60 



The sum of these products gives the volume of the first 17 envelop- 

 ing cones, or, what is the same, the volume the tree had when 17 

 years old. 



The volume of the first 27 enveloping cones — i. e., the volume the 

 tree had when 27 years old — is obtained as follows (see fig. 15 5 cone 

 sbk) : Determine the diameter of the first 21 central rings on the stump 

 section (difference between the ages of stump and second sections) • 

 determine the diameter of the first 10 central rings on the first cross 

 section (difterence between the ages of first and second sections); cal- 

 culate the volume of the portion between stump and first sections, con- 

 sidering it as frustum of cone or as a paraboloid ; calculate the volume 

 of the portion above the first section, considering it as a paraboloid. 

 The volume of stump the tree had when 27 years old is calculated by 

 considering it as a cylinder, with a diameter equal to that of the first 21 

 central rings taken on the stump of the tree. By adding together the 

 volumes thus calculated the volume the tree had when 27 years old is 

 obtained. The volumes the tree had when 39j 52, 70, 94, 133, and 161 

 years old are determined in the same manner (see fig. 15; cones tcJ, 

 udm, ven^ tcfo, and jcg})) — i. e., the volume of portions of tree between 

 two consecutive sections are calculated, considering them either as 

 frustums of cones or as frustums of paraboloids, while the volume of 

 the last portion of tree is calculated, considering it as a paraboloid; 

 the volume of stump is calculated, considering it as a cylinder with the 

 diameter taken on stump section. 



The total volume of the tree is also calculated as explained above. 

 The progressive development of volume growth may be then deter- 

 mined by means of graphical interi)olation, as shown by fig. 16, which 

 represents the volume growth of the average tree of the group under 

 analysis. 



The analysis is generally concluded by collating the figures relating 

 to height, diameter, area, and volume growth in the form of the follow- 

 ing table: 



