■^94: JOURNAL OP FORESTRY 



the terminal axis of the addition system. The scale unit necessary is 

 easily found by locating two known points at a one-unit interval by 

 intersections in the manner already described. 



SCHIFFEI. FORMULA 



The Schiffel formula for finding the volume of whole trees in cubic 

 feet may be written 



V= (.16B+ .66 6^0 H 



i67rD- . 667rD^ y^ 

 ^Xi44 4X14^ 

 = (.i6D^+ .66 D^/^ 



or V = + — — H 



V4X144 4X 144 / 



ttH 



4 X 144 

 H 



where \ is the volume in cubic feet, B the basal area breast high in 

 square feet, B^ the basal area in square feet at one-half the height, ?I 

 the height in feet, and D and D'^ the diameters in inches at breast 

 height and at one-half the height. 



This formula is similar in form to the Smalian formula already de- 

 scribed, and requires first an addition followed by a multiplication. The 

 general design of figure 13 is similar to that of figure 12. In this case, 

 however, since one of the diameter axes is graduated in terms of D- 

 and the other in terms of 4.1250^, a different unit for the two 

 original axes of the addition system is desirable. In figure 13 these two 

 scales are in a ratio of 10 to 3. As a result, the terminal axis of this 

 system is no longer evenly spaced between them, but is so located that 

 its distances from the two are in a 10 to 3 ratio. The V axis at the 

 right is graduated regularly with any convenient unit, but the diagonal 

 H axis is graduated entirely by intersections, using one or more known 

 points on the ungraduated final axis of the addition system, as has 

 already been described. A second series of graduations at the left of 

 the two D scales is next added, using a unit ten times as great. This 

 results in a second series in similar proportion on the V axis. In this 

 case, however, an additional complication seems desirable to permit 

 lower readings of H, and a second H scale is added to the left-hand 

 side of the diagonal, using a unit ten times as great. This necessitates 

 a third scale on the V axis, using a unit again multiplied by ten. To 

 prevent confusion, the scales on the left-hand vertical axis are desig- 

 nated I and II, respectively, and those on the diagonal A and B, re- 

 "v^ectively. The largest numbers on the V scale are then headed II B, 



