400 R. T, Patton : 



Spacing at 32 feet, and assuming the trees are so distributed 

 that the crowns are hexagonal, there would be 49.13 trees per acre,, 

 or say 50. 



Planting trees on the square does not fully utilise the ground. 

 If we now work back we can ascertain how many trees there are 

 in each crown class. Tlie crown class preceding the 32 ft. class^ 

 must be the IG ft. class si.nce trees are fixed in the one spot. If 

 there are 50 trees per acre in the 32 ft. crown class, there must, 

 be 200 trees per acre in the IG ft. class, that is by halving the 

 diameter we increase tlie number of trees four times. The crown 

 classes must be 32 ft., 16 ft., 8 ft., 4 ft., 2 ft., and 1 ft. When 

 any one crown class passes into the next higher class, 3 out of 

 every 4 trees are suppressed, and this is why thinning is necessary >. 

 The number of trees in any crown class may be found by the fol- 

 lowing expression. 



Where q = the required number of trees. 



fl = number of trees in the final crown class. 



r = 4. 



M = number of crow^n classes to and including class required.. 

 From this we find that in the 1 ft. crown class there would be- 

 51,200 trees. 



It is customary to set out tables showing the number of trees- 

 at each decade. Tliese tables are the result of experience. Nature- 

 does not work from decade to decade, but from crown class to crown 

 class, and suppression is her mode of working. If we can con- 

 ceive of a forest advancing from class to class, then we have a 

 scientific basis for thinning. We have,, however, to find some rela- 

 tion between the crown classes and the time taken to reach those- 

 crown classes. It lias already been noticed that Mountain Ash 

 starts with maximum effort in both diameter and height growth, 

 and it might be supposed that the growth of the crown would be 

 similar. However, the crown is not free to expand, but must 

 struggle for its expansion, hence its curve of growth must differ 

 from tliose of diameter and height. A study of the crowns 

 suggested that tlie expansion of the crowns could he expressed a» 

 follows : — 



Where ^ = required age of a particular crown class. 

 « = known age of a particular class. 

 r = ratio. 

 7? = number of crown classes concerned. 



