6G GENERAL CiKOWTH OF STUDIES 



tree in the proper place on the blank form and add for total 

 volume. 

 2. Now determine the rate of volume growth in board feel in a similar 

 manner to that just described, except as follows: 

 (a) Use only the merchantable portion of the stem, assuming -every- 

 thing merchantable above the stump down to 6 inches D.I.B. 

 at the top of the log. Tii)s and stumps, of course, must be 

 omitted, also logs whose top diameters are less than 6 inches. 

 (6) Use the International Log Rule as worked out in Problem 9 or any 

 other rule giving values down to 6 inch top diameters, for 

 determining the board foot values. 



(c) Record the values in their proper places in the blank forms, and 



total. 



(d) Make a final table showing only the volume in cubic feet and in 



board feet in 10-year age periods. 



C. Discussion. 



1. What would be some of the practical applications of such a table. 



PROBLEM 3L (Office.) The Determination of Volume Growth by 

 Graves' Modification of Mlodjianski's Method. 



Explanation. — A table showing growth based on age might be constructed 

 from analysis data by first calculating the volume growth of each individual 

 tree as was done in Problem 30, and averaging the results to determine the 

 average rate of growth. The student will realize fully from the foregoing 

 exercise without further emphasis the tremendous amount of work necessary 

 if a number of trees sufficient to give good average results are used. The 

 object of the method described in this problem is to reduce the number of cal- 

 culations to a minimum. Mlodjianski's principle is first to determine by 

 means of separate curves the average dimensions of the trees at different ages, 

 and from them to calculate the volume growth rather than to calculate the 

 volumes first and then determine the averages. Graves' modification con- 

 sists in arranging the averaged curves in graphic form on one sheet of cross- 

 section paper in such a manner that the dimensions of a tree of any age may be 

 determined at a glance. The principle underlying the method as proposed by 

 Graves is to have the curves for the diameter growth at each cross-cut placed 

 on the co-ordinate paper with reference to the total age of the tree instead of 

 the number of rings at the cross-cut in question. Remember, that the age at 

 the stump does not represent the total age of the tree, because no rings are 

 represented in the cut surface of the stump for those years during which the 

 tree grew to stump height. The problem, then, is to show in the diameter 

 growth curve for the stump how many years in the whole life of the tree it took 

 to produce a stump of a certain diameter and not how many years after the 

 tree had grown to stumj) height. In this problem the curve for each cross-cut 



