CHAPTER IV 

 LOG RULES BASED ON CUBIC CONTENTS 



31. Comparison of Log Rules Based on Diameter at Middle and 

 at Small End of Log. Log rules giving the contents of logs in cubic 

 feet should be based on the diameter inside bark at middle of log. If, 

 instead, the diameter is measured at the small end of the log, the indi- 

 cated contents falls short of the true cubic volume (§ 29). 



But the measurement of diameters at the small end of logs rather 

 than at the middle point is so great a convenience in log scaling (§ 83) 

 that efforts have been made to find a converting factor, or ratio, by 

 which the true contents of logs may be correlated with diameters at 

 the small end, and expressed directly in a log rule based on these diam- 

 eters. Since the true contents is assumed to be equal to the cylinder 

 whose diameter is that of the log at its middle point, the ratio or factor 

 desired is the multiple required for converting the volume of the smaller 

 cylinder whose diameter is measured at the small end of the log into 

 the true cubic volume of the log taken as equaling this large cylinder. 

 This ratio is influenced by three factors — namely, rate of taper, length, 

 and diameter of the log. 



A log rule, if based on the same conversion factor for logs of all sizes and tapers, 

 will give correct volumes only for a log of a given diameter, length and taper and 

 will be in error for logs of all other dimensions. 



A log rule based on separate conversion factors for logs of each diameter but 

 making no further distinction for different lengths or tapers will give correct volumes 

 only for logs of a specific length and rate of taper in each diameter class, and will 

 be in error for all other lengths and tapers. 



A log rule based on separate conversion factors for each different diameter and 

 length, can be applied accurately to obtain the average scale of logs of all diameters 

 and lengths only in case the average taper of the logs scaled agrees with that of the 

 logs measured in determining the factor used, and is in error when the average 

 $aper of the logs scaled is greater or less than this. 



While these conditions apply to log rules based on measurement at the small end 

 of log, a log rule based on measurement at middle of log is correct for all the above 

 conditions, incurring only the errors due to divergence in shape of log from that of 

 a paraboloid. 



The ratio of volumes, and the loss in scaling legs by a rule based on the cylinder 

 measured at small end, are illustrated in Table I. The figures in the last column 

 represent the loss in scale expressed in per cent of the volume scaled, e.g., a 16-foot 

 log 6 inches at the small end with 2-inch taper contains 36 per cent greater volume 

 than shown by the scale. 



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