THE INTRODUCTION OF TAPER INTO LOG RULES 



45 



Regarded as a 64-foot log scaled by middle diameter the scaling diameter is C, 

 and the log content is that of a cylinder 64 feet long and of size indicated by C C. 



Regarded as a 64-foot log scaled by end diameter, the scaling diameter is A 

 and the log content is that of a cylinder 64 feet long and of size indicated by A A'. 



Regarded as a 16-foot log scaled at small end, and not in middle, the loss in 

 scale is indicated by the shaded portions. This loss is common to all commercial 

 log scales based on small end of log. 



But if the contents of the 16-foot log as given in the scale when measured at A 

 is built up by measuring the log as four 4-foot cylinders whose scaling diameters 

 are A, B, C and D, this loss from taper common to all the commercial log rules, 

 except when applied at middle diameter, is avoided and practically full scale secured. 



A comparison of the results of these three methods of treating taper is brought 

 out in Table V. 



TABLE V 

 Effect of Different Methods of Scaling a Log 



The final col umn in each of the above examples is the contents of a log 4 feet 

 long as scaled by the International log rule. The difference in scale by the other 

 methods is due entirely to the length of section scaled as one piece. In column 4, 

 this cylinder, with top diameter indicated, extends the full length of the log. In 

 column 5, a new diameter measurement is made every 16 feet, but the cylinder of 

 this diameter is 16 feet long. In column 6, the diameter is taken at 16-foot intervals, 

 but the cylinder from which this 16-foot log is scaled is built up from four cylinders 

 each 4 feet long, and each J-inch greater in diameter than the one preceding it. 



If the average taper of logs is f-ineh for 4 feet, and pieces 4 feet long are mer- 

 chantable, then the scale in column 6 is correct. Based on this conclusion the loss 

 in scale through neglect of taper is as follows: 



Thus the loss in scale is proportional to the length and total taper of the log. 



