Constructing Volume Tables. 221 



In the latter case the assumption is involved that the curves 

 represented by the table of frustrum volumes are exactly of the 

 same shape, whether based on diameters or heights, as those of 

 the volume table we are trying to obtain. While this assumption 

 is rather extreme, yet it involves less serious errors even in indi- 

 vidual figures than might be expected, — (examine the percentage 

 variation in the table given above for larch of the individual figures 

 composing it from the general average) — and these errors would 

 be largely compensating in a stand estimate. It has the great ad- 

 vantage of allowing all the measurements obtained to be averaged 

 together directly. In the second case discussed the advantage of 

 the frustrum form factor method over that usually employed is less 

 obvious. It is not, here, a labor-saving device, but it tends to 

 make the resulting table slightly more accurate. We have seen 

 that in the case of the larch table mentioned in the earlier part of 

 this article its use brought to light irregularities in the values 

 which were imperceptible by ordinary means. Any errors which 

 it can detect it can, of course, prevent. In such a case, however, 

 its greatest value will be in strengthening the extremes of the 

 table. What seems, in a volume curve, to be a normal continu- 

 ation of curvature may be shown by the frustrum form factor to be 

 a rather sharp bend. But it is in the first case outlined that the 

 method is at its maximum efficiency. The assumption involved 

 therein is reasonable, has considerable evidence to support it, and 

 at worst is a very close approximation to the truth, and its effect 

 in aggregating the available measurements for purposes of averag- 

 ing makes a very decided reduction in the number of measure- 

 ments necessary for an accurate table. 



In conclusion, then, the following advantages are claimed for 

 the use of the frustrum form factor in the construction of volume 

 tables ; 



a. A table of fair accuracy can be constructed on a very few 

 measurements ; 



b. The number of m.easurements needed for a really satisfac- 

 tory table is much reduced ; 



c. The table constructed from a given number of measurements 

 is particularly strengthened at its weakest point, namely, its 

 extreme values; 



d. As a result of all these points, the cost of constructing a 

 volume table of any given accuracy is materially lessened. 



