APPLICATION OF GRAPHIC METHOD 169 



This saving in field work is from 100 to 500 per cent; in fact it would be impractical, 

 though possible, to get the same degree of accuracy by the averaging of field data 

 as in Table XXVII without using the graphic method. The application of these 

 principles would have greatly improved the construction of certain log rules, 

 notably the Scribner rule (§ 68). 



139. Application of Graphic Method in Constructing Volume Tables. — In 

 applying this method to the values in Table XXVII volume is evidently the variable 

 whose value is sought, while diameter and height are the two independent variables. 

 It is evident that not more than two values can be plotted in a single point, 

 nor more than two variables, as for instance, diameters and volumes in a single 

 curve. The volume of trees varies with both diameter and height, yet variations 

 due to height cannot be shown in the same curve with those due to diameter. But 

 if we select from the original table (XXVII) the volume of trees, all of which fall 

 in the same height class, the factor of height, for these volumes, becomes a constant, 

 except for deviations from the true average height of the class, which can be ignored 

 in plotting this curve. The curve formed by the volumes of this group of selected 

 trees will be designated as the volume curve based on diameters, for trees of the 

 specified height. Such a curve is shown in Fig. 27, with the original average volumes 

 plotted. 



In determining just where the curve should fall, the weight of each point is 

 influenced by the number of trees included in the average column for that diameter; 

 the weight of a point varies with the square root of the number of entries and not 

 directly with the number of entries. Thus an average of a point representing one 

 tree and a point representing four trees would be on a straight line connecting them 

 and one-third of the way from the "4" point to the "1" point. The number of 

 trees in each class should therefore be entered on the sheets opposite the point 

 representing the volume. 



The original volume for the trees of a given diameter class may represent a 

 diameter slightly larger or smaller than the exact inch. For instance, in Table 

 XXVII, the average diameter for 17-inch trees, 55 feet high, was 16.7 inches. This 

 volume should not be entered above 17 inches, but above its true average diameter. 



When the curve is completed, the values are read from it for each exact inch of 

 diameter. 



A comparison of the original and harmonized values from the above curve is given 

 in Table XXVIII, p. 171. 



The averages for 33 out of 38 trees and 6 out of 9 diameter classes fall within 

 2 per cent of the curve. 



140. Harmonized Curves for Standard Volume Tables Based on 

 Diameter. So far, the volumes of trees of different diameters for but 

 one height class have been shown. By the same method, a curve is 

 constructed for each separate height class, based on the scale of diam- 

 eters. If, instead of making each of these curves on separate sheets, 

 they are all placed on the same sheet, their relation to each other is 

 shown. 1 All curves should show the same general trend, in harmony 

 with the law of variation between diameter and volume. The set 



1 Where insufficient data are available and height divisions are small, the values 

 for different heights will frequently overlap. In such cases it is better to plot 

 every alternate height class first, and draw the respective curves before plotting the 

 intervening classes. 



