ALINlvMKNT CHARTS IK FOREST MENSURATION 793 



graduated regularly rather than logarithmically, the c form of multipli- 

 cation must be employed. Figure 12 is such a chart. The three ver- 

 tical axes at the left form the addition system, the central, or terminal, 

 axis of which is also the initial axis of the rj system, which extends to 

 the right. 



The method by which the axes are graduated is as follows : 



(a) The right-hand scales of the two diameter axes are first gradu- 

 ated, assigning to each successive value a number of units equal to its 

 square — that is, i is placed at i unit from the origin, 2 at 4 units, 3 at 

 9, etc. 



(b) The center axis of the three is drawn equidistant from the other 

 two and need not be graduated. All that is required on this axis is a 

 single known point easily obtained by an intersection, which will be 

 used in graduating the diagonal. 



(c) The right-hand side of the volume axis is next graduated regu- 

 larly in any convenient unit. 



tL 



(d) The diagonal is to be graduated in terms of , but these 



values need not be calculated, as their position can be more easily ob- 

 tained by a series of intersections from the known point described 

 under (b) . This process should be clear, from what has preceded. 



(c) The chart is now complete, but for logs of small size annoyingly 

 acute intersections with the diagonal result. A second scale is there- 

 fore added on the left-hand side of both the two D and the V scales, 

 using a unit ten times as great as before. As the proportions remain 

 unchanged, the same graduations on the diagonal or L axis will serve, 

 providing that all readings in a single computation are made either 

 entirely on the right or on the left-hand scales. The Roman numerals 

 at the head of the scales are intended to reduce the chance of error in 

 this respect. 



(/) The standard length for cutting logs when prepared for measure- 

 ments, in cubic feet is ten feet. Since many more computations involv- 

 ing this length will be made than for any other, it is obviously advan- 

 tageous to graduate the central axis of the .first system to provide for 

 the standard size. This can be done without disturbing the rest of the 

 chart, for if L^ lo, the formula becomes 



' 1152 



Since is a constant, it can be provided for in the graduating of 



II52 ^ t5 & 



