162 CONSTRUCTION OF STANDARD VOLUME TABLES 



Then 



For the sum of the volumes of the sections each end area except 

 the first and last is evidently used twice. A series of three such sec- 

 tions would total 



H'^H^hd^y 



When, as in systems A and B, equal lengths of section (I) are used, 

 the formula can be expressed 



i.e., average the first and last basal areas, and add the remaining areas. 

 Then multiply by length of one section to obtain the sum of volumes 

 of the sections. 



The areas in square feet, corresponding to the diameters of each 

 section are found in Table LXXVIII, Appendix C, p. 490. 



Sections different in length from the standard must be computed 

 separately. 



The tip, beyond the last taper, is computed as a paraboloid, by the 

 same formula, 



The volume of stump, needed to complete the tree when system B 

 is used, is standardized by custom as a cylinder, whose diameter is that 

 of the stump section, thus neglecting the variable factor of stump 

 taper. Its volume is therefore 



V=Bl. 



System A permits the volume of the section up to 4 or 4| feet to be 

 computed accurately if desired. 



Owing to the serious error incurred by measuring the butt section 

 by the Smalian method, the use of Huber's formula for the first 8- or 

 16-foot log may give more consistent results. In this case, for a 16- 

 foot log (0 the basal area at 8 feet (6') gives the log volume, or 



V = b'l. 



A check should be made by this method against the Smalian method 

 for the butt section (§29). 



The total cubic volume of branches and twigs is practically never 



