58 



mark or the end of the ninth interval along the measuring line 

 connects with peg B on the base line. It is mathematically true 

 that in every instance when the three sides of a triangle are as 

 3, 4, and 5, the angle opposite the longest side or hypotenuse is a 

 right-angled triangle. 



Another method, which may be used as an alternative, consists 

 in guessing a triangle and measuring the diagonal distances 

 between the opposite corners A, D, and E, C on the figure, unless 

 those distances are equal to a fraction of an inch the square 

 is not perfect, and by manipulating and shifting the pegs until 

 those two lengths coincide the desired lines running at right angles 

 to one another can be planned out. 



2 Diagonal planting has few, if any, advantages. As shown in 

 figure 2, the base line is first determined and a true corner found as 

 in the case of the square. On the lines thus determined rows of 

 trees will be set. The alternate rows are obtained by running 

 with a line a diagonal from two squares which have already been 

 mapped out. From the corner A, mark off one-fourth distance 

 along this diagonal and you have the spot where the first tree 

 along the second row will stand ; from these points plot out 

 parallel lines to A B, A C, etc., and along these lines mark off 

 the required distances as had already been done on the base lines. 



3 Hexagonal, Equilateral, or Septuple planting, so called because 

 seven trees enter into its figure ; which consists of six trees disposed 

 after the figure of the cells of the honeycomb 



