32 THE CONSTRITCTION OF VOLUME TABLES 



from 111 inclics to !;>.() iiiclics iiu'liisivc; and all lici^htclasses from 

 9 feet below to the even 10 feet above the value iiulicating the 

 class; i.e., the 80-foot height class includes all trees from 71 feet to 

 90 feet inclusive. 



2. Record the D.B.H. and computed volume of each tree in the space 



allotted to it according to its D.B.H. and total height. Tally 

 D.B.H. in inches and tenths, and full stem volume in cubic feet and 

 tenths. 



3. When all the trees are tallied, determine the total diameter and total 



volume for each diameter-height class by adding the recorded values 

 and divide each by the total number of trees added to obtain the 

 average diameter and average volume of that class. 



n. Plotting 



A new feature in plotting the values for this exercise arises which has not been 

 explained heretofore. (See Problem 8.) Instead of having one dependent and 

 one independent variable we now have two independent variables namely, 

 diameters and heights; and the volumes as the one dependent variable. Hence 

 three distinct values must be considered. Since a single plotted point on a piece 

 of cross-section paper cannot express more than two values it now becomes 

 necessary to draw a series of harmonized curves b}^ means of which it is possible 

 to express the three values. This is done by first plotting separate "volume-on- 

 diameter" curves for each height class. From the resulting series of curves we 

 obtain the volumes according to -the different diameters irrespective of average 

 heights. With the average volumes read from this series of curves we now con- 

 struct a series of " volume-on-height " curves for the different diameter classes, 

 and from them obtain the final values as follows: 



a. Averaging the Diameters. 



1. On a piece of cross-section paper lay off diameters as abscissae and 



volumes as ordinates. Since several curves must be drawn on a 

 single sheet of cross-section paper it will be well, in order to avoid 

 confusion, to use a scale such that 1 inch on the paper will repre- 

 sent at least 2| inches in D.B.H. values. It will also aid if the 

 different points of each height class are connected with lines in 

 different colored inks or crayons. 



2. Plot a curve for the first height class using each of the average 



values and average heights under that class; i.e., plot a curve 

 for the 80-foot height class using the D.B.H. and volumes on the 

 tabulation sheet in a vertical column under this class. Besides 

 each plotted point place the number of trees represented. Join 

 the points by fine lines and draw a smooth curve. Label this 

 curve with the height class it represents. 



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



nates, and on the same sheet of cross-section paper, plot the 



