ALINEMENT CHARTS IX I'OKKST MK.XSUKATIOX 801 



This chart avoids the difficulty of a geometrical progression in the 

 scale units, but introduces a difficulty, in that if a reasonably large 

 scale for d is employed, only limited values of \' are practicable. Thus, 

 figure 1 6 will serve for trees whose volumes do not exceed 40 cubic 

 feet, while figure 15 is applicable through a range over three times as 

 great. Figure 16, however, is entirely independent of the number of 

 logs. It is, therefore, preferable for very tall, slender trees. It can be 

 used for computations be3'ond its range by dividing a tree into two or 

 more parts and calculating each part separately and adding their sum. 



CONCIvUSIONS 



The advantages of this graphic method as compared to ordinary 

 computations are speed and consequent low cost. The actual saving 

 depends upon the particular formula in question and on the personal 

 equation of the computer ; but it appears that the graphic solution saves 

 from 80 to 90 per cent of the time of the complete computation and 

 about 50 per cent of that where use is made of all available tables and 

 of the slide rule. It is evident that a saving can often be made, even 

 where the graph must be prepared specifically for a given problem. 



The advantages of the alinement form of graph as contrasted with 

 that using rectangular co-ordinates are the following: First, it is 

 simpler in appearance. This greatly reduces the strain on the eyes 

 which results from using a chart involving a complicated maze of curves 

 crossing the lines of the co-ordinate paper. Second, it can in most 

 cases be constructed more quickly and more cheaply, when once the 

 principles involved are well understood. Third, interpolations are 

 readily handled in any one of the variables, while in the series of 

 curves that result from plotting a three-variable ecjuation in rectangular 

 co-ordinates interpolations betwen the curves are always uncertain and 

 unsatisfactory. 



