78 STUDIES IN GROWTH PER CENT 



PROBLEM 37. (Field.) The Determination of Future Volume in 

 Immature Even-aged Stands by Means of Growth Per Cent Calcu- 

 lated FROM Standing Trees. 



Illustration. — To determine what the volume of a stand will be ten years 

 hence by means of Pressler's formula for immature trees. 



Explanation. — In this formula Presslcr starts with the factors of volume, 



■kD'^HF 



V = as a basis and eliminates F, the form factor, by assuming that 



trees will not materially change in form in ten years, and by further assuming 

 that the change in height is proportional to the change in diameter he elimi- 

 nates the height factor, H, by finding its value in terms of the diameter thus 

 evolving the formula as given below for immature trees. For mature 

 trees he evolves the formula, 



D2-d2 200 



assuming that there is practically no change in either height or form factor. 



Directions: 



A. Formula. 



D^-d^ 200 



D^+d^ n 

 where p = growth per cent; 



D = D.B.H. of present tree; 



d = D.B.H. of tree 10 years ago; 



n = 10 years. 



B. Method of Procedure. 



1. Use the same plot used in the preceding problem. 



2. Find 3 standing trees of the requisite diameter, either on this plot or 



adjacent to it. 



3. With calipers find the average present diameter of each tree by means 



of two measurements at right angles to each other. 



4. With the increment borer, by means of two borings at right angles to 



each other on each tree, find the average diameter ten years ago. 



5. Substitute the averaged values for D and d of the three trees in the 



formula for growth per cent. 



6. Calculate what the volume of the tract (assume 40 acres) will be 



10 years hence. 



C References. — Numbers 06 and S2. 



D. Discussion. 



1. Show by means of the mathematical derivation of Pressler's formula 

 how he justifies the uso of this formula for immature stands. 



