12 



of the graduated rule. Calipers from 4 to 5 feet long will answer in 

 most cases.* 



Since trees are rarely cylindrical, being often larger in one direction 

 than in the otlier, it is advisable to make two measurements and take 

 tlie average, or else take care to measure tlie estimated average diam- 

 eter. Instead of measuring tbe diameter, the circumference may be 

 measured by a tape and the diameter determined by dividing it by 3.14, 

 which is the ratio of the circumference to the diameter. 



IHEASUREMENT OF VOLUME, 



In determining the volume of a standing tree the stem or bole only 

 is considered; the cubic contents of the branches maj' be estimated by 

 themselves. It is rather difficult to determine the volume of a standing 

 tree because geometrical forms which exactly correspond to the shape 

 of a stem are not known. Moreover, the shapes of trunks differ with 

 age, with species, and with the soil and forest conditions under which 

 they grow; hence we can obtain the volume only approximately^ by 

 comi^aring it to the mathematical form which it resembles most nearly. 

 The form of a stem of a tree is neither a cone nor a cylinder, but resem- 

 bles most closely the form known as a paraboloid. The volume of a 

 Ijaraboloid equals the product of its base by one-half of its height. 

 The base of the tree is taken at a distance from the ground, usually 

 breast-high, where the irregularities of the trunk caused by the root 

 swellings terminate. Here the tree is calipered, and the area for the 

 corresponding diameter (found in the area table, j). 37) is multiplied by 

 one-half of the height of the tree. 



Example: Let the height of the tree be 90 feet, the diameter, 



breast-high, 21 inches. The area corresponding to a circle of 21 inches 



diameter is 2.40 square feet. The volume of the tree then equals 



2.40x90 mo 1 .P 4- 

 ~y^ — = 108 cubic feet. 



Another method, devised by a German forester, Mr. Pressler, may 

 be recommended for determining the volume of a standing tree: Find 

 a place along the stem (fig. G) where its diameter {d) is exactly one- 



*The calipers should be so constructed that the arms -work strictly parallel to each 

 other aud at right angles to the rule; it should, therefore, he made of wood Avhich 

 is not easily affected by moisture. Air-dry jiear wood may be recommended as a 

 material least subject to shriukage. Swelling and shrinking of the wood makes the 

 shifting of the arm either difificult or too easy, often throwing the arm out of the 

 perpendicular, thus destroying the required parallelism between the arms. To 

 avoid this various constructions of calipers have been adopted. The calipers of 

 Gustav Heyer, a section of which is given in iig. 5, may be recommended. A repre- 

 sents the section of the movable arm; R is the cross section of the rule; S a spring 

 fastened at A pressing on thft rule and pushing it down ; w is the cross section of a 

 wedge made of brass and fastened to a screw which can be moved by the key K. 

 By moving the wedge backward and forward the rule can be tightened or released, 

 thus enabling the observer to regulate the shifting of the movable arm Avithout 

 throwing it out of the perpendicular. 



