4o8 Forestry Quarterly. 



-^ = ^,^=AB^xBC.and 

 BC D 2 



(I) BC 



25D 



2 



AB^ 



(AB^)^ = (AC^)'— {B'Cy 

 By substitution, 



(AB^)^=(25+ ^^r -(^~)' =(25)^+25D=25(25+D), 



(II) AB>r=V25 (25+D) 

 Substituting this value for AB^ in equation (i) 



-'5D 



V25 (25+D) 

 Since BC is the scale for ^ of the diameter of the circle, the 

 formula for the scale for the whole circle is 



Scaler !5D ^ • 



V25 (25XD) 



If it is more convenient to use a different arm length than 25 

 inches, this formula may be adapted by substituting the length 

 desired for the 25 wherever that number occurs in the formula. 



Using this formula for diameters of 10, 20, 30, 40, 50, 60, 70, 

 80, 90 and 100 inches, scale lengths for these respective diameters 

 were obtained. Points representing these lengths were plotted on 

 cross section paper where the abscissae represented inches in 

 diameter and the ordinates represented inches on the scale. 

 Through these points a smooth curve was drawn. From this 

 curve the scale was read for each even diameter from ten inches 

 to one hundred inches. This scale was then laid off and carefully 

 drawn on tracing linen. Strips an inch wide were cut length- 

 wise of this tracing thus producing the scale in a convenient form 

 for carrying or mailing. 



If it is desirable to indicate diameters smaller than ten inches 

 or larger than one hundred inches they may be derived directly 

 from the formula and marked on the scale. 



A check was made on the accuracy of the formula by construct- 



