DETERMINATION OF THE MIDDLE DIAMETER 803 



the same species, according to conditions of vegetation. Ordinarily it 

 is determined by previous measurements of felled sample trees selected 

 at random in the forest where one is working. This method, while not 

 bad, has nevertheless the inconvenience of being only approximate, 

 since one proceeds by comparison. It is, moreover, as radical as it is 

 slow, since it necessitates cuttings which require both labor and time. 

 Finally, it obliges the felling of trees the cutting of which would not be 

 desirable under certain circumstances. 



The following method permits the direct determination of the coeffi- 

 cient of form of any standing tree, thanks to the application of a very 

 simple formula which any estimator is capable of using on the ground : 



Let w and w' = the apparent diameters viewed from a point O of the 

 diameters d and d' on the tree at the height of the eye and at the middle 

 of the trunk; 



/ = the distance from O to a graduated scale ( held at arm's length ) 

 on which n and n are measured ; 



D = the horizontal distance from O to d; 



D' = the distance from O io d' ; 



H = the height of the trunk ; 



h = the height of the observer's eye above the ground. 



Then, as a result of the properties of similar triangles, 



d' = U ""^ .y = D- 



T. , n'U d' 



l^rom these two equations — r- -=— ■ 



Since —- :^ / by definition, — - :=: f ( I ) . 

 a 11 u 



This formula can be further simplified when D = // (the dis- 

 tance from d to d'). 



S(|uaring equation (I), we get 



iy= 



h.^ 



1^- + ( h\- in the right triangle formed by D. D'. and 



'' It will he noted that this is a right triangle only when the line from the ob- 

 server's eye to the tree is a horizontal one, and that the method is therefore ap- 

 plicable only on level or nearly level ground. — S. T. D. 



