PLANTING 



55 



right angles to each other. This distance may be called i. By 

 shifting every alternate row so that the trees in it come opposite 

 the vacancies in the neighbouring rows, the average distances 

 between the trees will be increased : in the rows shown ver- 

 tically on the paper the distances will still be I, but between 

 the trees in neighbouring rows they will be ri2. Such an 

 arrangement is known as the quincunx, or opposite vacancy 

 arrangement (Fig. 8, B). Each tree, it will be seen, is in the 

 centre of a hexagon formed by the six neighbouring trees around 

 it : but the hexagon is not a regular one, and to make it so, the 

 various distances must be increased somewhat in one direction, 

 and reduced in the other : when this is done, maintaining the 

 same average space per tree, the distance between every tree 



A. Square. B. Qu/ncunx 



FIG. 8 DIFFERENT ARRANGEMENTS OF THE SAME NUMBER 

 OF TREES IN A GIVEN SPACE. 



and all its nearest neighbours will be found to be ro88. This 

 is termed the hexagonal or equilateral triangular arrangement 

 (Fig. 8, C), for any three neighbouring trees in it form a triangle 

 of this description. It constitutes the ideal uniform arrangement 

 of similar objects, and is familiar to every one as being the 

 arrangement existing in the honeycomb, where it results from 

 the fact that it permits of the greatest number of bees to work 

 economically in a given space. 



Though the hexagonal arrangement is preferable to the square 

 arrangement in giving the trees the same amount of room in 

 all directions for their development, it will be seen that it is 

 not so convenient for cultivation, for the alleys between the 

 trees are narrower in the proportion of 0*942 to I. The laying 

 out of a plantation on the hexagonal system, also, is not so 

 simple as when the square system is adopted. The question 



