ALINEMENT CHARTS IN FOREST MENSURATION 791 



where V is the volume in cubic feet, F the form factor, B the basal area 

 in square feet, D the basal diameter in inches and H the height in feet. 



In this case it is necessarv first to multiply ( ) by H and then 



' -^ V 4 X 144 / 



multiply the product by F. This involves two systems of graphs, as 

 has already been described. Figure 11 utilizes the c form of chart. 

 For performing the first multiplication the left-hand vertical axis is 

 assigned values of H, the diagonal values of D, and the right-hand 

 vertical, while not graduated, measures the product of H and of the 

 expression involving D. The second multiplication uses the same axes 

 over again in the opposite direction. The diagonal has a second series 

 of graduations assigned to values of F, and the left-hand vertical, 

 which now becomes the final axis, is assigned values of V as w^ell as of 

 H. The last axis, however, uses exactly the same scale and gradua- 

 tions for both V and H. 



At first sight it may seem a complex matter to so calculate the scales 

 as to make this possible, but actually this is not the case. The starting 

 point is the H axis, which is regularly graduated, using any convenient 

 unit. It is obvious that the right-hand vertical axis, which is not 



graduated, must really express f -— J H, which expresses the 



volume in cubic feet of a cylinder of a height of H feet and a diameter 

 of D inches. Temporary regular graduations are, therefore, placed 

 itpon it, using a scale found by trial to locate the D values on the 

 diagonal in a convenient position. The D graduations are then located 

 by intersection in the manner already described. Computations in con- 

 nection with the location of the intersecting lines may be avoided by 

 the use of a table of volumes of cylinders, such as is commonly used in 

 forest mensuration. As the same graduations for V as for H are to be 

 used, the F values may next be added to the diagonals, again using the 

 method of intersections. Thus a given value on the right-hand axis is 

 successively joined by straight lines to varying values of V, which by a 

 simple and obvious calculation are found to require successive values 

 of F. 



THE SMALIAN FORMULA 



The Smalian formula for finding the volume of a log in cubic feet 

 mav be written either 



2 



V4X144 4X144/2 ^ ^ ^1152 



