78 THE LARCH. 



shoot adds its proportion of woody matter to the 

 general mass, so long, but no longer, than the branches 

 remain vital upon the tree and perform their proper 

 functions do the layers or zones maintain their 

 thickness. But as soon as thinning is discontinued, 

 and the lower branches are allowed to come so close 

 together as to destroy their vitality, so soon does 

 the thickness of the layers in the lower part of the 

 tree begin to decrease. Assuming that while the 

 branches were all vital, the layers or zones were of 

 equal thickness throughout its whole surface from top 

 to base, say Jth of an inch in thickness, five years 

 after the lower tiers of branches had decayed by reason 

 of confinement, the layers at base are now no longer Jth, 

 but are only yVth of an inch thick. Again, at five years 

 afterwards, the zones are reduced to yVth, while all 

 the time the layers higher up the tree, and specially 

 near the top branches, continue growing at the same 

 rate as before, viz., Jth of an inch. Allowing, therefore, 

 that thinning was discontinued at thirty years old, and 

 the plantation stood to seventy years, when it was cut 

 down as mature ; and assuming that the upper part of 

 the trunk during that forty years went on increasing at 

 the rate of Jth of an inch of layer, or :ith of an inch 

 diameter, and the lower part increasing only at yVth 

 during the same period, how much has the upper growth 

 gained upon the lower ? or, in other words, how much 

 nearer is the trunk to the form of a cylinder than it 

 was forty years ago ? 3 J- inches diameter. 



If a tree could survive long enough, and the branches 



