166 CONSTRUCTION OF STANDARD VOLUME TABLES 



The quotients represent respectively the actual average diameter, 

 height and volume for the class. These data, together with the number 

 of trees measured in each class, are entered on a large sheet in the form 

 shown in Table XXVII, p. 165, and constitute the basic or rough table 

 which is the first step in preparing a standard volume table. Thus 

 64.1 cubic feet is not the average volume for 13-inch trees 60 feet high 

 but for trees averaging 13.15 inches and 59.25 feet in height. 



138. The Graphic Plotting of Data— Its Advantages. The volumes shown in 

 such a table should increase with both diameter and height. If sufficient basic 

 data has been obtained, this rate of increase in the values of the table, both verti- 

 cally and horizontally, will follow the law of averages which expresses the true 

 relation of the two variables; for the vertical columns, volume and diameter; for 

 the horizontal, volume and height. But where only a few trees are obtained in a 

 class, these trees may not only be larger or smaller in diameter and height than the 

 true average, but may have too full or too slender a form, and the average of then- 

 volumes will be correspondingly higher or lower than the regular progression to be 

 expected. The form of this progression or increase will be determined by the 

 character of the two variables. For cubic volume based on diameter, with trees 

 of the same height and form, the increase in volume will be proportional to Z) 2 . 

 If these values are plotted on cross-section paper, the result will be a curve showing 

 graphically to the eye the law of increase in volume based on diameter. 



The increase in volume based on height can be shown in a similar manner by 

 plotting the volumes and heights. This curve will differ in shape from the first, 

 since volume tends to increase directly as height for trees of the same diameter, 

 and the curve showing this approaches a straight line. When thus presented to 

 the eye, any irregularities or inconsistencies in the average volumes obtained in 

 Table XXVII become evident at once, while to detect them by mere examination 

 or checking of the arithmetical table would be far from satisfactory. 



Since such irregular values do not conform to the general law of increase in 

 volume based on diameter and height, they cannot be depended upon to give the 

 true average volume of all the trees of a size class. One of two things must now 

 be done — either more data must be collected in the field in order to improve these 

 averages, or the averages obtained must be harmonized, and these irregular values 

 changed or corrected. The irregular volumes plotted would be based on sufficient 

 field data to bring out the real tendency or character of the law of the relations 

 sought. The minor irregularities in this case are not serious enough to prevent a 

 fairly accurate approximation of this law and a drawing of the curve as indicated 

 by the data. 



The principles of graphic plotting are treated in analytical geometry, or graphic 

 algebra. The relation of the two variable quantities is shown by a series of plotted 

 points in which the horizontal and vertical lines each represent a scale of values 

 corresponding to one of the quantities or variables. Both being positive quantities, 

 the lower left-hand corner of the chart is taken as zero, or the origin. The hori- 

 zontal line passing through this point along the base of the sheet is the axis of 

 abscissa; or horizontal scale, and the abscissa or value of each point is measured 

 parallel with this axis or along the scale thus indicated. The vertical line through 

 the origin, forming the left margin of sheet is the axis of ordinates or vertical scale. 

 The zero, or intersection of these two axes, is usually located to the right and above 

 the extreme lower corner of the sheet to give a margin for entering the scales. The 



