ALINKMKXT CHARTS I\ FORKST MENSURATION 789 



feet. The measurements actually taken are, however, L and D^, the 

 diameter in inches at the middle. The formula must therefore be 

 written 



V 4 X 144 / 

 Figure 10 is a chart which graphically solves this equation. It in- 

 volves merely the multiplication by L of the expression in the paren- 

 thesis involving D. The first form of multiplication chart has been 

 adopted, since acute intersections are thereby avoided. The original 

 axes are assigned to D and h and the intermediate terminal axis half 

 way between them to Y. The same graduations are used on both of the 

 original axes, as this has been found by experiment to make them of 

 approximately equal length when graduated to the desired range of 

 values. The final axis is. therefore, equidistant from them and gradu- 

 ated with a unit one-half as great. The L axis is graduated with dis- 

 tances from the origin corresponding to the logarithms of consecutive 

 digits from 4 to 40. and the V in a similar manner from i/io to 400. 

 The D axis is graduated with distances corresponding to the logarithm 

 of 



V4X 144/ 



No attention is given to the relative positions of the origins of the 

 three scales, but the graduations of the outer axes are arranged in a 

 convenient manner and the location of a single point on the interme- 

 diate axis is obtained by a single computation and the resulting intersec- 

 tion. The remainder of its graduations are then plotted from that as a 

 starting point. 



In graduating an axis such as the L axis, where the origin is not re- 

 quired, no attention is given to its location, although all graduating dis- 

 tances are measured from it. If the lowest value required is 2, as in 

 the present case, a scale may be laid along the axis with the value cor- 

 responding to 2 opposite any convenient point and the remaining gradu- 

 ations located directly without shifting the scale. 



FORM-FACTOR METHOD 



The formula for obtaining the volume of a tree from its form factor 

 may be written either: 



V = FBH or 



\ 4 X 144 ^ 



