Periodical Literature. . 631 



IV. Influence of Dimension Errors on Volume. 



Errors of diameter measurement. These depend on whether 

 only one or several cross section areas are used. 



If the cubing is done by the use of the middle cross section, as 

 is usual with logs in Germany, the volume errors are in direct 

 proportion to the diameter errors and the volume error per cent, 

 is double the diameter error per cent. If, e. g. in measuring a 

 diameter of 12 inches, an error of ^ inch or 4% has been made 

 the error in volume will be 8%. 



It can also be shown that the volume error per cent, grows 

 with the same diameter error as the diameters, or with equal 

 diameter error per cent, the volume error per cent, grows with 

 the diameter. Practically this means that the dropping of frac- 

 tions, the rounding off, should be gauged according to diameters, 

 if a certain volume error per cent, is not to be exceeded. 



If, for instance, a volume error of 5% is to be the limit, then 

 the following must be the maximum diameter errors : 



diameter, 6 8 10 12 14 16 18 



permissible error, 3.75 5 6.25 7.50 8.75 10 11.25 



The error increases in arithmetic progression. The errors 

 resulting in the use of different formulae for cubic contents are 

 similarly traced. 



It appears that by cubing logs on the basis of two cross sec- 

 tions errors of measurement are largely compensated, at least as 

 far as the faulty choice of place for measurement and the 

 measuring of diameters in an oblique plane to the diameter is 

 concerned. 



Errors in length measurement produce the same error in vol- 

 ume, that is to say, if a log has been measured 2% short it will 

 be calculated 2% short in volume if only one cross section area 

 has been used in the computation, and the same if several areas 

 are used. In the latter case, the error in length measurement 

 may also shift the position of the area whose diameter is to be 

 measured and complicates matters. 



In sumimarizing, the need of properly constructed calipers, the 

 close contact of scale stick of the caliper to the stem or log, are 

 accentuated. 



An example shows the importance of looking after little things. 



