80O JOURNAL OF FOKl{STRV 



the chart, only that portion of the diagonal axis upon which gradua- 

 tions appear is drawn. 



The difficulties involved in constructing a chart of this form will be 

 apparent from what has already been said. .Vs one proceeds to the left 

 across the chart, the graduating unit becomes smaller in an inverse 

 geometrical progression. Since the larger diameters of the tree are in 

 the lower logs, this tendency is helpful up to a certain point, but as a 

 matter of fact the progression rapidly becomes so marked that the left- 

 hand scales are progressively harder to read to the desired degree of 

 accuracy. This tendency limits the number of logs for which such a 

 chart can be readily prepared. On the other hand, the capacity of such 

 a chart in volume is very great, and it will be found better suited than 

 the next plate to the case of large, short trees. 



It is possible to use this chart for trees with a larger number of logs 

 than are provided for, by dividing the tree into two parts and comput- 

 ing the upper and lower parts separately. Thus, a 9-log tree can be 

 computed as a 5 and a 4, or as a 6 and a 3, and the results added 

 together. 



Figure 15 is a second chart for performing this same operation. In 

 this the number of axes in the addition system is reduced to 3 by using 

 in a reverse direction the subtraction graph which has been illustrated 

 in figure 3. It will be noted that the outer right-hand axis is graduated 

 from the bottom upward, the outer left-hand axis from the top 

 downward, and the intermediate axis from the center both up and 

 down. Each axis has two sets of graduations, one for d'- on the right 

 and one for y^ cP on the left, as in the case of the plate already de- 

 scribed. In each addition in this case one of the outer axes and the 

 central axis are the initial and the other outer axis the final. In w^ork- 

 ing from right to left the lower half of the central axis is used, and in 

 working from left to right the upper half. First and last values of D 

 are read on the left-hand, or I, scales and all intermediate values on the 

 right-hand, or II, scales. The final sum may appear on either one of 

 the two outer axes, according to whether the number of logs was odd 

 or even and according to the axis from which the computation was 

 started. There are, therefore, two identical .c charts, symmetrically 

 placed, one for use with each of the outer D axes. On the vertical 

 members of these a regularly graduated volume scale is placed, using 

 any convenient unit, and the diagonal L scales are graduated by inter- 

 sections, as has already been described. 



