VOLUiME GROWTH IN AN INDIVIDUAL TREE 65 



(b) Calculate the volume of the tree according to its present dimen- 



sions by calculating the volume of each section separately, and 

 add all of them for total volume. The dimensions of the diam- 

 eters may be determined from the last set of figures recorded 

 on the analysis sheet, for each section analyzed. As they are 

 radius measurements they should be doubled. 



(c) In a similar manner calculate the volume of the tree by recon- 



structing from the analysis its dimensions at 10, 20, 30, 40 years 

 ago and so on down to within the first 10-year period in the life 

 of the tree. (Make only 5 to 7 calculations.) The diameters 

 of the successive 10-year periods are again determined from the 

 radius measurements recorded on the analysis sheet. For ten 

 years ago, for example, the radius at each cross-section will be 

 represented by the next to the last series of radius measure- 

 ments; for twenty years ago by the third from the last, and so 

 on. The lengths of the logs or sections are recorded on the 

 front of the analysis sheet, including the height of the stump 

 and the length of the tip of the present tree. The lengths of 

 the tips of the reconstructed trees, however, must be determined 

 by special calculations, because the tips usually end somewhere 

 between the last cross-cut and the original tip, or between two 

 successive cross-cuts. 

 Determine the lengths of the individual tips by proportion as 

 follows : 



(1) Determine the periodic annual height growth of the section 



above the last log in the reduced tree under consideration 

 by dividing the length of the section by the number of 

 years it took the tree to gi-ow that length. 



(2) Multiply the periodic annual height growth by the number 



of rings at the base of the tip whose height you wish to find. 

 If the tip of the reduced tree happens to be in the tip of 

 the present tree, the length of the present tip divided by 

 the number of rings at its base will equal the periodic 

 annual height growth. If the tip of the reconstructed 

 tree falls within any of the sections below the present tip, 

 the total number of rings at the top of the section sub- 

 tracted from the total number of rings at the bottom of 

 the section will equal the number of years it took the tree 

 to grow the length of the section. Then divide the length 

 of the section by this number of years, as just determined, 

 to obtain the periodic annual growth (P. A. G.) in height. 

 Multiply this by the number of rings at the base oj the tip 

 U'hose height it is desired to find. 



(d) Determine volume of tip as usual B.A.X^H. 



(e) Enter the volumes of the separate sections of each reconstructed 



