798 JOURNAL OF FORESTRY 



nected with the scales. The axis designated 7 and that designated 5 

 may be considered as the initial axes, which should therefore be gradu- 

 ated on the same scale. The 6 axis, lying between them, is the final 

 axis of this first system, and as such should be graduated to one-half the 

 scale. These graduations are, however, never read and do not appear. 

 Six then becomes the initial axis in a combination composed of 4, 5, 

 and 6. Four should therefore be graduated with the same unit as 6, 

 namely, ^ of that used for 7. Five now becomes the final axis of this 

 second combination, and as such would be read, using a unit again 

 divided by 2, or one-fourth as great as the unit originally used. This, 

 however, need not appear on the axis. Five next serves as an initial 

 axis in the 3, 4, 5 combination, with the result that 3 is graduated with 

 a unit one-fourth as large as the original unit. In a similar way the 

 addition proceeds across the chart from right to left. It will be noted 

 that each of the interior axes serves in a threefold capacity : first, as an 

 initial axis of the combination lying to the right ; second, as the final axis 

 of the combination of which it is the center; and, third, as the initial 

 axis of the combination lying to its left. In these three functions two 

 different scales for each are involved, but the graduations need be read 

 only in the first, as in the other cases a point located by intersection is 

 merely held and used as a starting point for the next operation. The 

 unnumbered axes to the left function obviously in but a single or dual 

 capacity. 



So far the fact is neglected that the first and last values are divided 

 by two in our equation. It is necessary on this account to graduate 

 each axis which may serve as a starting point or a terminal point to 

 correspond to ^ D- as well as to D^ To distinguish them, this series 

 of graduations are placed on the left of all axes. Certain axes for 

 obvious reasons only require one of the two sets of values — that is, 

 either the >4 D- or the D^, while others require both. 



The final sum of all the additions is accumulated on the second ver- 

 tical axis from the Jeft. This sum cannot, however, be read from its 

 graduations, since these apply only to its function as an initial axis in 

 connection with axes i and 2, the other set of graduations applying to 

 its function as a final axis, being for simplicity omitted. The V scale 

 at the right is graduated regularly in any convenient unit. The diagonal 

 L scale connecting the origin of the V scale with that of the second 

 axis from the left is graduated by intersections from one or more 

 known points, which are themselves found by intersection in the man- 

 ner previously described. To avoid complicating the appearance of 



