cruised in every important timber type in this country and undoubtedly knows 

 more about the form of trees and their taper than any other individual 



A taper of 0„5 inch in 4 feet is applicable to almost all timber types with 

 the possible exception of old-growth southern pines, some species of hard- 

 wood in the Mississippi delta, and some very short (stunted or open grown) 

 second growth • Even to these a 0#5~inch taper can be applied without much 

 inaccuracy. The old-growth southern pines (longleaf , short leaf , loblolly, 

 and slash) usually taper at the rate of 0«4 inch in 4 feet. Some but not 

 all of the Mississippi delta hardwoods and bottomland hardwoods in the 

 South have a heavy taper which averages C 6 inch in 4 feet. The short 

 second growth referred to has 0,6-inch taper., but from a type standpoint 

 is unimportant* 



It is recognized, of course, that all the logs in a tree may not have exact3y 

 the taper presupposed by the cubic-foot rule adopted ior use Top logs 

 are apt to have more taper than average and contain slightly more volume 

 than the rule indicates. In most commercial scaling, however, the slight 

 variations which will occur because individual logs deviate slightly from 

 the average shape seem to be of slight importance » 



The Computation of Cubical Volum e 



A careful inspection shows that the surface lines lengthwise of a log 

 are not perfectly straight but usually slightly curved „ In the majority 

 of logs the curving shows convexity and the shape of the entire log is 

 comparable to that of a frustum of a paraboloid, illustrated in figure ?• 

 Such being the case^ the cubical volume of logs can be computed by use of 

 the SmaHan formula, which gives the volume of the frustum of a paraboloid 

 based on its length and end areas e The formula reads? V s A f where 

 "V" is the volume, "A" the area of the large end,, "a" the "~2~"^ irea of > 

 the small end, and "L" the length «, 



Figure 7© The frustum of a paraboloid c A paraboloid 

 is a solid generated by revolving a parabola on its axis. 



