

 other. A tree is planted at each corner of the rectangle. When 

 the trees are planted as in figure i, there is considerable waste of 

 land, which may be seen between the circumference of the cir- 

 cles in the center of the square. 



PROBLEM. 



When the distance between the trees is 40 feet in the rectangular 

 system, as in figure 1, which is a square, what is the area of the waste 

 land? 



In the quincunx arrangement it is shown in figure 2 that 

 there is overlapping of the circles. Thus when the tree foliage 

 has spread until it covers a space equal in area to the circles 

 there is a crowded condition. 



PROBLEM. 



What is the area of space overlapped by the circles in figure 2 if the 

 trees are planted 30 feet apart? 



The hexagonal system is shown in figure 3 and shows by the 

 following problem that it is a more economical use of land than 

 either of the other systems given. 



PROBLEMS. 



In planting seven trees according to the figure given under the 

 hexagonal plan, what is the amount of land wasted if the distance be- 

 tween the trees is given as 35 feet in figure 3? 



In a ten-acre orchard the trees were planted -40 feet apart according 

 to the rectangular system; how many more trees would there have been 

 if they had been planted the same distance apart under the hexagonal 

 system ? 



Fruit. 



PROBLEMS IN PLANTING. 



Rule. Multiply the distance in feet between the rows by the 

 distance tae plants are apart in the rows and the product will be 

 the number of square feet for each plant or hill; divide this 

 number into the number of square feet in an acre (43,560) and 

 this will give the number of hills or plants per acre. 



