172 CONSTRUCTION OF STANDARD VOLUME TABLES 



within each height class separately, but this does not prevent the values 

 of all the trees of a given height class from being too low or too high. 

 In fact, if one of the volume curves representing a height class is incor- 

 rectly drawn lower or higher than it should be, this very result is pro- 

 duced. 1 



The law of variation of volume based on height may be expressed 

 by the equation y = px, since volume (y) increases approximately in 

 direct proportion to height (x). For trees of the same diameter, whose 

 volumes lie on the same ordinate in Fig. 28, the curves of volumes for 

 regular gradations of height should be spaced at about equal distances. 

 This interval, of course, increases with each diameter class. Since this 

 is known, the first set of curves based on diameter may be harmonized, 

 not only in direction but in spacing, being placed at equal intervals 

 on each successive ordinate. The resultant table will then show volumes 

 increasing regularly by height. 



A still better method of securing this regularity is to plot, from the 

 values obtained from the first set of curves, a second set in which 

 heights are the determinate variable, or basis plotted on the horizontal 

 scale, and volumes are plotted vertically as before. Diameter must 

 now be eliminated as a variable, by plotting all the volumes for trees 

 of a single diameter class in the same curve. Beginning with the first 

 diameter class in Fig. 28, which is intersected by two or more curves 

 of volume representing different height classes, these volumes at the 

 intersecting points are read, beginning with the lowest. The series 

 of values thus obtained represents the volumes of successive height 

 classes, and as such are plotted on the new sheet, and connected to 

 form a new curve, which represents only trees of the diameter class 

 so taken. 



Each point so plotted should be placed above the actual average 

 height for the class, as found in the original averages shown in Table 

 XXVII, e.g., for the 15-inch curve, the 55-foot class must be plotted, 

 not above 55 feet, but above 57 feet, which is the actual average 

 height for this class. 



Separate new curves are thus plotted for the trees in each diameter 

 class. Instead of plotting these values direct from the first set of 

 curves, a table may be made from the values read from these curves, 



1 The tendency to error may be greatly reduced in the original curves if the 

 the square of the diameter is made the basis of the table, or abscissae scale, in which 

 case the curves take the form of straight lines characteristic of those based on 

 height. The same result may be obtained by plotting on logarithmic cross-section 

 paper. (Logarithmic Cross-section Paper in Forest Mensuration, Donald Bruce, 

 Journal of Forestry, Vol. XV, 1917, p. 335.) 



