VOLUME TABLES BASED ON STANDARD TAPERS PER LOG 145 



diminishing in top diameter by the indicated taper, are totaled, and 

 the' sum taken as the volume of the tree. These computations do hot 

 require the measurement of .the tree but are performed in the office 

 from the log rule. 



The volumes in such a table are the scaled contents of logs by a given log rule, 

 and will apply only to regions where this same log rule is used. But it is a simple 

 matter to compute a new table for any other log rule, by the same method, since 

 no field work is required. Wherever the log rule is the standard, such a table is 

 applied to all species, types and character of trees, and in this sense is universal. 

 The assumption underlying such a table is that the merchantable portion of all 

 trees have the shape of the frustums of cones, hence the determination of the three 

 factors, average taper per log, diameter at top of first log, and number of logs in 

 the tree, determine the scaled contents of the tree as given in the table. As shown 

 below, the assumption is not correct. 



In applying this table, these cruisers seldom attempt to tally the dimensions 

 of each tree. The trees are counted, separately by species, and also by classes, 

 as large, medium or small. Then the average diameter, average number of logs per 

 tree, and average taper per log is decided on usually by guess or by judgment. 

 The volume table merely serves to give the assumed volume of a tree of this 

 diameter, height and taper. The estimate or total for the species is obtained by 

 multiplying this volume by the tree count. 



The advantages of obtaining a universal and elastic volume table, applicable to 

 any species, region and character of timbers are self-evident. The defects in 

 uniform or universal volume tables based on the frustums of cones are: 



1. The form of the average tree of any species, when the merchantable portion 

 only is considered, resembles more nearly the frustum of a paraboloid than that of 

 a cone (§ 26). While the merchantable portion may be treated as the frustum of 

 a cone, yet investigation shows that the average volume of trees of different species 

 and diameters is usually either less or greater than that assumed by the table. 

 This possible error is consistently neglected. 



2. For accurate application, the universal table requires the determination of 

 three dimensions for every tree whose volume is to be ascertained, namely, diam- 

 eter, height and taper. A tally of every tree by diameter and height is possible, 

 but the separation of a third factor, tree by tree, makes the tally too complicated, 

 and requires the substitution of average tapers for a species, or for groups of 

 diameters as indicated above. But the trees in any given stand or area never taper 

 uniformly. The larger trees have the greater taper. Those growing in dense 

 stands have the least. No average can be found which will apply even to the 

 trees of one diameter class, much less to trees of all classes. The assumption of a 

 definite taper for the trees on a plot will tend to over-estimate the volume of trees 

 larger than the selected average tree, and under-estimate those of small diameter. 

 Whether these errors balance depends more on luck than on skill. 



3. The use of such a table presupposes the system of counting rather than of 

 tallying each tree, and assumes the risk of error in selecting, largely by eye, an 

 average tree which, when multiplied by the count, will give the approximate 

 estimate. It does not lend itself to an accurate inventory of the timber, tree 

 by tree, in which the diameter and merchantable length of each tree is 

 recorded. 



4. Since such tables assume that upper diameters differ by gradations of 1 inch 

 per log, a 4-log tree will show top diameters in the table differing by 4-inch classes, 



