2 Forest Mensuration 



The body of a tree, considered as a conoid (a solid body formed by 

 the revolution of a curve about an axis), is very complicated, being 

 formed by a curve of high power. This is the case even in straight and 

 clear boled conifers. The tree bole shows, however, in certain sections 

 of its body frequently a close resemblance to a truncated neilloid, cylinder, 

 paraboloid and cone. 



The longitudinal section of conoids is outlined by a curve correspond- 

 ing with the general equation 



y' = px" 



in which 3; is the ordinate (corresponding with the radius of the basal 

 area), x the abscissa (representing the height of the conoid), n the 

 power of the curve; whilst p is merely a constant factor. The volume 

 v of the conoid is obtained by integral calculus : 

 V = y2_7rx 

 n + 1 



It is equal to sectional area, s, times height, h, over (n-f-i). 



The truncated volumes are developed by deducting a small top conoid 

 from a large total conoid. 



s^ s 2 h 2 



vol. tronc.= 



n + 1 



In the general curve equation 



y = px 

 we find represented: 



A. For H equal to o, the cylinder; 



B. For n equal to I, the Apollonian paraboloid, wherein the ratio 



between sectional area and height is constant ; 



C. For n equal to 2, the cone, wherein the ratio between radius of 



sectional area and height is constant; 



D. For n equal to 3, Neill's paraboloid, the truncated form of which 



is found at the basis of our trees. 



The top of the tree resembles a cone or Neilloid; the main bole 

 resembles the cylinder or the Apollonian paraboloid. 



The cross section (see Par. XIII.) through a tree taken perpen- 

 dicular to its axis shows a more or less circular form. Near 

 sets of branches and near the roots, however, the outline is 

 irregular. The center of the circle usually fails to coincide with 

 the axis of the tree. 



PARAGRAPH IV. 



CYLINDER. 



The cubic contents v of a cylinder are equal to the height h of the 

 cylinder, multiplied by the sectional area s of the cylinder. 



vol. cylinder = h. s 



