Forest Mensuration 5 



inary) log sections of equal length, considering each of such sections 

 as a cylinder or as a truncated paraboloid. The shorter the length of 

 the sections, the greater the accuracy of the result. In scientific research, 

 the length of a section varies from 5 feet to 10 feet. Obviously, at the 

 top of the bole an uneven length is left, which it might be wise to ascer- 

 tain as a cone (or paraboloid Bulletin 20). The volume of the total 

 bole, from stump to tip, equals, if the length of such full section is "1," 

 and that of the top cone is "b," and 



1 ) if sectional areas si, s%,ss, Sn are measured at the big end of each 



section : 



vol. bole = -i- (B! + 2 s 2 + 2 s 3 + s n ) + -j~ 



2) if sectional areas si,sn, Sm, s m are measured in the midst of each 



full section, and sectional area s n at the basis of the top cone : 



b.Sn 

 vol. bole = 1 (si -f Su + SHI 4- s m ) -f 



The former formula is based on Smalian and the latter on Huber. 



In a similar way, and with still greater accuracy, the more complicated 

 formulas of Riecke, Hossfeld and Simony might be adapted to sectional 

 measurements. 



REMARK : If the diameter in the middle of a log is larger than the 

 arithmetical mean of the end diameters, then the log contains more vol- 

 ume than the truncated cone, and vice versa. 



If the sectional area at the midst of the log is larger than the arith- 

 metical mean of the end sectional areas, then the log contains more 

 volume than the truncated paraboloid, and vice versa. 



PARAGRAPH XII. 



MEASURING THE LENGTH OF A LOG. 



The length of a log is measured with tape, stick or axe handle. In 

 American logging, logs are usually cut in lengths of even feet, increased 

 by an addition of two inches to six inches, which addition allows for 

 shrinkage, for season checks, for damage to the log ends inflicted by 

 snaking or driving, and for the trimming in the saw mill required to 

 removed such end defects. 



In Continental Europe, the standard log lengths are multiples of even 

 decimeters. An excess-length of up to eight inches is neglected. 



Crooked logs are made straight by deductions either from the length 

 or from the diameter. Crooked trees should be dissected into very short 

 logs. 



The standard length of a New England log is 13 feet. 



In the case of big logs, great care must be taken by the sawyers to 

 obtain end-cuts perpendicular to the axis of the log. 



The sum of the lengths of logs cut from a tree is termed "used length." 

 The total length of that portion of a bole which is merchantable under 

 given conditions is called "merchantable length." 



