630 Forestry Quarterly. 



cussed, hence these errors may compensate. But this is not to 

 be relied upon, since an error of 4% due to a loose caliper arm, 

 would not be compensated by a less than 15% shifting of the 

 caliper from the diameter plane. 



3. The error resulting from omitting fractions of inches (cen- 

 timeter) and rounding off downward, is, of course, percentically 

 less for stout, than for small diameters ; it is a function of the 

 diameter, and assuming that the average neglect is .45 cm., the. per- 



•45 

 centage of error is p = ~ . Translating 5 centimeters into 2 



inches the following relations appear: 



diameter, 4 6 8 10 12 



per cent, of error, 4.5 3 2.25 1.8 1.5 



The error is decreasing with the diameter, but at 18 inches it is 

 still 1%, if only 1/5 of an inch is dropped. 



When measuring two diameters of the same cross section the 

 dropping should be applied not to each but to the arithmetic mean, 

 when the error is minimized. This double measuring also checks 

 errors in mere reading of the scale. 



//. Errors in Determining Cross Sections. 



If measuring two diameters and the result is nearly the same 

 the cross section may be assumed to be a circle; but if the dif- 

 ference is great, the question may arise how to determine the 

 area. Three ways are practicable : namely, to determine the. area 

 for each diameter and take the mean ; calculating the area from 

 the mean of the two diameters; or taking the diameters as the 

 axes of an ellipse and calculating its area. Usually the second 

 method is used. G. Heyer proved long ago that the calculation as 

 ellipse gives always the smallest areas. That is to say, the usual 

 practice of calculating the cross section area from the mean of 

 two very unlike diameters as circle gives too high results. An 

 investigation shows that, as a rule, the error is so small that it 

 does not call for correction. Only with small diameters and 

 great difference of the two does the error appear significant : 

 e. g., if d = 4, d2 = 6, then p = 4.17%. 



///. Errors in Measuring Log Lengths. 

 These are too simple to require discussion. 



