DIAMETERS AND AREAS OF CROSS SECTIONS 17 



25. Diameters and Areas of Cross sections. Cross sectional areas 

 are assumed to be circular in form, and were this assumption correct 

 the measurement of any average diameter would give the cross section. 



If B = "basal" area, or area of circle, 



D = Diameter of circle, 



x= Ratio, or 3.1416. 



Then 



■wD 2 

 B=— = .7S54D 2 . 

 4 



But practically every cross section departs slightly from a true 

 circle, and a large proportion are very eccentric, some showing a dif- 

 ference of several inches between their longest and shortest diameters, 

 and having an elliptical or oval form. 1 



No attempt is ever made to compute the actual cross sectional area 

 of such eccentric sections. Instead, two diameter measurements are 

 taken at right angles and the average of these is assumed to be the 

 average diameter. A circle with corresponding diameter is assumed to 

 have the same cross sectional area as that of the actual section. Usually 

 the longest diameter is taken, and one at right angles to it, through the 

 geometric center of the section. 2 



Abnormal cross sections are occasionally encountered in which the average 

 diameter of the section and its area are either too large or too small to give the volume 

 accurately owing to some distortion in form of the log as a whole or of the portion 



1 The area of an ellipse is 



vDd 



when D and d represent the long and short axes. 



D+d 



The area of a circle whose diameter is calculated as is 



2 



T(D+d)* 



4(2) ' 

 Then 



TJD+d) 2 jirDd _tt (D-d) 1 

 4(2) 4 ~4 (2) ' 



which is equal to the area of a circle whose diameter equals one-half the difference 

 between D and d. This correction which is always minus, is ignored in measuring 

 cross-sections. 



2 In determining the average diameter, no attention is paid to the growth rings 

 or the position of the pith or growth center of the section. In eccentric cross sections 

 the pith is always found some distance to one side of the geometric center, which is 

 the point through which the diameter measurement must fall. 



