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JOURNAL OF FORESTRY 



respectively, and CD is the final axis on which .:: is measured. BDF is 

 a straight line connecting the zero points of the three axes, and GHI a 

 position of the straight-edge which connects corresponding values of 

 X, y, and s. It is evident that since CD is equidistant from AB and EF, 

 then if the straight line BJI is drawn, HJ = 3^ GB and JD = >4 IF; 

 therefore HD = HJ + JD = i/^ (GB + IF) ; or, if the scale with 

 which values on CD are measured is one-half that used on AB and EF, 



Fig. 3. — Elementary chart for subtraction. 



HD will give values of s equal to x -f 31. Graduations so proportioned 

 are shown on the figure. 



It is often desirable to use two different scales for the two initial 

 axes. This modifies the chart merely to the extent of shifting the posi- 

 tion of the final axis. In figure 2 the scale on EF is only half that on 

 AB. If CD is so placed that its distance from EF is one-half its dis- 

 tance from AB — that is, at one-third the distance from EF to AB — it 

 will be seen that HJ = J^ GB and JD = ^ IF ; therefore HD = HJ + 

 JD = ys GB -)- ^ IF. CD must therefore be graduated with a scale 

 one-third that of GB to secure the same result as before. 



