GRAVES' MODIFICATION OF MLODJIANSKI'S METHOD 67 



will then begin to the right of the original zero, at th(> intersection of the 

 co-ordinate axes, as many units (years) as it took the tree to grow from the 

 ground to the respective cross-cuts. 



Directions: 



A. Data Required. — Complete stem analysis of trees cut into logs of equal 



length where possible. Unless other data are available the three 

 selected trees of Data Series V. will suffice for purposes of illustration. 



B. Method. — Plotting the values before averaging. 



C. Method of Procedure. 



1. Construct a height growth table showing the average time required 



for the trees to grow from the ground to the various cross-cuts. 



2. Determine the average stump heights. 



3. Draw a diameter growth curve for the stump just as was done in 



Problem 26. Label it Stump Curve and indicate the average stump 

 height on it. 



4. In a similar manner, and with the same values for abscissae and ordi- 



nates, draw a separate diameter growth curve for each of the suc- 

 ceeding cross-cuts, i.e., if the average stump height is 2 feet and the 

 logs are cut in 16-foot lengths, the second curve will represent the 

 growth at a point 18 feet above the ground, the third at a point 

 34 feet above the ground and so on. Label each with its average 

 distance above ground 



5. Now transfer all the curves to one sheet in such a manner that the 



growth at the respective cross-cuts will be shown on the basis of 

 total age, i.e., let each curve begin as many years to the right of the 

 intersection of the two axes as it took the tree to grow to the height 

 of the cross-cut in question. Determine this point in each case 

 from the height growth table. Do not transfer the curves by 

 means of pin pricks, but plot the average values. 



6. Determine the average height of the oldest trees from the height 



growth curve. Indicate this average by drawing a short perpen- 

 dicular through the age axis at the proper point, and label it "Aver- 

 age Total Age," below the axis. Just above the axis at this point 

 write in the average total height and label. 



7. These curves represent the diameter growth at their respective dis- 



tances above ground, on the basis of total age (the age at the ground) 

 and not on the basis of the age at the respective cross-cuts. The 

 points on the age axis together with the average total age, the 

 average total height and the points where the curves at different 

 heights cross the axis represent height growth. Hence this series 

 of curves will give for any age the dimensions of the trees, D.I.B. 

 at various points along the bole, and the total heights. For points 

 at distances above the ground that are intermediate between the 



