LAWS OF TALL-TREE GROWTH 551 



or ^ 3 fg 



r7-2 = l-25V- 



as in (A). 



The hole a paraboloid of revolution. 



If we assume that the bole of the tree has the form of a paraboloid 

 of revolution, with the equation, 



r- = Smx 

 the neutral axis, as in the foregoing cases, has the equation 



^^ dx 



■wp-rrj^r 



r^(^£\ = -wp7r Lr'dx, 



.■.4mEp,x^^]=-wpx^ 

 dx { dx] 



.'. differentiating, dividing by x, and letting xp = Z, we have tht 

 linear equation, 



^+^7 = 



dx' ^AEm 



: .ior p = o, the height (greatest) is given by, 



^ 'iw' 

 2 ■V£^ = " 

 And if r is the stump radius, 



2 w 



H 3/x2 , IE 





.71 ^ 



1L 



