548 JOURNAL OF FORESTRY 



California Incense Cedar 



These incense cedars are only about one-fourth the height they 

 could reach in still air. 



The tallest cedar of the Forest Service lumbering operations, 76 

 feet high on a stump diameter of 23 . 7 inches, was not as high as the 

 160-year old trees of the table, p. 541, on the same diameter. The 

 highest tree here is higher than the height given for the maximimi 

 height in the height table. 



Pacific Coast Douglas Fir 



Both as relates to actual height and height relative to H, the Douglas 

 fir is the most remarkable of American trees. UnHke the redwood the 



value of /^-^Vr^ steadily increases up to the 200th year. Its average 

 value from the 70th to the 140th year is 25 . 4 and the average from the 

 140th to the 300th year is 29.3. 



For the tallest Douglas firs measured by the Forest Service, see 

 section (F). 



Proof of the Formulas in (A) 



Imagine that the trunk of the tree has the form of a tall cone taper- 

 ing to a point and of small constant angle. Take the origin of coordin- 

 ates at the vertex, ^c-axis vertically downward, j-axis horizontal. Let 

 (x, y) be any point on the neutral axis, {%', y') any other point between 

 {x, y) and the top, W the weight of the tree above {x, y), E the modulus 

 of elasticity, I the moment of inertia of cross-section. Imagine the 

 tree tilted slightly out of the vertical. 



.rf. 



dy 

 If we assume that -t^ = P is small compared with unity, then 



-E/^,= / {y'-y)^j:: ■ dx, nearly. 



dx 



^m-'r^'" 



■pw 



■KtH^ 



Here I = --^, where t is the tangent of the half angle at the vertex. 



