LOGARITHMIC CROSS-SECTION PAPER IN FOREST 



MENSURATION 



By Donald Bruce 



Assistant Professor of Forestry, University of California 



While logarithmic cross-section paper has been in use for many 

 years, its convenience for certain problems in forest mensuration has 

 not been generally recognized. In fact, its use is so uncommon that 

 a brief description may not be out of place. It is a form of coordinate 

 paper in which the lines, both horizontal and vertical, are (like the 

 graduations of a slide rule) spaced at logarithmic instead of at equal 

 intervals. Since the number whose logarithm is 'is 1, the origin or 

 lower lefthand corner of the sheet is 1 instead of 0, but this 1 may 

 have the decimal point at any convenient place, and may be called 

 10, 100, .1, or .01 at will. The paper is sometimes printed with gradua- 

 tions running from 1 to 10 only on both horizontal and vertical axes 

 (or from 10 to 100, etc., if preferred). It is decidedly more con- 

 venient, however, if the scales are repeated at least once, thus giving 

 a range of from 1 to 100. Figure 2 is drawn on logarithmic paper 

 with the vertical scale repeated three times. Unhke the ordinary 

 cross-section paper, the numbering of these scales cannot be modified, 

 except for the shift of the decimal point. 



The property of this paper which has been of greatest general 

 utility is that on it a large number of equations, which when plotted 

 on ordinary coordinate paper are curves, appear as straight lin^'^. 

 For example, an equation of the type 



y = ax^ 



may be written in logarithmic form 



log y = log a -{- b log x. 



This, as a first degree equation, is when platted a straight line. Un- 

 fortunately, however, the laws which govern tree form and tree 

 growth are apparently not generally susceptible of being expressed 

 by equations of this type. 



There are other properties of the paper, however, which render 

 it of direct assistance to forest mensuration. These may be best 

 explained by a concrete example, the preparation of the harmonized 



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