6 Forest Mensuration 



PARAGRAPH XIII. 



MEASURING THE SECTIONAL AREA. 



The sectional areas are ascertained with the help of measuring tape, 

 caliper, tree shears, tree compasses, Biltmore measuring stick, etc. 



The sectional area is thus derived from the measurement either of the 

 diameter or of the circumference. 



For exact scientific investigations the planimeter or the weight of an 

 even-sized piece of paper. may be used. 



It is best to consider the sectional area of a tree as an ellipse, the 

 surface of which is : 



7T 



surface = D.d, 

 4 



the big diameter D being measured vertically to the small diameter d. 



Usually, however, the average diameter of the tree at a given point 

 is found as the arithmetical mean of the big and small diameter at that 

 point measured crosswise and not as the square root of the product of 

 such diameters. Since 



D + d , 



>^D,d, 



the average diameter is invariably, though slightly, over-estimated by 

 crosswise measurement. Hence it is wise to drop, as an arbitrary offset, 

 the excess of fractions of inches over full inches. 



The arithmetical mean of the sectional areas belonging to diameters 

 measured crosswise leads to still greater mistakes. 



PARAGRAPH XIV. 



INSTRUMENTS FOR MEASURING DIAMETERS. 



Log calipers are made of pyrus wood or of metal. American make 

 (Morley Bros., Saginaw, Mich.) cost $4.00 each. The moving leg of the 

 caliper is kept in place by a spring or a screw or a wedge. 



The best European makes are the "Friedrich" and the "Heyer and 

 Staudinger." Wimmenauer's "addition-caliper" counts the trees and adds 

 their sectional areas automatically. 



Short legged calipers, named "Dachshunds" by C. A. Schenck, can be 

 used for trees the radius of which exceeds the length of the legs. The 

 diameter is, in that case, indirectly found by the help of the secant joining 

 the tips of the legs, which are about 5" long. 



"Tree compasses," opening from six inches to thirty-six inches, and 

 made of nickel-plated steel, cost (at Morley Bros.) $7.50. "Tree shears" 

 (Treffurth) find the angle formed by the shear-legs when pressed against 

 the tree and directly derive therefrom the diameter or the sectional area 

 of the tree. 



The "diameter tape" slung around the tree usually yields too large a 

 diameter, since the circle embraces the maximum of surface by the min- 

 imum of length. 



