THE TECHNIC OF MEASURING LOGS 23 



This gives a slightly smaller volume than by the correct method. The error increases 

 as the square of the difference between the top and the bottom diameters. 1 



This error, expressed in per cent of total contents, falls below 1 per cent for logs 

 not over 16 feet long with a taper of 2 inches or less. It also tends to offset the plus 

 error caused by the use of the Smalian method as a whole (§ 28). The error increases 

 with length of log scaled as one piece. 



A far more serious source of error by this method is that due to the flare of butt 

 logs. Due to the excessively large cross-section thus obtained at the butt, this 

 error may give an excess cubic volume for the log of from 10 to 20 per cent. Chiefly 

 for this reason, the end area method is confined in practice to scientific studies of 

 volume, in which the length of the sections can be regulated to reduce this error, 

 and time is not the determining factor. For such studies, the computation of average 

 basal areas is no drawback. The volumes of the lengths into which the log is to be 

 divided are more conveniently computed by the Smalian formula than by the Huber 

 formula, which requires the middle diameter of each short section. Smalian's 

 mean end formula is therefore universally adopted in these studies, 



Diameter Measured at Middle of Log. Since it is impossible to 

 measure the diameter at the middle of a log unless the log is exposed, 

 logs cannot be scaled by this method if they lie in large railways or 

 piled one on another. The scaling for cubic contents therefore requires 

 a time and place for the work where each log is exposed for its entire 

 length and is less convenient than scaling for board feet ( § 83) . 



By measuring the middle diameter, the error due to flaring butts 

 is avoided. But this practice requires, in addition to total length, 

 the determination of this middle point. The use of calipers is required, 

 since it is impossible to obtain consistent accuracy by placing a scale 

 stick across a log and judging the diameter; the error thus incurred 

 is always minus. This method is therefore termed a caliper scale. 



In applying a caliper scale, the double width of bark is subtracted 

 either by taking off a fixed average thickness or by adjusting the calipers 



1 The error in use of mean diameters is shown as follows : 

 Volume of truncated cone may be expressed as, 



V=^h(D 2 +Dd+d"). 



Volume of cylinder having a basal area equal to the mean diameter of the log is, 



(D+dY 



Then, 



y=r 



TT TV (D-d)* TT (D-d)* 



- hiD * +D d + d*)- t ^=-k^. 



The minus error thus shown is equivalent to the volume of a cone having a basal 

 area equal to the difference between the mean end diameters of the log. For the 

 paraboloid, this error equals the contents of a cylinder with a basal area equal to 

 that of the above cone. The error thus increases with the total taper of the log. 



