AUXEMEXT CHARTS IX FOREST .MEXSURATIOX ^ 



By Donald Brucu 

 Division of I'orcstry. University of California 



It is only in comparatively recent years that the value of alinement 

 charts in the graphic solution of such formulae as are constantly used by 

 engineers has been appreciated, and to the forester they are still prac- 

 tically unknown ; yet forest mensuration in particular involves problems 

 peculiarly adapted to their application. There are two reasons for this : 

 First, it is common to find that relatively simple formulae must be ap- 

 plied repeatedly to very large masses of data ; and, second, the accuracy 

 of the field measurements on which the computations are based is not 

 of a high degree, so that the moderate precision obtained by a graphic 

 solution is entirely consistent and acceptable. 



An alinement chart is a graph in which three variables involved in a 

 given equation are expressed in lengths on three axes, of which two at 

 least are usually parallel straight lines, and which are so arranged that 

 corresponding values of the variables are always in line with one 

 another. To use such a graph a straight-edge is laid across the assigned 

 values of the two independent variables, and at its intersection with the 

 third axis the proper value of the dependent variable is found. The 

 axes to which the independent variables are assigned may be called the 

 initial and the remaining axis the final axis. 



It will be seen that the alinement chart is peculiarly adapted to for- 

 mulae involving three variables. More than three can be provided for, 

 as will later be explained; but if there are but two, one axis is reduced 

 to a single point through which the determining straight line must pivot. 

 Such cases are not commonly of interest or value, and it is where three 

 variables appear that the advantage of the method over the more com- 



1 This paper has been submitted for critical examination to a number of mathe- 

 maticians and foresters competent to verify the theory and to judge the useful- 

 ness of the method. Several of the critics express doubt as to the superiority of 

 the charts in their usefulness over the common slide rule and the use of tables. 

 It is pointed out that the charts may be serviceable where the range in values is 

 not great, as in investigating growth of spruce and balsam for pulpwood. The}- 

 overcome the chief objection to tables, nameh', the strain on the eye after a few 

 hours' use. They are accurate enough for all mensuration problems in forestry, 

 in which, as a rule, the measurement itself is not very accurate. At least, the 

 discussion is suggestive and may lead to practical application. — Editor. 



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