30 MEASUREMENT OF FELLED TREES. 



bulk between these extremes approaches in shape a truncated 

 Apollonian paraboloid or a cylinder. 

 If h = the height, or length, 



S = the lower section, 



s = the upper section, and 



*,= the middle section (Fig. 22), 



the volume of each of the above-mentioned truncated solids is, 

 according to Simpson's rule : 



6 

 This formula reduces : 



For the cylinder to V = S x h 



For the cone to V = S -^JL 



3 



And for the Ap. paraboloid to V = ' S + s x A or =S m x h. 



By means of these formulas it would be possible to calculate 

 the volume of each part of the stem, provided its particular 

 shape had first been ascertained. This, 

 however, would be a tedious business, and 

 it is necessary to search for a more simple 

 procedure. 



It has been found that by far the greater 

 portion of the stem approaches in shape 

 that of a paraboloid, and that, if the stem 

 is divided into a number of sections of 

 moderate length, each can, without com- 

 mitting any appreciable error, be considered as a truncated 

 paraboloid, the volume of which is 



Or, 



V=s m xh. 



Of these two formulae the latter is the more convenient, and 

 experience has shown that it is even more accurate than the 

 former. 



