22 THE MEASUREMENT OP LOGS. CUBIC CONTENTS 



neiloid than the paraboloid, the errors in the use of the Huber or the 

 Smalian formula may easily be checked by the above formula. 1 



29. The Technic of Measuring Logs. By either of the two para- 

 boloidal formulae, Huber's or Smalian's, the area of a single average 

 cross-section is obtained which, multiplied by the length of log, gives 

 the cubic contents. By the Smalian method, this area is the average 

 of two cross-sections, while by the Huber method it is obtained directly. 

 The volume of the frustum, or log, is thus equal to that of a cylinder 

 of equal height, with a base equal in diameter to the average cross- 

 section. 



Diameters Measured at Ends of Log. Diameter inside the bark is 

 usually required, and is best obtained at the exposed ends of the log. 

 But if only the small end is measured, the corresponding cylinder 

 does not give the cubic contents of the log on account of neglect of its 

 taper (§26). Although almost universally practiced in scaling for 

 board feet, this single measurement is never used to scale cubic contents. 

 The choice lies, therefore, between the single measurement at middle 

 of log, or the averaging of two end areas. 



The volumes of cylinders vary directly as their basal areas, or as D 2 , and not as 

 their diameters. Hence an accurate procedure would require first, measurement 

 of each diameter; second, determination of each corresponding area; third, averag- 

 ing these areas; fourth, computing the corresponding diameter. The volume of a 

 cylinder of this diameter and length is required. Such a procedure is practical only 

 in scientific studies; in scaling, the two end-diameters are averaged directly. The 

 assumption is that, 



1 The following formulae are cited by Guttenberg, in Lorey's Handbuch der 

 Forstwissenschaft, 3d Ed., Chapter XII, 1913. 



While the substitution of the Hossfeld formulae for that of Smalian on butt logs 

 would give far more accurate results, and would be closer than the Huber formula 

 the point one-third from butt is not ordinarily measured in the field and is trouble- 

 some to ascertain. Hence this formula is impractical. The same objection applies 

 to Breymann's. Simoney's formula has no advantage over either Huber's or 

 Smalian's, since by using the small lengths, one-fourth log, the latter formulae will 

 secure results within 1 per cent of the true volume for the standard 16-feet length. 



