A FORMULA METHOD FOR ESTIMATIXG TIMBER 417 



be constructed from the data as arranged in Table 2, which should give 

 much more accurate results than the formula, and perhaps more accu- 

 rate than volume tables made up in the ordinary manner. The usual 

 method in constructing tables based on diameters and log lengths is to 

 plot on one sheet a; set of curves — each curve for a given length of 

 tree. When a table is constructed, even for half-log lengths (to say 

 nothing of shorter length units), the curves as plotted are generally 

 very irregular, crossing and recrossing one another in a tangled net- 

 work. Of course, they can be straightened out by the process of "even- 

 ing" and "harmonizing," but after that has been done the most com- 

 petent and conscientious compiler may seriously question whether he 

 has not "evened out" a large percentage of their accuracy. By the 

 following method that disadvantage is overcome, for only one curve 

 need be drawn in constructing the entire table. 



From the basic formula (see page 416) the following equation may 

 be deduced : 



^ ^ .785 X D^ X F X R ^ .785 X D- XP 

 144 144 



b being a factor which, when multiplied by the merchantable length, 

 will give the board- foot contents of the tree, as expressed by the equa- 

 tion 



Bi = bXh 



The value of b must be determined for each diameter class, and these 

 values can then be plotted and evened with a curve. 

 Values for b may also be derived from the formula 



Bf=P'XL 



n 



by dividing the square of each diameter by n. But a table of values 

 thus derived will exhibit the same defect as the formula, namely, that 

 with increasing size of the tree the true variation in contents from 

 diameter class to diameter class is not determined. Figure i shows 

 the curve (solid line) for the values of b; also, for comparison, the 

 curve (broken line) which is obtained by plotting the points for each 

 diameter as derived from the equation b'^ = D-/57. The exact value of 

 n (disregarding the fraction) has been used in this case instead of the 

 round number 60. The curve thus derived is, of course, a perfectly 

 even curve, giving values partly higher and partly lower than the curve 



