A FORMULA METHOD FOR ESTIMATIXG TIMBER 415 



R when multiplied together give the cubic volume of the merchantable 

 stem of a tree of a given diameter, and if the volume be multipHed by 

 the number expressing the ratio of board to cubic feet for trees of that 

 diameter, the contents in board feet will be obtained. This equation 

 may be reduced to the form 



Bf=51>lL 



and 



144 



.785 X F X R 



But it is evident that n, although correct for any diameter for which 

 it may be determined, will not be the same for any other diameter, 

 unless F and R remain constant for all diameters — which they do not — ■ 

 or unless the products of F and R for every diameter are approximately 

 equal. It is here that an inspection of Table 2, and especially of 

 columns F, R, and P (P = F X R). is interesting as showing the rela- 

 tion between the form factors and the board foot-cubic foot ratios with 

 change of diameter. As the diameter increases, the numerical value of 

 the form factor decreases (though not very regularly), while the ratio 

 increases, with the result that the range of values for P varies so 

 slightly throughout the range of diameters for Rocky Mountain yellow 

 pine (12 to 36 inches) that the average value for all diameters (3.213) 

 may be used for each diameter class without involving an excessive 

 error, and one which is compensating when applied to a fairly large 

 number of trees. The greatest variation above the mean (that for the 

 34-inch class) is 12 per cent, and the greatest below the mean (for the 

 25-inch class) is 10 per cent, while for most diameter classes the differ- 

 ence is much less. Substituting, therefore, the average value of P for 

 F X R in the formula for n, we have for any diameter 



H4 

 571 



•7»5 X 3-213 



or, approximately, 60, which is close enough to use in the formula. The 

 resultant formula, therefore, for Rocky Mountain yellow pine is': 



D^XL 



Bf = 



60 



In the Pikes Peak region, where practically all the merchantable 

 yellow pine (exclusive of tie-timber) ranges between i6 and 30 inches 

 d. b. h., I have used this formula with satisfactory results. The volumes 

 obtained by it show an average variation of about 10 per cent from those 



